Bayesian inference and Markov chain Monte Carlo in imaging
NASA Astrophysics Data System (ADS)
Higdon, David M.; Bowsher, James E.
1999-05-01
Over the past 20 years, many problems in Bayesian inference that were previously intractable can now be fairly routinely dealt with using a computationally intensive technique for exploring the posterior distribution called Markov chain Monte Carlo (MCMC). Primarily because of insufficient computing capabilities, most MCMC applications have been limited to rather standard statistical models. However, with the computing power of modern workstations, a fully Bayesian approach with MCMC, is now possible for many imaging applications. Such an approach can be quite useful because it leads not only to `point' estimates of an underlying image or emission source, but it also gives a means for quantifying uncertainties regarding the image. This paper gives an overview of Bayesian image analysis and focuses on applications relevant to medical imaging. Particular focus is on prior image models and outlining MCMC methods for these models.
Ancestry inference in complex admixtures via variable-length Markov chain linkage models.
Rodriguez, Jesse M; Bercovici, Sivan; Elmore, Megan; Batzoglou, Serafim
2013-03-01
Inferring the ancestral origin of chromosomal segments in admixed individuals is key for genetic applications, ranging from analyzing population demographics and history, to mapping disease genes. Previous methods addressed ancestry inference by using either weak models of linkage disequilibrium, or large models that make explicit use of ancestral haplotypes. In this paper we introduce ALLOY, an efficient method that incorporates generalized, but highly expressive, linkage disequilibrium models. ALLOY applies a factorial hidden Markov model to capture the parallel process producing the maternal and paternal admixed haplotypes, and models the background linkage disequilibrium in the ancestral populations via an inhomogeneous variable-length Markov chain. We test ALLOY in a broad range of scenarios ranging from recent to ancient admixtures with up to four ancestral populations. We show that ALLOY outperforms the previous state of the art, and is robust to uncertainties in model parameters. PMID:23421795
Inferring Sequential Order of Somatic Mutations during Tumorgenesis based on Markov Chain Model.
Kang, Hao; Cho, Kwang-Hyun; Zhang, Xiaohua Douglas; Zeng, Tao; Chen, Luonan
2015-01-01
Tumors are developed and worsen with the accumulated mutations on DNA sequences during tumorigenesis. Identifying the temporal order of gene mutations in cancer initiation and development is a challenging topic. It not only provides a new insight into the study of tumorigenesis at the level of genome sequences but also is an effective tool for early diagnosis of tumors and preventive medicine. In this paper, we develop a novel method to accurately estimate the sequential order of gene mutations during tumorigenesis from genome sequencing data based on Markov chain model as TOMC (Temporal Order based on Markov Chain), and also provide a new criterion to further infer the order of samples or patients, which can characterize the severity or stage of the disease. We applied our method to the analysis of tumors based on several high-throughput datasets. Specifically, first, we revealed that tumor suppressor genes (TSG) tend to be mutated ahead of oncogenes, which are considered as important events for key functional loss and gain during tumorigenesis. Second, the comparisons of various methods demonstrated that our approach has clear advantages over the existing methods due to the consideration on the effect of mutation dependence among genes, such as co-mutation. Third and most important, our method is able to deduce the ordinal sequence of patients or samples to quantitatively characterize their severity of tumors. Therefore, our work provides a new way to quantitatively understand the development and progression of tumorigenesis based on high throughput sequencing data. PMID:26451822
PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure.
Boomsma, Wouter; Frellsen, Jes; Harder, Tim; Bottaro, Sandro; Johansson, Kristoffer E; Tian, Pengfei; Stovgaard, Kasper; Andreetta, Christian; Olsson, Simon; Valentin, Jan B; Antonov, Lubomir D; Christensen, Anders S; Borg, Mikael; Jensen, Jan H; Lindorff-Larsen, Kresten; Ferkinghoff-Borg, Jesper; Hamelryck, Thomas
2013-07-15
We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.
Murakami, Yohei; Takada, Shoji
2013-01-01
When model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Conventional MCMC needs likelihood to evaluate a posterior distribution of acceptable parameters, while the approximate Bayesian computation (ABC) MCMC evaluates posterior distribution with use of qualitative fitness measure. However, none of these algorithms can deal with mixture of quantitative, i.e., likelihood, and qualitative fitness measures simultaneously. Here, to deal with this mixture, we formulated Bayesian formula for hybrid fitness measures (HFM). Then we implemented it to MCMC (MCMC-HFM). We tested MCMC-HFM first for a kinetic toy model with a positive feedback. Inferring kinetic parameters mainly related to the positive feedback, we found that MCMC-HFM reliably infer them using both qualitative and quantitative fitness measures. Then, we applied the MCMC-HFM to an apoptosis signal transduction network previously proposed. For kinetic parameters related to implicit positive feedbacks, which are important for bistability and irreversibility of the output, the MCMC-HFM reliably inferred these kinetic parameters. In particular, some kinetic parameters that have experimental estimates were inferred without using these data and the results were consistent with experiments. Moreover, for some parameters, the mixed use of quantitative and qualitative fitness measures narrowed down the acceptable range of parameters.
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data. PMID:26353069
Transport map-accelerated Markov chain Monte Carlo for Bayesian parameter inference
NASA Astrophysics Data System (ADS)
Marzouk, Y.; Parno, M.
2014-12-01
We introduce a new framework for efficient posterior sampling in Bayesian inference, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use transport maps to transform typical Metropolis proposal mechanisms (e.g., random walks, Langevin methods, Hessian-preconditioned Langevin methods) into non-Gaussian proposal distributions that can more effectively explore the target density. Our approach adaptively constructs a lower triangular transport map—i.e., a Knothe-Rosenblatt re-arrangement—using information from previous MCMC states, via the solution of an optimization problem. Crucially, this optimization problem is convex regardless of the form of the target distribution. It is solved efficiently using Newton or quasi-Newton methods, but the formulation is such that these methods require no derivative information from the target probability distribution; the target distribution is instead represented via samples. Sequential updates using the alternating direction method of multipliers enable efficient and parallelizable adaptation of the map even for large numbers of samples. We show that this approach uses inexact or truncated maps to produce an adaptive MCMC algorithm that is ergodic for the exact target distribution. Numerical demonstrations on a range of parameter inference problems involving both ordinary and partial differential equations show multiple order-of-magnitude speedups over standard MCMC techniques, measured by the number of effectively independent samples produced per model evaluation and per unit of wallclock time.
NASA Astrophysics Data System (ADS)
Volchenkov, Dima; Dawin, Jean René
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
On a Result for Finite Markov Chains
ERIC Educational Resources Information Center
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
Using Games to Teach Markov Chains
ERIC Educational Resources Information Center
Johnson, Roger W.
2003-01-01
Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…
Handling target obscuration through Markov chain observations
NASA Astrophysics Data System (ADS)
Kouritzin, Michael A.; Wu, Biao
2008-04-01
Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.
Markov chains for testing redundant software
NASA Technical Reports Server (NTRS)
White, Allan L.; Sjogren, Jon A.
1988-01-01
A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.
Entropy Computation in Partially Observed Markov Chains
NASA Astrophysics Data System (ADS)
Desbouvries, François
2006-11-01
Let X = {Xn}n∈N be a hidden process and Y = {Yn}n∈N be an observed process. We assume that (X,Y) is a (pairwise) Markov Chain (PMC). PMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient parameter estimation and Bayesian restoration algorithms. In this paper we propose a fast (i.e., O(N)) algorithm for computing the entropy of {Xn}n=0N given an observation sequence {yn}n=0N.
Likelihood free inference for Markov processes: a comparison.
Owen, Jamie; Wilkinson, Darren J; Gillespie, Colin S
2015-04-01
Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka-Volterra predator-prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schlögl system, a test case which exhibits bi-modal state stability in some regions of parameter space. PMID:25720092
The cutoff phenomenon in finite Markov chains.
Diaconis, P
1996-01-01
Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists. PMID:11607633
Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Markov Chain Monte Carlo and Irreversibility
NASA Astrophysics Data System (ADS)
Ottobre, Michela
2016-06-01
Markov Chain Monte Carlo (MCMC) methods are statistical methods designed to sample from a given measure π by constructing a Markov chain that has π as invariant measure and that converges to π. Most MCMC algorithms make use of chains that satisfy the detailed balance condition with respect to π; such chains are therefore reversible. On the other hand, recent work [18, 21, 28, 29] has stressed several advantages of using irreversible processes for sampling. Roughly speaking, irreversible diffusions converge to equilibrium faster (and lead to smaller asymptotic variance as well). In this paper we discuss some of the recent progress in the study of nonreversible MCMC methods. In particular: i) we explain some of the difficulties that arise in the analysis of nonreversible processes and we discuss some analytical methods to approach the study of continuous-time irreversible diffusions; ii) most of the rigorous results on irreversible diffusions are available for continuous-time processes; however, for computational purposes one needs to discretize such dynamics. It is well known that the resulting discretized chain will not, in general, retain all the good properties of the process that it is obtained from. In particular, if we want to preserve the invariance of the target measure, the chain might no longer be reversible. Therefore iii) we conclude by presenting an MCMC algorithm, the SOL-HMC algorithm [23], which results from a nonreversible discretization of a nonreversible dynamics.
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS
THIEDE, ERIK; VAN KOTEN, BRIAN; WEARE, JONATHAN
2015-01-01
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations. PMID:26491218
Growth and Dissolution of Macromolecular Markov Chains
NASA Astrophysics Data System (ADS)
Gaspard, Pierre
2016-07-01
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.
Stochastic seismic tomography by interacting Markov chains
NASA Astrophysics Data System (ADS)
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-10-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches, they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high-dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case, the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on importance resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non-linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper, the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a simulated annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet-based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Stochastic seismic tomography by interacting Markov chains
NASA Astrophysics Data System (ADS)
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-07-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Markov Chain Analysis of Musical Dice Games
NASA Astrophysics Data System (ADS)
Volchenkov, D.; Dawin, J. R.
2012-07-01
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
Equilibrium Control Policies for Markov Chains
Malikopoulos, Andreas
2011-01-01
The average cost criterion has held great intuitive appeal and has attracted considerable attention. It is widely employed when controlling dynamic systems that evolve stochastically over time by means of formulating an optimization problem to achieve long-term goals efficiently. The average cost criterion is especially appealing when the decision-making process is long compared to other timescales involved, and there is no compelling motivation to select short-term optimization. This paper addresses the problem of controlling a Markov chain so as to minimize the average cost per unit time. Our approach treats the problem as a dual constrained optimization problem. We derive conditions guaranteeing that a saddle point exists for the new dual problem and we show that this saddle point is an equilibrium control policy for each state of the Markov chain. For practical situations with constraints consistent to those we study here, our results imply that recognition of such saddle points may be of value in deriving in real time an optimal control policy.
Active Inference for Binary Symmetric Hidden Markov Models
NASA Astrophysics Data System (ADS)
Allahverdyan, Armen E.; Galstyan, Aram
2015-10-01
We consider active maximum a posteriori (MAP) inference problem for hidden Markov models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We focus on the binary symmetric HMM, and employ its known mapping to 1d Ising model in random fields. From the statistical physics viewpoint, the active MAP inference problem reduces to analyzing the ground state of the 1d Ising model under modified external fields. We develop an analytical approach and obtain a closed form solution that relates the expected error reduction to model parameters under the specified active inference scheme. We then use this solution to determine most optimal active inference scheme in terms of error reduction, and examine the relation of those schemes to heuristic principles of uncertainty reduction and solution unicity.
ERIC Educational Resources Information Center
Kim, Jee-Seon; Bolt, Daniel M.
2007-01-01
The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…
Parameter estimation in deformable models using Markov chain Monte Carlo
NASA Astrophysics Data System (ADS)
Chalana, Vikram; Haynor, David R.; Sampson, Paul D.; Kim, Yongmin
1997-04-01
Deformable models have gained much popularity recently for many applications in medical imaging, such as image segmentation, image reconstruction, and image registration. Such models are very powerful because various kinds of information can be integrated together in an elegant statistical framework. Each such piece of information is typically associated with a user-defined parameter. The values of these parameters can have a significant effect on the results generated using these models. Despite the popularity of deformable models for various applications, not much attention has been paid to the estimation of these parameters. In this paper we describe systematic methods for the automatic estimation of these deformable model parameters. These methods are derived by posing the deformable models as a Bayesian inference problem. Our parameter estimation methods use Markov chain Monte Carlo methods for generating samples from highly complex probability distributions.
Differential evolution Markov chain with snooker updater and fewer chains
Vrugt, Jasper A; Ter Braak, Cajo J F
2008-01-01
Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50--100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5--26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25--50 dimensional Student T{sub 3} distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.
Accelerating Monte Carlo Markov chains with proxy and error models
NASA Astrophysics Data System (ADS)
Josset, Laureline; Demyanov, Vasily; Elsheikh, Ahmed H.; Lunati, Ivan
2015-12-01
In groundwater modeling, Monte Carlo Markov Chain (MCMC) simulations are often used to calibrate aquifer parameters and propagate the uncertainty to the quantity of interest (e.g., pollutant concentration). However, this approach requires a large number of flow simulations and incurs high computational cost, which prevents a systematic evaluation of the uncertainty in the presence of complex physical processes. To avoid this computational bottleneck, we propose to use an approximate model (proxy) to predict the response of the exact model. Here, we use a proxy that entails a very simplified description of the physics with respect to the detailed physics described by the "exact" model. The error model accounts for the simplification of the physical process; and it is trained on a learning set of realizations, for which both the proxy and exact responses are computed. First, the key features of the set of curves are extracted using functional principal component analysis; then, a regression model is built to characterize the relationship between the curves. The performance of the proposed approach is evaluated on the Imperial College Fault model. We show that the joint use of the proxy and the error model to infer the model parameters in a two-stage MCMC set-up allows longer chains at a comparable computational cost. Unnecessary evaluations of the exact responses are avoided through a preliminary evaluation of the proposal made on the basis of the corrected proxy response. The error model trained on the learning set is crucial to provide a sufficiently accurate prediction of the exact response and guide the chains to the low misfit regions. The proposed methodology can be extended to multiple-chain algorithms or other Bayesian inference methods. Moreover, FPCA is not limited to the specific presented application and offers a general framework to build error models.
Unsupervised Segmentation of Hidden Semi-Markov Non Stationary Chains
NASA Astrophysics Data System (ADS)
Lapuyade-Lahorgue, Jérôme; Pieczynski, Wojciech
2006-11-01
In the classical hidden Markov chain (HMC) model we have a hidden chain X, which is a Markov one and an observed chain Y. HMC are widely used; however, in some situations they have to be replaced by the more general "hidden semi-Markov chains" (HSMC) which are particular "triplet Markov chains" (TMC) T = (X, U, Y), where the auxiliary chain U models the semi-Markovianity of X. Otherwise, non stationary classical HMC can also be modeled by a triplet Markov stationary chain with, as a consequence, the possibility of parameters' estimation. The aim of this paper is to use simultaneously both properties. We consider a non stationary HSMC and model it as a TMC T = (X, U1, U2, Y), where U1 models the semi-Markovianity and U2 models the non stationarity. The TMC T being itself stationary, all parameters can be estimated by the general "Iterative Conditional Estimation" (ICE) method, which leads to unsupervised segmentation. We present some experiments showing the interest of the new model and related processing in image segmentation area.
Bayesian inference for Markov jump processes with informative observations.
Golightly, Andrew; Wilkinson, Darren J
2015-04-01
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis. PMID:25720091
Inferring phenomenological models of Markov processes from data
NASA Astrophysics Data System (ADS)
Rivera, Catalina; Nemenman, Ilya
Microscopically accurate modeling of stochastic dynamics of biochemical networks is hard due to the extremely high dimensionality of the state space of such networks. Here we propose an algorithm for inference of phenomenological, coarse-grained models of Markov processes describing the network dynamics directly from data, without the intermediate step of microscopically accurate modeling. The approach relies on the linear nature of the Chemical Master Equation and uses Bayesian Model Selection for identification of parsimonious models that fit the data. When applied to synthetic data from the Kinetic Proofreading process (KPR), a common mechanism used by cells for increasing specificity of molecular assembly, the algorithm successfully uncovers the known coarse-grained description of the process. This phenomenological description has been notice previously, but this time it is derived in an automated manner by the algorithm. James S. McDonnell Foundation Grant No. 220020321.
On a Markov chain roulette-type game
NASA Astrophysics Data System (ADS)
El-Shehawey, M. A.; El-Shreef, Gh A.
2009-05-01
A Markov chain on non-negative integers which arises in a roulette-type game is discussed. The transition probabilities are p01 = ρ, pNj = δNj, pi,i+W = q, pi,i-1 = p = 1 - q, 1 <= W < N, 0 <= ρ <= 1, N - W < j <= N and i = 1, 2, ..., N - W. Using formulae for the determinant of a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-type game is deduced. The present analysis is supported by two mathematical models from tumor growth and war with bargaining.
Hidden Markov chain modeling for epileptic networks identification.
Le Cam, Steven; Louis-Dorr, Valérie; Maillard, Louis
2013-01-01
The partial epileptic seizures are often considered to be caused by a wrong balance between inhibitory and excitatory interneuron connections within a focal brain area. These abnormal balances are likely to result in loss of functional connectivities between remote brain structures, while functional connectivities within the incriminated zone are enhanced. The identification of the epileptic networks underlying these hypersynchronies are expected to contribute to a better understanding of the brain mechanisms responsible for the development of the seizures. In this objective, threshold strategies are commonly applied, based on synchrony measurements computed from recordings of the electrophysiologic brain activity. However, such methods are reported to be prone to errors and false alarms. In this paper, we propose a hidden Markov chain modeling of the synchrony states with the aim to develop a reliable machine learning methods for epileptic network inference. The method is applied on a real Stereo-EEG recording, demonstrating consistent results with the clinical evaluations and with the current knowledge on temporal lobe epilepsy. PMID:24110697
Markov chain Monte Carlo methods: an introductory example
NASA Astrophysics Data System (ADS)
Klauenberg, Katy; Elster, Clemens
2016-02-01
When the Guide to the Expression of Uncertainty in Measurement (GUM) and methods from its supplements are not applicable, the Bayesian approach may be a valid and welcome alternative. Evaluating the posterior distribution, estimates or uncertainties involved in Bayesian inferences often requires numerical methods to avoid high-dimensional integrations. Markov chain Monte Carlo (MCMC) sampling is such a method—powerful, flexible and widely applied. Here, a concise introduction is given, illustrated by a simple, typical example from metrology. The Metropolis-Hastings algorithm is the most basic and yet flexible MCMC method. Its underlying concepts are explained and the algorithm is given step by step. The few lines of software code required for its implementation invite interested readers to get started. Diagnostics to evaluate the performance and common algorithmic choices are illustrated to calibrate the Metropolis-Hastings algorithm for efficiency. Routine application of MCMC algorithms may be hindered currently by the difficulty to assess the convergence of MCMC output and thus to assure the validity of results. An example points to the importance of convergence and initiates discussion about advantages as well as areas of research. Available software tools are mentioned throughout.
Influence of credit scoring on the dynamics of Markov chain
NASA Astrophysics Data System (ADS)
Galina, Timofeeva
2015-11-01
Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.
Students' Progress throughout Examination Process as a Markov Chain
ERIC Educational Resources Information Center
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
Some Interesting Characteristics of Markov Chain Transition Matrices.
ERIC Educational Resources Information Center
Egelston, Richard L.
A Monte Carlo investigation of Markov chain matrices was conducted to create empirical distributions for two statistics created from the transition matrices. Curve fitting techniques developed by Karl Pearson were used to deduce if theoretical equations could be fit to the two sets of distributions. The set of distributions which describe the…
Markov chain for estimating human mitochondrial DNA mutation pattern
NASA Astrophysics Data System (ADS)
Vantika, Sandy; Pasaribu, Udjianna S.
2015-12-01
The Markov chain was proposed to estimate the human mitochondrial DNA mutation pattern. One DNA sequence was taken randomly from 100 sequences in Genbank. The nucleotide transition matrix and mutation transition matrix were estimated from this sequence. We determined whether the states (mutation/normal) are recurrent or transient. The results showed that both of them are recurrent.
Exploring Mass Perception with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
Adiabatic condition and the quantum hitting time of Markov chains
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-08-15
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P{sup '} where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP{sup '} and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
Fuzzy Markov random fields versus chains for multispectral image segmentation.
Salzenstein, Fabien; Collet, Christophe
2006-11-01
This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.
Fuzzy Markov random fields versus chains for multispectral image segmentation.
Salzenstein, Fabien; Collet, Christophe
2006-11-01
This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data. PMID:17063681
Time operator of Markov chains and mixing times. Applications to financial data
NASA Astrophysics Data System (ADS)
Gialampoukidis, I.; Gustafson, K.; Antoniou, I.
2014-12-01
We extend the notion of Time Operator from Kolmogorov Dynamical Systems and Bernoulli processes to Markov processes. The general methodology is presented and illustrated in the simple case of binary processes. We present a method to compute the eigenfunctions of the Time Operator. Internal Ages are related to other characteristic times of Markov chains, namely the Kemeny time, the convergence rate and Goodman’s intrinsic time. We clarified the concept of mixing time by providing analytic formulas for two-state Markov chains. Explicit formulas for mixing times are presented for any two-state regular Markov chain. The mixing time of a Markov chain is determined also by the Time Operator of the Markov chain, within its Age computation. We illustrate these results in terms of two realistic examples: A Markov chain from US GNP data and a Markov chain from Dow Jones closing prices. We propose moreover a representation for the Kemeny constant, in terms of internal Ages.
Markov chain Monte Carlo posterior sampling with the Hamiltonian method.
Hanson, Kenneth M.
2001-01-01
A major advantage of Bayesian data analysis is that provides a characterization of the uncertainty in the model parameters estimated from a given set of measurements in the form of a posterior probability distribution. When the analysis involves a complicated physical phenomenon, the posterior may not be available in analytic form, but only calculable by means of a simulation code. In such cases, the uncertainty in inferred model parameters requires characterization of a calculated functional. An appealing way to explore the posterior, and hence characterize the uncertainty, is to employ the Markov Chain Monte Carlo technique. The goal of MCMC is to generate a sequence random of parameter x samples from a target pdf (probability density function), {pi}(x). In Bayesian analysis, this sequence corresponds to a set of model realizations that follow the posterior distribution. There are two basic MCMC techniques. In Gibbs sampling, typically one parameter is drawn from the conditional pdf at a time, holding all others fixed. In the Metropolis algorithm, all the parameters can be varied at once. The parameter vector is perturbed from the current sequence point by adding a trial step drawn randomly from a symmetric pdf. The trial position is either accepted or rejected on the basis of the probability at the trial position relative to the current one. The Metropolis algorithm is often employed because of its simplicity. The aim of this work is to develop MCMC methods that are useful for large numbers of parameters, n, say hundreds or more. In this regime the Metropolis algorithm can be unsuitable, because its efficiency drops as 0.3/n. The efficiency is defined as the reciprocal of the number of steps in the sequence needed to effectively provide a statistically independent sample from {pi}.
Singer, Philipp; Helic, Denis; Taraghi, Behnam; Strohmaier, Markus
2014-01-01
One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work. PMID:25013937
Bayesian Smoothing Algorithms in Partially Observed Markov Chains
NASA Astrophysics Data System (ADS)
Ait-el-Fquih, Boujemaa; Desbouvries, François
2006-11-01
Let x = {xn}n∈N be a hidden process, y = {yn}n∈N an observed process and r = {rn}n∈N some auxiliary process. We assume that t = {tn}n∈N with tn = (xn, rn, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, these smoothers reduce to a set of algorithms which include, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms (originally designed for HMC) such as the RTS algorithms, the Two-Filter algorithms or the Bryson and Frazier algorithm.
Constructing 1/ωα noise from reversible Markov chains
NASA Astrophysics Data System (ADS)
Erland, Sveinung; Greenwood, Priscilla E.
2007-09-01
This paper gives sufficient conditions for the output of 1/ωα noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/ωα condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/ω noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/ωα noise which also has a long memory.
Parallel algorithms for simulating continuous time Markov chains
NASA Technical Reports Server (NTRS)
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
Pereyra, Marcelo; Dobigeon, Nicolas; Batatia, Hadj; Tourneret, Jean-Yves
2013-06-01
This paper addresses the problem of estimating the Potts parameter β jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on β requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method, the estimation of β is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating β jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of β. On the other hand, choosing an incorrect value of β can degrade estimation performance significantly. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.
Topological Charge Evolution in the Markov-Chain of QCD
Derek Leinweber; Anthony Williams; Jian-bo Zhang; Frank Lee
2004-04-01
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
Efficient Parallel Learning of Hidden Markov Chain Models on SMPs
NASA Astrophysics Data System (ADS)
Li, Lei; Fu, Bin; Faloutsos, Christos
Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.
NASA Astrophysics Data System (ADS)
Yushkevich, A. A.; Chitashvili, R. Ya
1982-12-01
CONTENTSIntroduction Chapter I. Foundations of the general theory of controlled random sequences and Markov chains with the expected reward criterion § 1. Controlled random sequences, Markov chains, and models § 2. Necessary and sufficient conditions for optimality § 3. The Bellman equation for the value function and the existence of (ε-) optimal strategies Chapter II. Some problems in the theory of controlled homogeneous Markov chains § 4. Description of the solutions of the Bellman equation, a characterization of the value function, and the Bellman operator § 5. Sufficiency of stationary strategies in homogeneous Markov models § 6. The lexicographic Bellman equation References
Vrugt, Jasper A; Hyman, James M; Robinson, Bruce A; Higdon, Dave; Ter Braak, Cajo J F; Diks, Cees G H
2008-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.
Uncovering and Testing the Fuzzy Clusters Based on Lumped Markov Chain in Complex Network
Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu
2013-01-01
Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club. PMID:24391729
Submodular Relaxation for Inference in Markov Random Fields.
Osokin, Anton; Vetrov, Dmitry P
2015-07-01
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al. [29] SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.
Markov Chain Monte-Carlo Models of Starburst Clusters
NASA Astrophysics Data System (ADS)
Melnick, Jorge
2015-01-01
There are a number of stochastic effects that must be considered when comparing models to observations of starburst clusters: the IMF is never fully populated; the stars can never be strictly coeval; stars rotate and their photometric properties depend on orientation; a significant fraction of massive stars are in interacting binaries; and the extinction varies from star to star. The probability distributions of each of these effects are not a priori known, but must be extracted from the observations. Markov Chain Monte-Carlo methods appear to provide the best statistical approach. Here I present an example of stochastic age effects upon the upper mass limit of the IMF of the Arches cluster as derived from near-IR photometry.
On the Multilevel Solution Algorithm for Markov Chains
NASA Technical Reports Server (NTRS)
Horton, Graham
1997-01-01
We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.
Nonequilibrium thermodynamic potentials for continuous-time Markov chains
NASA Astrophysics Data System (ADS)
Verley, Gatien
2016-01-01
We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.
Projection methods for the numerical solution of Markov chain models
NASA Technical Reports Server (NTRS)
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
Markov Chain Monte Carlo Bayesian Learning for Neural Networks
NASA Technical Reports Server (NTRS)
Goodrich, Michael S.
2011-01-01
Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.
On the multi-level solution algorithm for Markov chains
Horton, G.
1996-12-31
We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.
Kinetics and thermodynamics of first-order Markov chain copolymerization
Gaspard, P.; Andrieux, D.
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
Bayesian seismic tomography by parallel interacting Markov chains
NASA Astrophysics Data System (ADS)
Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas
2014-05-01
The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the
Efficient inference of hidden Markov models from large observation sequences
NASA Astrophysics Data System (ADS)
Priest, Benjamin W.; Cybenko, George
2016-05-01
The hidden Markov model (HMM) is widely used to model time series data. However, the conventional Baum- Welch algorithm is known to perform poorly when applied to long observation sequences. The literature contains several alternatives that seek to improve the memory or time complexity of the algorithm. However, for an HMM with N states and an observation sequence of length T, these alternatives require at best O(N) space and O(N2T) time. Given the preponderance of applications that increasingly deal with massive amounts of data, an alternative whose time is O(T)+poly(N) is desired. Recent research presents an alternative to the Baum-Welch algorithm that relies on nonnegative matrix factorization. This document examines the space complexity of this alternative approach and proposes further optimizations using approaches adopted from the matrix sketching literature. The result is a streaming algorithm whose space complexity is constant and time complexity is linear with respect to the size of the observation sequence. The paper also presents a batch algorithm that allow for even further improved space complexity at the expense of an additional pass over the observation sequence.
A study of deleterious gene structure in plants using Markov chain Monte Carlo.
Lee, J K; Lascoux, M; Newton, M A; Nordheim, E V
1999-06-01
The characteristics of deleterious genes have been of great interest in both theory and practice in genetics. Because of the complex genetic mechanism of these deleterious genes, most current studies try to estimate the overall magnitude of mortality effects on a population, which is characterized classically by the number of lethal equivalents. This number is a combination of several parameters, each of which has a distinct biological effect on genetic mortality. In conservation and breeding programs, it is important to be able to distinguish among different combinations of these parameters that lead to the same number of lethal equivalents, such as a large number of mildly deleterious genes or a few lethal genes, The ability to distinguish such parameter combinations requires more than one generation of mating. We propose a model for survival data from a two-generation mating experiment on the plant species Brassica rapa, and we enable inference with Markov chain Monte Carlo. This computational strategy is effective because a vast amount of missing genotype information must be accounted for. In addition to the lethal equivalents, the two-generation data provide separate information on the average intensity of mortality and the average number of deleterious genes carried by an individual. In our Markov chain Monte Carlo algorithm, we use a vector proposal distribution to overcome inefficiency of a single-site Gibbs sampler. Information about environmental effects is obtained from an outcrossing experiment conducted in parallel with the two-generation mating experiments.
NASA Astrophysics Data System (ADS)
Zhu, Yanzheng; Zhang, Lixian; Sreeram, Victor; Shammakh, Wafa; Ahmad, Bashir
2016-10-01
In this paper, the resilient model approximation problem for a class of discrete-time Markov jump time-delay systems with input sector-bounded nonlinearities is investigated. A linearised reduced-order model is determined with mode changes subject to domination by a hierarchical Markov chain containing two different nonhomogeneous Markov chains. Hence, the reduced-order model obtained not only reflects the dependence of the original systems but also model external influence that is related to the mode changes of the original system. Sufficient conditions formulated in terms of bilinear matrix inequalities for the existence of such models are established, such that the resulting error system is stochastically stable and has a guaranteed l2-l∞ error performance. A linear matrix inequalities optimisation coupled with line search is exploited to solve for the corresponding reduced-order systems. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.
Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Vousden, W. D.; Farr, W. M.; Mandel, I.
2016-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multimodal probability distributions. Most popular methods, such as MCMC sampling, perform poorly on strongly multimodal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems, a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.
Rottman, Benjamin M; Hastie, Reid
2016-06-01
Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X1→Y→X2, common cause structures X1←Y→X2, and common effect structures X1→Y←X2, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative "explaining away" pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations.
Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research
Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.
2002-01-01
Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.
A Markov-Chain Monte-Carlo Based Method for Flaw Detection in Beams
Glaser, R E; Lee, C L; Nitao, J J; Hickling, T L; Hanley, W G
2006-09-28
A Bayesian inference methodology using a Markov Chain Monte Carlo (MCMC) sampling procedure is presented for estimating the parameters of computational structural models. This methodology combines prior information, measured data, and forward models to produce a posterior distribution for the system parameters of structural models that is most consistent with all available data. The MCMC procedure is based upon a Metropolis-Hastings algorithm that is shown to function effectively with noisy data, incomplete data sets, and mismatched computational nodes/measurement points. A series of numerical test cases based upon a cantilever beam is presented. The results demonstrate that the algorithm is able to estimate model parameters utilizing experimental data for the nodal displacements resulting from specified forces.
Pooley, C. M.; Bishop, S. C.; Marion, G.
2015-01-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob–Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed ‘model-based proposal’ (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2–8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
Pooley, C M; Bishop, S C; Marion, G
2015-06-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob-Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed 'model-based proposal' (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2-8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
Pooley, C M; Bishop, S C; Marion, G
2015-06-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob-Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed 'model-based proposal' (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2-8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large.
MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD
K. HANSON
2001-02-01
The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence.
ENSO informed Drought Forecasting Using Nonhomogeneous Hidden Markov Chain Model
NASA Astrophysics Data System (ADS)
Kwon, H.; Yoo, J.; Kim, T.
2013-12-01
The study aims at developing a new scheme to investigate the potential use of ENSO (El Niño/Southern Oscillation) for drought forecasting. In this regard, objective of this study is to extend a previously developed nonhomogeneous hidden Markov chain model (NHMM) to identify climate states associated with drought that can be potentially used to forecast drought conditions using climate information. As a target variable for forecasting, SPI(standardized precipitation index) is mainly utilized. This study collected monthly precipitation data over 56 stations that cover more than 30 years and K-means cluster analysis using drought properties was applied to partition regions into mutually exclusive clusters. In this study, six main clusters were distinguished through the regionalization procedure. For each cluster, the NHMM was applied to estimate the transition probability of hidden states as well as drought conditions informed by large scale climate indices (e.g. SOI, Nino1.2, Nino3, Nino3.4, MJO and PDO). The NHMM coupled with large scale climate information shows promise as a technique for forecasting drought scenarios. A more detailed explanation of large scale climate patterns associated with the identified hidden states will be provided with anomaly composites of SSTs and SLPs. Acknowledgement This research was supported by a grant(11CTIPC02) from Construction Technology Innovation Program (CTIP) funded by Ministry of Land, Transport and Maritime Affairs of Korean government.
Threshold partitioning of sparse matrices and applications to Markov chains
Choi, Hwajeong; Szyld, D.B.
1996-12-31
It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.
Markov chain Monte Carlo method for tracking myocardial borders
NASA Astrophysics Data System (ADS)
Janiczek, Robert; Ray, N.; Acton, Scott T.; Roy, R. J.; French, Brent A.; Epstein, F. H.
2005-03-01
Cardiac magnetic resonance studies have led to a greater understanding of the pathophysiology of ischemic heart disease. Manual segmentation of myocardial borders, a major task in the data analysis of these studies, is a tedious and time consuming process subject to observer bias. Automated segmentation reduces the time needed to process studies and removes observer bias. We propose an automated segmentation algorithm that uses an active contour to capture the endo- and epicardial borders of the left ventricle in a mouse heart. The contour is initialized by computing the ellipse corresponding to the maximal gradient inverse of variation (GICOV) value. The GICOV is the mean divided by the normalized standard deviation of the image intensity gradient in the outward normal direction along the contour. The GICOV is maximal when the contour lies along strong, relatively constant gradients. The contour is then evolved until it maximizes the GICOV value subject to shape constraints. The problem is formulated in a Bayesian framework and is implemented using a Markov Chain Monte Carlo technique.
Ensemble bayesian model averaging using markov chain Monte Carlo sampling
Vrugt, Jasper A; Diks, Cees G H; Clark, Martyn P
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
Asteroid mass estimation using Markov-Chain Monte Carlo techniques
NASA Astrophysics Data System (ADS)
Siltala, Lauri; Granvik, Mikael
2016-10-01
Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to a 13-dimensional inverse problem where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid using astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations into the OpenOrb asteroid-orbit-computation software: the very rough 'marching' approximation, in which the asteroid orbits are fixed at a given epoch, reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-Chain Monte Carlo (MCMC) approach. We will introduce each of these algorithms with particular focus on the MCMC algorithm, and present example results for both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans, particularly in connection with ESA's Gaia mission.
Markov Chain Monte-Carlo Orbit Computation for Binary Asteroids
NASA Astrophysics Data System (ADS)
Oszkiewicz, D.; Hestroffer, D.; Pedro, David C.
2013-11-01
We present a novel method of orbit computation for resolved binary asteroids. The method combines the Thiele, Innes, van den Bos method with a Markov chain Monte Carlo technique (MCMC). The classical Thiele-van den Bos method has been commonly used in multiple applications before, including orbits of binary stars and asteroids; conversely this novel method can be used for the analysis of binary stars, and of other gravitationally bound binaries. The method requires a minimum of three observations (observing times and relative positions - Cartesian or polar) made at the same tangent plane - or close enough for enabling a first approximation. Further, the use of the MCMC technique for statistical inversion yields the whole bundle of possible orbits, including the one that is most probable. In this new method, we make use of the Metropolis-Hastings algorithm to sample the parameters of the Thiele-van den Bos method, that is the orbital period (or equivalently the double areal constant) together with three randomly selected observations from the same tangent plane. The observations are sampled within their observational errors (with an assumed distribution) and the orbital period is the only parameter that has to be tuned during the sampling procedure. We run multiple chains to ensure that the parameter phase space is well sampled and that the solutions have converged. After the sampling is completed we perform convergence diagnostics. The main advantage of the novel approach is that the orbital period does not need to be known in advance and the entire region of possible orbital solutions is sampled resulting in a maximum likelihood solution and the confidence regions. We have tested the new method on several known binary asteroids and conclude a good agreement with the results obtained with other methods. The new method has been implemented into the Gaia DPAC data reduction pipeline and can be used to confirm the binary nature of a suspected system, and for deriving
Technical manual for basic version of the Markov chain nest productivity model (MCnest)
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
User’s manual for basic version of MCnest Markov chain nest productivity model
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
Weighted Markov Chains and Graphic State Nodes for Information Retrieval.
ERIC Educational Resources Information Center
Benoit, G.
2002-01-01
Discusses users' search behavior and decision making in data mining and information retrieval. Describes iterative information seeking as a Markov process during which users advance through states of nodes; and explains how the information system records the decision as weights, allowing the incorporation of users' decisions into the Markov…
NASA Astrophysics Data System (ADS)
Jamaluddin, Fadhilah; Rahim, Rahela Abdul
2015-12-01
Markov Chain has been introduced since the 1913 for the purpose of studying the flow of data for a consecutive number of years of the data and also forecasting. The important feature in Markov Chain is obtaining the accurate Transition Probability Matrix (TPM). However to obtain the suitable TPM is hard especially in involving long-term modeling due to unavailability of data. This paper aims to enhance the classical Markov Chain by introducing Exponential Smoothing technique in developing the appropriate TPM.
Reliability analysis and prediction of mixed mode load using Markov Chain Model
NASA Astrophysics Data System (ADS)
Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.
2014-06-01
The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading.
Reliability analysis and prediction of mixed mode load using Markov Chain Model
Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.
2014-06-19
The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading.
Tokunaga self-similarity for symmetric homogeneous Markov chains
NASA Astrophysics Data System (ADS)
Kovchegov, Y.; Zaliapin, I.
2010-12-01
Hierarchical branching organization is ubiquitous in nature. It is readily seen in river basins, drainage networks, bronchial passages, botanical trees, and snowflakes, to mention but a few. Empirical evidence suggests that one can describe many natural hierarchies by so-called Tokunaga self-similar trees (SSTs) [Shreve, 1969; Tokunaga, 1978; Ossadnik, 1992; Peckham, 1995; Newman et al., 1997; Pelletier and Turcotte, 2000]; Tokunaga SST have been proven to describe the Galton-Watson critical branching [Burd et al., 2000] and a general particle coagulation process [Gabrielov et al., 1999]. Tokunaga SSTs form a special two-parametric class of SSTs that preserves its statistical properties under the operation of pruning, i.e., cutting the leaves. It has been conjectured (Webb and Zaliapin, 2009; Zaliapin et al. 2009) that Tokunaga self-similarity is a characteristic property of the inverse aggregation (coagulation) process. This study provides further evidence in support of this hypothesis by focusing on trees that describe the topological structure of level sets of a time series, so-called level-set trees (LST). We prove that the LST for a symmetric homogeneous Markov chain (HMC) is a Tokunaga SST with the same parameters as the famous Shreve tree and critical Galton-Watson tree. We show, furthermore, that the Tokunaga property holds for any transformation F[X(G(t))] of a symmetric HMC X(t), where F and G are monotone increasing functions, and as a result - for the regular Brownian motion. At the same time, the Tokunaga property does not hold in general in asymmetric HMCs, a Brownian motion with a drift, ARMA, and some other conventional models. We discuss the relation of our results to the Tokunaga self-similarity of the nearest-neighbor trees for random point sets. References: 1. Gabrielov, A., W.I. Newman, D.L. Turcotte (1999) An exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling. Phys. Rev. E, 1999, 60, 5293-5300. 2
Monte Carlo Markov chain DEM reconstruction of isothermal plasmas
NASA Astrophysics Data System (ADS)
Landi, E.; Reale, F.; Testa, P.
2012-02-01
Context. Recent studies carried out with SOHO and Hinode high-resolution spectrometers have shown that the plasma in the off-disk solar corona is close to isothermal. If confirmed, these findings may have significant consequences for theoretical models of coronal heating. However, these studies have been carried out with diagnostic techniques whose ability to reconstruct the plasma distribution with temperature has not been thoroughly tested. Aims: In this paper, we carry out tests on the Monte Carlo Markov chain (MCMC) technique with the aim of determining: 1) its ability to retrieve isothermal plasmas from a set of spectral line intensities, with and without random noise; 2) to what extent can it discriminate between an isothermal solution and a narrow multithermal distribution; and 3) how well it can detect multiple isothermal components along the line of sight. We also test the effects of 4) atomic data uncertainties on the results, and 5) the number of ions whose lines are available for the DEM reconstruction. Methods: We first use the CHIANTI database to calculate synthetic spectra from different thermal distributions: single isothermal plasmas, multithermal plasmas made of multiple isothermal components, and multithermal plasmas with a Gaussian DEM distribution with variable width. We then apply the MCMC technique on each of these synthetic spectra, so that the ability of the MCMC technique at reconstructing the original thermal distribution can be evaluated. Next, we add a random noise to the synthetic spectra, and repeat the exercise, in order to determine the effects of random errors on the results. We also we repeat the exercise using a different set of atomic data from those used to calculate synthetic line intensities, to understand the robustness of the results against atomic physics uncertainties. The size of the temperature bin of the MCMC reconstruction is varied in all cases, in order to determine the optimal width. Results: We find that the MCMC
Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms.
Rechner, Steffen; Berger, Annabell
2016-01-01
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442
Finding noncommunicating sets for Markov chain Monte Carlo estimations on pedigrees
Lin, S. ); Thompson, E.; Wijsman, E. )
1994-04-01
Markov chain Monte Carlo (MCMC) has recently gained use as a method of estimating required probability and likelihood functions in pedigree analysis, when exact computation is impractical. However, when a multiallelic locus is involved, irreducibility of the constructed Markov chain, an essential requirement of the MCMC method, may fail. Solutions proposed by several researchers, which do not identify all the noncommunicating sets of genotypic configurations, are inefficient with highly polymorphic loci. This is a particularly serious problem in linkage analysis, because highly polymorphic markers are much more informative and thus are preferred. In the present paper, the authors describe an algorithm that finds all the noncommunicating classes of genotypic configurations on any pedigree. This leads to a more efficient method of defining an irreducible Markov chain. Examples, including a pedigree from a genetic study of familial Alzheimer disease, are used to illustrate how the algorithm works and how penetrances are modified for specific individuals to ensure irreducibility. 20 refs., 7 figs., 6 tabs.
Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms.
Rechner, Steffen; Berger, Annabell
2016-01-01
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time.
Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms
Rechner, Steffen; Berger, Annabell
2016-01-01
We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments.
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments. PMID:25113201
Granum, E; Thomason, M G
1990-01-01
A structural pattern recognition approach to the analysis and classification of metaphase chromosome band patterns is presented. An operational method of representing band pattern profiles as sharp edged idealized profiles is outlined. These profiles are nonlinearly scaled to a few, but fixed number of "density" levels. Previous experience has shown that profiles of six levels are appropriate and that the differences between successive bands in these profiles are suitable for classification. String representations, which focuses on the sequences of transitions between local band pattern levels, are derived from such "difference profiles." A method of syntactic analysis of the band transition sequences by dynamic programming for optimal (maximal probability) string-to-network alignments is described. It develops automatic data-driven inference of band pattern models (Markov networks) per class, and uses these models for classification. The method does not use centromere information, but assumes the p-q-orientation of the band pattern profiles to be known a priori. It is experimentally established that the method can build Markov network models, which, when used for classification, show a recognition rate of about 92% on test data. The experiments used 200 samples (chromosome profiles) for each of the 22 autosome chromosome types and are designed to also investigate various classifier design problems. It is found that the use of a priori knowledge of Denver Group assignment only improved classification by 1 or 2%. A scheme for typewise normalization of the class relationship measures prove useful, partly through improvements on average results and partly through a more evenly distributed error pattern. The choice of reference of the p-q-orientation of the band patterns is found to be unimportant, and results of timing of the execution time of the analysis show that recent and efficient implementations can process one cell in less than 1 min on current standard
Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes.
Dixit, Purushottam D; Jain, Abhinav; Stock, Gerhard; Dill, Ken A
2015-11-10
We are interested inferring rate processes on networks. In particular, given a network's topology, the stationary populations on its nodes, and a few global dynamical observables, can we infer all the transition rates between nodes? We draw inferences using the principle of maximum caliber (maximum path entropy). We have previously derived results for discrete-time Markov processes. Here, we treat continuous-time processes, such as dynamics among metastable states of proteins. The present work leads to a particularly important analytical result: namely, that when the network is constrained only by a mean jump rate, the rate matrix is given by a square-root dependence of the rate, kab ∝ (πb/πa)(1/2), on πa and πb, the stationary-state populations at nodes a and b. This leads to a fast way to estimate all of the microscopic rates in the system. As an illustration, we show that the method accurately predicts the nonequilibrium transition rates in an in silico gene expression network and transition probabilities among the metastable states of a small peptide at equilibrium. We note also that the method makes sensible predictions for so-called extra-thermodynamic relationships, such as those of Bronsted, Hammond, and others. PMID:26574334
Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression.
Wiedenhoeft, John; Brugel, Eric; Schliep, Alexander
2016-05-01
By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings. PMID:27177143
Fast Bayesian Inference of Copy Number Variants using Hidden Markov Models with Wavelet Compression
Wiedenhoeft, John; Brugel, Eric; Schliep, Alexander
2016-01-01
By integrating Haar wavelets with Hidden Markov Models, we achieve drastically reduced running times for Bayesian inference using Forward-Backward Gibbs sampling. We show that this improves detection of genomic copy number variants (CNV) in array CGH experiments compared to the state-of-the-art, including standard Gibbs sampling. The method concentrates computational effort on chromosomal segments which are difficult to call, by dynamically and adaptively recomputing consecutive blocks of observations likely to share a copy number. This makes routine diagnostic use and re-analysis of legacy data collections feasible; to this end, we also propose an effective automatic prior. An open source software implementation of our method is available at http://schlieplab.org/Software/HaMMLET/ (DOI: 10.5281/zenodo.46262). This paper was selected for oral presentation at RECOMB 2016, and an abstract is published in the conference proceedings. PMID:27177143
Experiences with Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples
ERIC Educational Resources Information Center
Sinharay, Sandip
2004-01-01
There is an increasing use of Markov chain Monte Carlo (MCMC) algorithms for fitting statistical models in psychometrics, especially in situations where the traditional estimation techniques are very difficult to apply. One of the disadvantages of using an MCMC algorithm is that it is not straightforward to determine the convergence of the…
A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis
ERIC Educational Resources Information Center
Edwards, Michael C.
2010-01-01
Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…
Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
ERIC Educational Resources Information Center
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
Nelis, Lisa Castillo; Wootton, J Timothy
2010-02-22
What are the relative roles of mechanisms underlying plant responses in grassland communities invaded by both plants and mammals? What type of community can we expect in the future given current or novel conditions? We address these questions by comparing Markov chain community models among treatments from a field experiment on invasive species on Robinson Crusoe Island, Chile. Because of seed dispersal, grazing and disturbance, we predicted that the exotic European rabbit (Oryctolagus cuniculus) facilitates epizoochorous exotic plants (plants with seeds that stick to the skin an animal) at the expense of native plants. To test our hypothesis, we crossed rabbit exclosure treatments with disturbance treatments, and sampled the plant community in permanent plots over 3 years. We then estimated Markov chain model transition probabilities and found significant differences among treatments. As hypothesized, this modelling revealed that exotic plants survive better in disturbed areas, while natives prefer no rabbits or disturbance. Surprisingly, rabbits negatively affect epizoochorous plants. Markov chain dynamics indicate that an overall replacement of native plants by exotic plants is underway. Using a treatment-based approach to multi-species Markov chain models allowed us to examine the changes in the importance of mechanisms in response to experimental impacts on communities.
Treatment-based Markov chain models clarify mechanisms of invasion in an invaded grassland community
Nelis, Lisa Castillo; Wootton, J. Timothy
2010-01-01
What are the relative roles of mechanisms underlying plant responses in grassland communities invaded by both plants and mammals? What type of community can we expect in the future given current or novel conditions? We address these questions by comparing Markov chain community models among treatments from a field experiment on invasive species on Robinson Crusoe Island, Chile. Because of seed dispersal, grazing and disturbance, we predicted that the exotic European rabbit (Oryctolagus cuniculus) facilitates epizoochorous exotic plants (plants with seeds that stick to the skin an animal) at the expense of native plants. To test our hypothesis, we crossed rabbit exclosure treatments with disturbance treatments, and sampled the plant community in permanent plots over 3 years. We then estimated Markov chain model transition probabilities and found significant differences among treatments. As hypothesized, this modelling revealed that exotic plants survive better in disturbed areas, while natives prefer no rabbits or disturbance. Surprisingly, rabbits negatively affect epizoochorous plants. Markov chain dynamics indicate that an overall replacement of native plants by exotic plants is underway. Using a treatment-based approach to multi-species Markov chain models allowed us to examine the changes in the importance of mechanisms in response to experimental impacts on communities. PMID:19864293
Avian life history profiles for use in the Markov chain nest productivity model (MCnest)
The Markov Chain nest productivity model, or MCnest, quantitatively estimates the effects of pesticides or other toxic chemicals on annual reproductive success of avian species (Bennett and Etterson 2013, Etterson and Bennett 2013). The Basic Version of MCnest was developed as a...
Modelling Faculty Replacement Strategies Using a Time-Dependent Finite Markov-Chain Process.
ERIC Educational Resources Information Center
Hackett, E. Raymond; Magg, Alexander A.; Carrigan, Sarah D.
1999-01-01
Describes the use of a time-dependent Markov-chain model to develop faculty-replacement strategies within a college at a research university. The study suggests that a stochastic modelling approach can provide valuable insight when planning for personnel needs in the immediate (five-to-ten year) future. (MSE)
Fitting optimum order of Markov chain models for daily rainfall occurrences in Peninsular Malaysia
NASA Astrophysics Data System (ADS)
Deni, Sayang Mohd; Jemain, Abdul Aziz; Ibrahim, Kamarulzaman
2009-06-01
The analysis of the daily rainfall occurrence behavior is becoming more important, particularly in water-related sectors. Many studies have identified a more comprehensive pattern of the daily rainfall behavior based on the Markov chain models. One of the aims in fitting the Markov chain models of various orders to the daily rainfall occurrence is to determine the optimum order. In this study, the optimum order of the Markov chain models for a 5-day sequence will be examined in each of the 18 rainfall stations in Peninsular Malaysia, which have been selected based on the availability of the data, using the Akaike’s (AIC) and Bayesian information criteria (BIC). The identification of the most appropriate order in describing the distribution of the wet (dry) spells for each of the rainfall stations is obtained using the Kolmogorov-Smirnov goodness-of-fit test. It is found that the optimum order varies according to the levels of threshold used (e.g., either 0.1 or 10.0 mm), the locations of the region and the types of monsoon seasons. At most stations, the Markov chain models of a higher order are found to be optimum for rainfall occurrence during the northeast monsoon season for both levels of threshold. However, it is generally found that regardless of the monsoon seasons, the first-order model is optimum for the northwestern and eastern regions of the peninsula when the level of thresholds of 10.0 mm is considered. The analysis indicates that the first order of the Markov chain model is found to be most appropriate for describing the distribution of wet spells, whereas the higher-order models are found to be adequate for the dry spells in most of the rainfall stations for both threshold levels and monsoon seasons.
Combining Monte Carlo and mean-field-like methods for inference in hidden Markov random fields.
Forbes, Florence; Fort, Gersende
2007-03-01
Issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables. Approximations are required, and most of them are based either on simulation methods or on deterministic variational methods. While variational methods provide fast and reasonable approximate estimates in many scenarios, simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost. In this work, we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden Markov random fields (HMRFs). These algorithms can be viewed as stochastic perturbations of variational expectation maximization (VEM) algorithms, which are not tractable for HMRF. We focus more specifically on one of these perturbations and we prove their (almost sure) convergence to the same limit set as the limit set of VEM. In addition, experiments on synthetic and real-world images show that the algorithm performance is very close and sometimes better than that of other existing simulation-based and variational EM-like algorithms.
NASA Astrophysics Data System (ADS)
Marshall, L. A.; Nott, D.; Sharma, A.
An important aspect of practical hydrological engineering is modelling the catch- ment's response to rainfall. An abundance of models exist to do this, including con- ceptual rainfall-runoff models (CRRMs), which model the catchment as a configura- tion of interconnected storages aimed at providing a simplified representation of the physical processes responsible for runoff generation. While CRRMs have been a use- ful and popular tool for catchment modelling applications, as with most modelling approaches the challenge in using them is accurately assessing the best values to be assigned to the model variables. There are many obstacles to accurate parameter in- ference. Often, a single optimal set of parameter values do not exist. A range of values will often produce a suitable result. The interaction between parameters can also com- plicate the task of parameter inference, and if the data are limited this interaction may be difficult to characterise. An appealing solution is the use of Bayesian statistical inference, with computations carried out using Markov Chain Monte Carlo (MCMC) methods. This approach allows the combination of any pre-existing knowledge about the model parameters to be combined with the available catchment data. The uncer- tainty about a parameter is characterised in terms of its posterior distribution. This study assessed two MCMC schemes that characterise the parameter uncertainty of a CRRM. The aim of the study was to compare an established, complex MCMC scheme to a proposed, more automated scheme that requires little specification on the part of the user to achieve the desired results. The proposed scheme utilises the posterior co- variance between parameters to generate future parameter values. The attributes of the algorithm are ideal for hydrological models, which often exhibit a high degree of correlation between parameters. The Australian Water Balance Model (AWBM), a 8- parameter CRRM that has been tested and used in several
A Bayesian method for inferring transmission chains in a partially observed epidemic.
Marzouk, Youssef M.; Ray, Jaideep
2008-10-01
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
First and second order semi-Markov chains for wind speed modeling
NASA Astrophysics Data System (ADS)
Prattico, F.; Petroni, F.; D'Amico, G.
2012-04-01
The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [3] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [1], by using two models, first
Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
NASA Astrophysics Data System (ADS)
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver
Application of Markov chain to the pattern of mitochondrial deoxyribonucleic acid mutations
NASA Astrophysics Data System (ADS)
Vantika, Sandy; Pasaribu, Udjianna S.
2014-03-01
This research explains how Markov chain used to model the pattern of deoxyribonucleic acid mutations in mitochondrial (mitochondrial DNA). First, sign test was used to see a pattern of nucleotide bases that will appear at one position after the position of mutated nucleotide base. Results obtained from the sign test showed that for most cases, there exist a pattern of mutation except in the mutation cases of adenine to cytosine, adenine to thymine, and cytosine to guanine. Markov chain analysis results on data of mutations that occur in mitochondrial DNA indicate that one and two positions after the position of mutated nucleotide bases tend to be occupied by particular nucleotide bases. From this analysis, it can be said that the adenine, cytosine, guanine and thymine will mutate if the nucelotide base at one and/or two positions after them is cytosine.
Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.
Heath, S C
1997-01-01
A new method for segregation and linkage analysis, with pedigree data, is described. Reversible jump Markov chain Monte Carlo methods are used to implement a sampling scheme in which the Markov chain can jump between parameter subspaces corresponding to models with different numbers of quantitative-trait loci (QTL's). Joint estimation of QTL number, position, and effects is possible, avoiding the problems that can arise from misspecification of the number of QTL's in a linkage analysis. The method is illustrated by use of a data set simulated for the 9th Genetic Analysis Workshop; this data set had several oligogenic traits, generated by use of a 1,497-member pedigree. The mixing characteristics of the method appear to be good, and the method correctly recovers the simulated model from the test data set. The approach appears to have great potential both for robust linkage analysis and for the answering of more general questions regarding the genetic control of complex traits. PMID:9326339
Convergence measure and some parallel aspects of Markov-chain Monte Carlo algorithms
NASA Astrophysics Data System (ADS)
Malfait, Maurits J.; Roose, Dirk; Vandermeulen, Dirk
1993-10-01
We examine methods to assess the convergence of Markov chain Monte Carlo (MCMC) algorithms and to accelerate their execution via parallel computing. We propose a convergence measure based on the deviations between simultaneously running MCMC algorithms. We also examine the acceleration of MCMC algorithms when independent parallel sampler are used and report on some experiments with coupled samplers. As applications we use small Ising model simulations and a larger medical image processing algorithm.
Korostil, Igor A; Peters, Gareth W; Cornebise, Julien; Regan, David G
2013-05-20
A Bayesian statistical model and estimation methodology based on forward projection adaptive Markov chain Monte Carlo is developed in order to perform the calibration of a high-dimensional nonlinear system of ordinary differential equations representing an epidemic model for human papillomavirus types 6 and 11 (HPV-6, HPV-11). The model is compartmental and involves stratification by age, gender and sexual-activity group. Developing this model and a means to calibrate it efficiently is relevant because HPV is a very multi-typed and common sexually transmitted infection with more than 100 types currently known. The two types studied in this paper, types 6 and 11, are causing about 90% of anogenital warts. We extend the development of a sexual mixing matrix on the basis of a formulation first suggested by Garnett and Anderson, frequently used to model sexually transmitted infections. In particular, we consider a stochastic mixing matrix framework that allows us to jointly estimate unknown attributes and parameters of the mixing matrix along with the parameters involved in the calibration of the HPV epidemic model. This matrix describes the sexual interactions between members of the population under study and relies on several quantities that are a priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters as well as unknown sexual mixing matrix parameters related to assortativity. Finally, we explore the ability of an extension to the class of adaptive Markov chain Monte Carlo algorithms to incorporate a forward projection strategy for the ordinary differential equation state trajectories. Efficient exploration of the Bayesian posterior distribution developed for the ordinary differential equation parameters provides a challenge for any Markov chain sampling methodology, hence the interest in adaptive Markov chain methods. We conclude with simulation studies on synthetic and recent actual data. PMID
Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.
Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka
2014-02-01
In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain. PMID:24246289
Covariate adjustment of event histories estimated from Markov chains: the additive approach.
Aalen, O O; Borgan, O; Fekjaer, H
2001-12-01
Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet. PMID:11764270
Information Security Risk Assessment of Smart Grid Based on Absorbing Markov Chain and SPA
NASA Astrophysics Data System (ADS)
Jianye, Zhang; Qinshun, Zeng; Yiyang, Song; Cunbin, Li
2014-12-01
To assess and prevent the smart grid information security risks more effectively, this paper provides risk index quantitative calculation method based on absorbing Markov chain to overcome the deficiencies that links between system components were not taken into consideration and studies mostly were limited to static evaluation. The method avoids the shortcomings of traditional Expert Score with significant subjective factors and also considers the links between information system components, which make the risk index system closer to the reality. Then, a smart grid information security risk assessment model on the basis of set pair analysis improved by Markov chain was established. Using the identity, discrepancy, and contradiction of connection degree to dynamically reflect the trend of smart grid information security risk and combining with the Markov chain to calculate connection degree of the next period, the model implemented the smart grid information security risk assessment comprehensively and dynamically. Finally, this paper proves that the established model is scientific, effective, and feasible to dynamically evaluate the smart grid information security risks.
State space orderings for Gauss-Seidel in Markov chains revisited
Dayar, T.
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
NASA Astrophysics Data System (ADS)
Bacher, C.; Filgueira, R.; Guyondet, T.
2016-01-01
Markov chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g., depletion index, carrying capacity assessment. Markov chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.
NASA Astrophysics Data System (ADS)
Blanchard, Ph.; Dawin, J. R.; Volchenkov, D.
2010-06-01
Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of Lévy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.
Chen, C; Lin, C-H; Long, Z; Chen, Q
2014-02-01
To quickly obtain information about airborne infectious disease transmission in enclosed environments is critical in reducing the infection risk to the occupants. This study developed a combined computational fluid dynamics (CFD) and Markov chain method for quickly predicting transient particle transport in enclosed environments. The method first calculated a transition probability matrix using CFD simulations. Next, the Markov chain technique was applied to calculate the transient particle concentration distributions. This investigation used three cases, particle transport in an isothermal clean room, an office with an underfloor air distribution system, and the first-class cabin of an MD-82 airliner, to validate the combined CFD and Markov chain method. The general trends of the particle concentrations vs. time predicted by the Markov chain method agreed with the CFD simulations for these cases. The proposed Markov chain method can provide faster-than-real-time information about particle transport in enclosed environments. Furthermore, for a fixed airflow field, when the source location is changed, the Markov chain method can be used to avoid recalculation of the particle transport equation and thus reduce computing costs. PMID:23789964
Animal vocal sequences: not the Markov chains we thought they were.
Kershenbaum, Arik; Bowles, Ann E; Freeberg, Todd M; Jin, Dezhe Z; Lameira, Adriano R; Bohn, Kirsten
2014-10-01
Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the 'renewal process' (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037
Animal vocal sequences: not the Markov chains we thought they were
Kershenbaum, Arik; Bowles, Ann E.; Freeberg, Todd M.; Jin, Dezhe Z.; Lameira, Adriano R.; Bohn, Kirsten
2014-01-01
Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the ‘renewal process’ (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037
A Markov Chain Analysis of Fish Movements to Determine Entrainment Zones
Johnson, Gary E.; Hedgepeth, J; Skalski, John R.; Giorgi, Albert E.
2004-10-01
Fish can become entrained at water withdrawal locations such as fish bypasses or cooling water intakes. Accordingly, the size of a fish entrainment zone (FEZ) is often of interest to fisheries managers and facility operators. This study developed a new technique to map the FEZ, defined here as the region immediately upstream of a portal where the probability of fish movement toward the portal is greater than 90%. To map the FEZ, we applied a Markov chain analysis to fish movement data collected with an active tracking sonar. This device locks onto and follows a target, recording positions through a set of volumetric cells comprising the sampled volume. The probability of a fish moving from one cell to another was calculated from fish position data, which was used to populate a Markov transition matrix. We developed and applied the technique using data on salmon smolts migrating near the ice/trash sluiceway at The Dalles Dam on the Columbia River. The FEZ of the sluiceway entrance in 2000 as determined with this procedure was approximately 5 m across and extended 6-8 m out from the face of the dam in the surface layer 2-3 m deep. In conclusion, using a Markov chain analysis of fish track data we were able to describe and quantify the FEZ of the sluiceway at The Dalles Dam. This technique for FEZ mapping is applicable to other bioengineering efforts aimed at protecting fish populations affected by water withdrawals.
NASA Astrophysics Data System (ADS)
Zhang, Junlong; Li, Yongping; Huang, Guohe; Chen, Xi; Bao, Anming
2016-07-01
Without a realistic assessment of parameter uncertainty, decision makers may encounter difficulties in accurately describing hydrologic processes and assessing relationships between model parameters and watershed characteristics. In this study, a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis (MCMC-MFA) method is developed, which can not only generate samples of parameters from a well constructed Markov chain and assess parameter uncertainties with straightforward Bayesian inference, but also investigate the individual and interactive effects of multiple parameters on model output through measuring the specific variations of hydrological responses. A case study is conducted for addressing parameter uncertainties in the Kaidu watershed of northwest China. Effects of multiple parameters and their interactions are quantitatively investigated using the MCMC-MFA with a three-level factorial experiment (totally 81 runs). A variance-based sensitivity analysis method is used to validate the results of parameters' effects. Results disclose that (i) soil conservation service runoff curve number for moisture condition II (CN2) and fraction of snow volume corresponding to 50% snow cover (SNO50COV) are the most significant factors to hydrological responses, implying that infiltration-excess overland flow and snow water equivalent represent important water input to the hydrological system of the Kaidu watershed; (ii) saturate hydraulic conductivity (SOL_K) and soil evaporation compensation factor (ESCO) have obvious effects on hydrological responses; this implies that the processes of percolation and evaporation would impact hydrological process in this watershed; (iii) the interactions of ESCO and SNO50COV as well as CN2 and SNO50COV have an obvious effect, implying that snow cover can impact the generation of runoff on land surface and the extraction of soil evaporative demand in lower soil layers. These findings can help enhance the hydrological model
Algorithm Optimally Orders Forward-Chaining Inference Rules
NASA Technical Reports Server (NTRS)
James, Mark
2008-01-01
People typically develop knowledge bases in a somewhat ad hoc manner by incrementally adding rules with no specific organization. This often results in a very inefficient execution of those rules since they are so often order sensitive. This is relevant to tasks like Deep Space Network in that it allows the knowledge base to be incrementally developed and have it automatically ordered for efficiency. Although data flow analysis was first developed for use in compilers for producing optimal code sequences, its usefulness is now recognized in many software systems including knowledge-based systems. However, this approach for exhaustively computing data-flow information cannot directly be applied to inference systems because of the ubiquitous execution of the rules. An algorithm is presented that efficiently performs a complete producer/consumer analysis for each antecedent and consequence clause in a knowledge base to optimally order the rules to minimize inference cycles. An algorithm was developed that optimally orders a knowledge base composed of forwarding chaining inference rules such that independent inference cycle executions are minimized, thus, resulting in significantly faster execution. This algorithm was integrated into the JPL tool Spacecraft Health Inference Engine (SHINE) for verification and it resulted in a significant reduction in inference cycles for what was previously considered an ordered knowledge base. For a knowledge base that is completely unordered, then the improvement is much greater.
The optimum order of a Markov chain model for daily rainfall in Nigeria
NASA Astrophysics Data System (ADS)
Jimoh, O. D.; Webster, P.
1996-11-01
Markov type models are often used to describe the occurrence of daily rainfall. Although models of Order 1 have been successfully employed, there remains uncertainty concerning the optimum order for such models. This paper is concerned with estimation of the optimum order of Markov chains and, in particular, the use of objective criteria of the Akaike and Bayesian Information Criteria (AIC and BIC, respectively). Using daily rainfall series for five stations in Nigeria, it has been found that the AIC and BIC estimates vary with month as well as the value of the rainfall threshold used to define a wet day. There is no apparent system to this variation, although AIC estimates are consistently greater than or equal to BIC estimates, with values of the latter limited to zero or unity. The optimum order is also investigated through generation of synthetic sequences of wet and dry days using the transition matrices of zero-, first- and second-order Markov chains. It was found that the first-order model is superior to the zero-order model in representing the characteristics of the historical sequence as judged using frequency duration curves. There was no discernible difference between the model performance for first- and second-order models. There was no seasonal varation in the model performance, which contrasts with the optimum models identified using AIC and BIC estimates. It is concluded that caution is needed with the use of objective criteria for determining the optimum order of the Markov model and that the use of frequency duration curves can provide a robust alternative method of model identification. Comments are also made on the importance of record length and non-stationarity for model identification
A Markov Chain Monte Carlo method for the groundwater inverse problem.
Lu, Z.; Higdon, D. M.; Zhang, D.
2004-01-01
In this study, we develop a Markov Chain Monte Carlo method (MCMC) to estimate the hydraulic conductivity field conditioned on the direct measurements of hydraulic conductivity and indirect measurements of dependent variables such as hydraulic head for saturated flow in randomly heterogeneous porous media. The log hydraulic conductivity field is represented (parameterized) by the combination of some basis kernels centered at fixed spatial locations. The prior distribution for the vector of coefficients {theta} are taken from a posterior distribution {pi}({theta}/d) that is proportional to the product of the likelihood function of measurements d given parameter vector {theta} and the prior distribution of {theta}. Starting from any initial setting, a partial realization of a Markov chain is generated by updating only one component of {theta} at a time according to Metropolis rules. This ensures that output from this chain has {pi}({theta}/d) as its stationary distribution. The posterior mean of the parameter {theta} (and thus the mean log hydraulic conductivity conditional to measurements on hydraulic conductivity, and hydraulic head) can be estimated from the Markov chain realizations (ignoring some early realizations). The uncertainty associated with the mean filed can also be assessed from these realizations. In addition, the MCMC approach provides an alternative for estimating conditional predictions of hydraulic head and concentration and their associated uncertainties. Numerical examples for flow in a hypothetic random porous medium show that estimated log hydraulic conductivity field from the MCMC approach is closer to the original hypothetical random field than those obtained using kriging or cokriging methods.
Dodds, Michael G; Vicini, Paolo
2004-09-01
Advances in computer hardware and the associated computer-intensive algorithms made feasible by these advances [like Markov chain Monte Carlo (MCMC) data analysis techniques] have made possible the application of hierarchical full Bayesian methods in analyzing pharmacokinetic and pharmacodynamic (PK-PD) data sets that are multivariate in nature. Pharmacokinetic data analysis in particular has been one area that has seized upon this technology to refine estimates of drug parameters from sparse data gathered in a large, highly variable population of patients. A drawback in this type of analysis is that it is difficult to quantitatively assess convergence of the Markov chains to a target distribution, and thus, it is sometimes difficult to assess the reliability of estimates gained from this procedure. Another complicating factor is that, although the application of MCMC methods to population PK-PD problems has been facilitated by new software designed for the PK-PD domain (specifically PKBUGS), experts in PK-PD may not have the necessary experience with MCMC methods to detect and understand problems with model convergence. The objective of this work is to provide an example of a set of diagnostics useful to investigators, by analyzing in detail three convergence criteria (namely the Raftery and Lewis, Geweke, and Heidelberger and Welch methods) on a simulated problem and with a rule of thumb of 10,000 chain elements in the Markov chain. We used two publicly available software packages to assess convergence of MCMC parameter estimates; the first performs Bayesian parameter estimation (PKBUGS/WinBUGS), and the second is focused on posterior analysis of estimates (BOA). The main message that seems to emerge is that accurately estimating confidence regions for the parameters of interest is more demanding than estimating the parameter means. Together, these tools provide numerical means by which an investigator can establish confidence in convergence and thus in the
A MONTE CARLO MARKOV CHAIN BASED INVESTIGATION OF BLACK HOLE SPIN IN THE ACTIVE GALAXY NGC 3783
Reynolds, Christopher S.; Lohfink, Anne M.; Trippe, Margaret L.; Brenneman, Laura W.; Miller, Jon M.; Fabian, Andrew C.; Nowak, Michael A. E-mail: alohfink@astro.umd.edu
2012-08-20
The analysis of relativistically broadened X-ray spectral features from the inner accretion disk provides a powerful tool for measuring the spin of supermassive black holes in active galactic nuclei (AGNs). However, AGN spectra are often complex and careful analysis employing appropriate and self-consistent models is required if one has to obtain robust results. In this paper, we revisit the deep 2009 July Suzaku observation of the Seyfert galaxy NGC 3783 in order to study in a rigorous manner the robustness of the inferred black hole spin parameter. Using Monte Carlo Markov chain techniques, we identify a (partial) modeling degeneracy between the iron abundance of the disk and the black hole spin parameter. We show that the data for NGC 3783 strongly require both supersolar iron abundance (Z{sub Fe} = 2-4 Z{sub Sun }) and a rapidly spinning black hole (a > 0.89). We discuss various astrophysical considerations that can affect the measured abundance. We note that, while the abundance enhancement inferred in NGC 3783 is modest, the X-ray analysis of some other objects has found extreme iron abundances. We introduce the hypothesis that the radiative levitation of iron ions in the innermost regions of radiation-dominated AGN disks can enhance the photospheric abundance of iron. We show that radiative levitation is a plausible mechanism in the very inner regions of high accretion rate AGN disks.
Markov chain Monte Carlo based analysis of post-translationally modified VDAC gating kinetics
Tewari, Shivendra G.; Zhou, Yifan; Otto, Bradley J.; Dash, Ranjan K.; Kwok, Wai-Meng; Beard, Daniel A.
2015-01-01
The voltage-dependent anion channel (VDAC) is the main conduit for permeation of solutes (including nucleotides and metabolites) of up to 5 kDa across the mitochondrial outer membrane (MOM). Recent studies suggest that VDAC activity is regulated via post-translational modifications (PTMs). Yet the nature and effect of these modifications is not understood. Herein, single channel currents of wild-type, nitrosated, and phosphorylated VDAC are analyzed using a generalized continuous-time Markov chain Monte Carlo (MCMC) method. This developed method describes three distinct conducting states (open, half-open, and closed) of VDAC activity. Lipid bilayer experiments are also performed to record single VDAC activity under un-phosphorylated and phosphorylated conditions, and are analyzed using the developed stochastic search method. Experimental data show significant alteration in VDAC gating kinetics and conductance as a result of PTMs. The effect of PTMs on VDAC kinetics is captured in the parameters associated with the identified Markov model. Stationary distributions of the Markov model suggest that nitrosation of VDAC not only decreased its conductance but also significantly locked VDAC in a closed state. On the other hand, stationary distributions of the model associated with un-phosphorylated and phosphorylated VDAC suggest a reversal in channel conformation from relatively closed state to an open state. Model analyses of the nitrosated data suggest that faster reaction of nitric oxide with Cys-127 thiol group might be responsible for the biphasic effect of nitric oxide on basal VDAC conductance. PMID:25628567
Markov chain Monte Carlo based analysis of post-translationally modified VDAC gating kinetics.
Tewari, Shivendra G; Zhou, Yifan; Otto, Bradley J; Dash, Ranjan K; Kwok, Wai-Meng; Beard, Daniel A
2014-01-01
The voltage-dependent anion channel (VDAC) is the main conduit for permeation of solutes (including nucleotides and metabolites) of up to 5 kDa across the mitochondrial outer membrane (MOM). Recent studies suggest that VDAC activity is regulated via post-translational modifications (PTMs). Yet the nature and effect of these modifications is not understood. Herein, single channel currents of wild-type, nitrosated, and phosphorylated VDAC are analyzed using a generalized continuous-time Markov chain Monte Carlo (MCMC) method. This developed method describes three distinct conducting states (open, half-open, and closed) of VDAC activity. Lipid bilayer experiments are also performed to record single VDAC activity under un-phosphorylated and phosphorylated conditions, and are analyzed using the developed stochastic search method. Experimental data show significant alteration in VDAC gating kinetics and conductance as a result of PTMs. The effect of PTMs on VDAC kinetics is captured in the parameters associated with the identified Markov model. Stationary distributions of the Markov model suggest that nitrosation of VDAC not only decreased its conductance but also significantly locked VDAC in a closed state. On the other hand, stationary distributions of the model associated with un-phosphorylated and phosphorylated VDAC suggest a reversal in channel conformation from relatively closed state to an open state. Model analyses of the nitrosated data suggest that faster reaction of nitric oxide with Cys-127 thiol group might be responsible for the biphasic effect of nitric oxide on basal VDAC conductance. PMID:25628567
Markov chain Monte Carlo methods for statistical analysis of RF photonic devices.
Piels, Molly; Zibar, Darko
2016-02-01
The microwave reflection coefficient is commonly used to characterize the impedance of high-speed optoelectronic devices. Error and uncertainty in equivalent circuit parameters measured using this data are systematically evaluated. The commonly used nonlinear least-squares method for estimating uncertainty is shown to give unsatisfactory and incorrect results due to the nonlinear relationship between the circuit parameters and the measured data. Markov chain Monte Carlo methods are shown to provide superior results, both for individual devices and for assessing within-die variation. PMID:26906783
Green, P. L.; Worden, K.
2015-01-01
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories. PMID:26303916
D. L. Kelly
2007-06-01
Markov chain Monte Carlo (MCMC) techniques represent an extremely flexible and powerful approach to Bayesian modeling. This work illustrates the application of such techniques to time-dependent reliability of components with repair. The WinBUGS package is used to illustrate, via examples, how Bayesian techniques can be used for parametric statistical modeling of time-dependent component reliability. Additionally, the crucial, but often overlooked subject of model validation is discussed, and summary statistics for judging the model’s ability to replicate the observed data are developed, based on the posterior predictive distribution for the parameters of interest.
A Markov chain technique for determining the acquisition behavior of a digital tracking loop
NASA Technical Reports Server (NTRS)
Chadwick, H. D.
1972-01-01
An iterative procedure is presented for determining the acquisition behavior of discrete or digital implementations of a tracking loop. The technique is based on the theory of Markov chains and provides the cumulative probability of acquisition in the loop as a function of time in the presence of noise and a given set of initial condition probabilities. A digital second-order tracking loop to be used in the Viking command receiver for continuous tracking of the command subcarrier phase was analyzed using this technique, and the results agree closely with experimental data.
A multi-level solution algorithm for steady-state Markov chains
NASA Technical Reports Server (NTRS)
Horton, Graham; Leutenegger, Scott T.
1993-01-01
A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.
NASA Astrophysics Data System (ADS)
Chen, X.; Rubin, Y.; Baldocchi, D. D.
2005-12-01
Understanding the interactions between soil, plant, and the atmosphere under water-stressed conditions is important for ecosystems where water availability is limited. In such ecosystems, the amount of water transferred from the soil to the atmosphere is controlled not only by weather conditions and vegetation type but also by soil water availability. Although researchers have proposed different approaches to model the impact of soil moisture on plant activities, the parameters involved are difficult to measure. However, using measurements of observed latent heat and carbon fluxes, as well as soil moisture data, Bayesian inversion methods can be employed to estimate the various model parameters. In our study, actual Evapotranspiration (ET) of an ecosystem is approximated by the Priestley-Taylor relationship, with the Priestley-Taylor coefficient modeled as a function of soil moisture content. Soil moisture limitation on root uptake is characterized in a similar manner as the Feddes' model. The inference of Bayesian inversion is processed within the framework of graphical theories. Due to the difficulty of obtaining exact inference, the Markov chain Monte Carlo (MCMC) method is implemented using a free software package, BUGS (Bayesian inference Using Gibbs Sampling). The proposed methodology is applied to a Mediterranean Oak-Savanna FLUXNET site in California, where continuous measurements of actual ET are obtained from eddy-covariance technique and soil moisture contents are monitored by several time domain reflectometry probes located within the footprint of the flux tower. After the implementation of Bayesian inversion, the posterior distributions of all the parameters exhibit enhancement in information compared to the prior distributions. The generated samples based on data in year 2003 are used to predict the actual ET in year 2004 and the prediction uncertainties are assessed in terms of confidence intervals. Our tests also reveal the usefulness of various
NASA Astrophysics Data System (ADS)
Cavers, M. S.; Vasudevan, K.
2015-10-01
Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series. Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour. Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain. Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.
Farr, W M; Mandel, I; Stevens, D
2015-06-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient 'global' proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
NASA Astrophysics Data System (ADS)
Maginnis, P. A.; West, M.; Dullerud, G. E.
2016-10-01
We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a "black-box", i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.
Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures
NASA Astrophysics Data System (ADS)
Datta, Nilanjana; Wilde, Mark M.
2015-12-01
A short quantum Markov chain is a tripartite state {ρ }{ABC} such that system A can be recovered perfectly by acting on system C of the reduced state {ρ }{BC}. Such states have conditional mutual information I(A;B| C) equal to zero and are the only states with this property. A quantum channel {N} is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ from {N}(ρ ) and σ from {N}(σ ). The relative entropy difference D(ρ \\parallel σ )-D({N}(ρ )\\parallel {N}(σ )) is equal to zero if and only if {N} is sufficient for ρ and σ. In this paper, we show that these properties extend to Rényi generalizations of these information measures which were proposed in (Berta et al 2015 J. Math. Phys. 56 022205; Seshadreesan et al 2015 J. Phys. A: Math. Theor. 48 395303), thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.
Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Norton, Larry; Kuhn, Peter
2013-05-01
The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, although not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as "spreaders" or "sponges" and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multidirectional aspects of cancer progression. We quantify three types of multidirectional mechanisms of progression: (i) self-seeding of the primary tumor, (ii) reseeding of the primary tumor from a metastatic site (primary reseeding), and (iii) reseeding of metastatic tumors (metastasis reseeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. PMID:23447576
Farr, W M; Mandel, I; Stevens, D
2015-06-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient 'global' proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently.
A Markov chain probability model to describe wet and dry patterns of weather at Colombo
NASA Astrophysics Data System (ADS)
Sonnadara, D. U. J.; Jayewardene, D. R.
2015-01-01
The hypothesis that the wet and dry patterns of daily precipitation observed in Colombo can be modeled by a first order Markov chain model was tested using daily rainfall data for a 60-year period (1941-2000). The probability of a day being wet or dry was defined with respect to the status of the previous day. Probabilities were assumed to be stationary within a given month. Except for isolated single events, the model is shown to describe the observed sequence of wet and dry spells satisfactorily depending on the season. The accuracy of modeling wet spells is high compared to dry spells. When the model-predicted mean length of wet spells for each month was compared with the estimated values from the data set, a reasonable agreement between the model prediction and estimation is seen (within ±0.1). In general, the data show a higher disagreement for the months having longer dry spells. The mean annual duration of wet spells is 2.6 days while the mean annual duration of dry spells is 3.8 days. It is shown that the model can be used to explore the return periods of long wet and dry spells. We conclude from the study that the Markov chain of order 1 is adequate to describe wet and dry patterns of weather in Colombo.
Sampling graphs with a prescribed joint degree distribution using Markov Chains.
Pinar, Ali; Stanton, Isabelle
2010-10-01
One of the most influential results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, i.e. the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest that the joint degree distribution of graphs is an interesting avenue of study for further research into network structure. We provide a simple greedy algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov Chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov Chain by using experiments based on the autocorrelation of each edge.
Wang, Ying; Hu, Haiyan; Li, Xiaoman
2016-08-01
Metagenomics is a next-generation omics field currently impacting postgenomic life sciences and medicine. Binning metagenomic reads is essential for the understanding of microbial function, compositions, and interactions in given environments. Despite the existence of dozens of computational methods for metagenomic read binning, it is still very challenging to bin reads. This is especially true for reads from unknown species, from species with similar abundance, and/or from low-abundance species in environmental samples. In this study, we developed a novel taxonomy-dependent and alignment-free approach called MBMC (Metagenomic Binning by Markov Chains). Different from all existing methods, MBMC bins reads by measuring the similarity of reads to the trained Markov chains for different taxa instead of directly comparing reads with known genomic sequences. By testing on more than 24 simulated and experimental datasets with species of similar abundance, species of low abundance, and/or unknown species, we report here that MBMC reliably grouped reads from different species into separate bins. Compared with four existing approaches, we demonstrated that the performance of MBMC was comparable with existing approaches when binning reads from sequenced species, and superior to existing approaches when binning reads from unknown species. MBMC is a pivotal tool for binning metagenomic reads in the current era of Big Data and postgenomic integrative biology. The MBMC software can be freely downloaded at http://hulab.ucf.edu/research/projects/metagenomics/MBMC.html . PMID:27447888
Markov Chain Monte Carlo simulation for projection of end stage renal disease patients in Greece.
Rodina-Theocharaki, A; Bliznakova, K; Pallikarakis, N
2012-07-01
End stage renal disease (ESRD) treatment methods are considered to be among the most expensive procedures for chronic conditions worldwide which also have severe impact on patients' quality of life. During the last decade, Greece has been among the countries with the highest incidence and prevalence, while at the same time with the lowest kidney transplantation rates. Predicting future patients' number on Renal Replacement Therapy (RRT) is essential for health care providers in order to achieve more effective resource management. In this study a Markov Chain Monte Carlo (MCMC) simulation is presented for predicting the future number of ESRD patients for the period 2009-2020 in Greece. The MCMC model comprises Monte Carlo sampling techniques applied on probability distributions of the constructed Markov Chain. The model predicts that there will be 15,147 prevalent patients on RRT in Greece by 2020. Additionally, a cost-effectiveness analysis was performed on a scenario of gradually reducing the hemodialysis patients in favor of increasing the transplantation number by 2020. The proposed scenario showed net savings of 86.54 million Euros for the period 2009-2020 compared to the base-case prediction. PMID:22024418
Short-term droughts forecast using Markov chain model in Victoria, Australia
NASA Astrophysics Data System (ADS)
Rahmat, Siti Nazahiyah; Jayasuriya, Niranjali; Bhuiyan, Muhammed A.
2016-04-01
A comprehensive risk management strategy for dealing with drought should include both short-term and long-term planning. The objective of this paper is to present an early warning method to forecast drought using the Standardised Precipitation Index (SPI) and a non-homogeneous Markov chain model. A model such as this is useful for short-term planning. The developed method has been used to forecast droughts at a number of meteorological monitoring stations that have been regionalised into six (6) homogenous clusters with similar drought characteristics based on SPI. The non-homogeneous Markov chain model was used to estimate drought probabilities and drought predictions up to 3 months ahead. The drought severity classes defined using the SPI were computed at a 12-month time scale. The drought probabilities and the predictions were computed for six clusters that depict similar drought characteristics in Victoria, Australia. Overall, the drought severity class predicted was quite similar for all the clusters, with the non-drought class probabilities ranging from 49 to 57 %. For all clusters, the near normal class had a probability of occurrence varying from 27 to 38 %. For the more moderate and severe classes, the probabilities ranged from 2 to 13 % and 3 to 1 %, respectively. The developed model predicted drought situations 1 month ahead reasonably well. However, 2 and 3 months ahead predictions should be used with caution until the models are developed further.
NASA Astrophysics Data System (ADS)
Gonthier, Peter L.; Koh, Yew-Meng; Kust Harding, Alice
2016-04-01
We present preliminary results of a new population synthesis of millisecond pulsars (MSP) from the Galactic disk using Markov Chain Monte Carlo techniques to better understand the model parameter space. We include empirical radio and gamma-ray luminosity models that are dependent on the pulsar period and period derivative with freely varying exponents. The magnitudes of the model luminosities are adjusted to reproduce the number of MSPs detected by a group of thirteen radio surveys as well as the MSP birth rate in the Galaxy and the number of MSPs detected by Fermi. We explore various high-energy emission geometries like the slot gap, outer gap, two pole caustic and pair starved polar cap models. The parameters associated with the birth distributions for the mass accretion rate, magnetic field, and period distributions are well constrained. With the set of four free parameters, we employ Markov Chain Monte Carlo simulations to explore the model parameter space. We present preliminary comparisons of the simulated and detected distributions of radio and gamma-ray pulsar characteristics. We estimate the contribution of MSPs to the diffuse gamma-ray background with a special focus on the Galactic Center.We express our gratitude for the generous support of the National Science Foundation (RUI: AST-1009731), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program (NNX09AQ71G).
NASA Astrophysics Data System (ADS)
Durán, E.
2012-04-01
The interbeded sandstones, siltstones and shale layers within the stratigraphic units of the Oficina Formation were stochastically characterized. The units within the Oritupano field are modeled using the information from 12 wells and a post-stack 3-D seismic cube. The Markov Chain algorithm was successful at maintaining the proportion of lithotypes of the columns in the study area. Different transition probability matrixes are evaluated by changing the length of the sequences represented in the transition matrix and how this choice of length affects ciclicity and the genetic relations between lithotypes. The Gibbs algorithm, using small sequences as building blocks for modeling, kept the main stratigraphic succession according to the geology. Although the modeled stratigraphy depends strongly on initial conditions, the use of longer sequences in the substitution helps not to overweight the transition counts from one lithotype to the same in the main diagonal of the probability matrix of the Markov Chain in the Gibbs algorithm. A methodology based on the phase spectrum of the seismic trace for tying the modeled sequences with the seismic data is evaluated and discussed. The results point to the phase spectrum as an alternate way to cross-correlate synthetic seismograms with the seismic trace in favor of the well known amplitude correlation. Finally, a map of net sand over the study area is generated from the modeled columns and compared with previous stratigraphic and facies analysis at the levels of interest.
Farr, W. M.; Mandel, I.; Stevens, D.
2015-01-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks
NASA Astrophysics Data System (ADS)
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011), 10.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011), 10.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
Markov chain modelling of reliability analysis and prediction under mixed mode loading
NASA Astrophysics Data System (ADS)
Singh, Salvinder; Abdullah, Shahrum; Nik Mohamed, Nik Abdullah; Mohd Noorani, Mohd Salmi
2015-03-01
The reliability assessment for an automobile crankshaft provides an important understanding in dealing with the design life of the component in order to eliminate or reduce the likelihood of failure and safety risks. The failures of the crankshafts are considered as a catastrophic failure that leads towards a severe failure of the engine block and its other connecting subcomponents. The reliability of an automotive crankshaft under mixed mode loading using the Markov Chain Model is studied. The Markov Chain is modelled by using a two-state condition to represent the bending and torsion loads that would occur on the crankshaft. The automotive crankshaft represents a good case study of a component under mixed mode loading due to the rotating bending and torsion stresses. An estimation of the Weibull shape parameter is used to obtain the probability density function, cumulative distribution function, hazard and reliability rate functions, the bathtub curve and the mean time to failure. The various properties of the shape parameter is used to model the failure characteristic through the bathtub curve is shown. Likewise, an understanding of the patterns posed by the hazard rate onto the component can be used to improve the design and increase the life cycle based on the reliability and dependability of the component. The proposed reliability assessment provides an accurate, efficient, fast and cost effective reliability analysis in contrast to costly and lengthy experimental techniques.
Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model
NASA Astrophysics Data System (ADS)
Novkaniza, F.; Ivana, Aldila, D.
2016-04-01
Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i - 1, or i. Approximation probability of an outbreak with gambler's ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.
Fisher information and asymptotic normality in system identification for quantum Markov chains
Guta, Madalin
2011-06-15
This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
Minimal diffusion formulation of Markov chain ensembles and its application to ion channel clusters
NASA Astrophysics Data System (ADS)
Güler, Marifi
2015-06-01
We study ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. A diffusion approximation, composed of two specifically coupled Ornstein-Uhlenbeck processes in stochastic differential equation representation, is formulated to deduce how the number of chains in a given particular state evolves in time. This particular form of the formulation builds upon a theoretical argument adduced here. The formulation is minimal in the sense that it is always a two-dimensional stochastic process regardless of the state space size or the transition matrix density, and that it requires no matrix square root operations. A set of criteria, put forward here as to be necessarily captured by any consistent approximation scheme, is used together with the master equation to determine uniquely the parameter values and noise variances in the formulation. The model is applied to the gating dynamics in ion channel clusters.
Entropy and long-range memory in random symbolic additive Markov chains.
Melnik, S S; Usatenko, O V
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory. PMID:27415245
Entropy and long-range memory in random symbolic additive Markov chains
NASA Astrophysics Data System (ADS)
Melnik, S. S.; Usatenko, O. V.
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.
NASA Technical Reports Server (NTRS)
Leutenegger, Scott T.; Horton, Graham
1994-01-01
Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.
Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.
Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C
2014-12-01
D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase
NASA Astrophysics Data System (ADS)
Li, Xuesong; Northrop, William F.
2016-04-01
This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.
Mikhailov, I.D.; Zhuravskii, L.V.
1987-11-01
A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for along polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type.
Minsley, Burke J.
2011-01-01
A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a signiﬁcant degree of ﬂexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and conﬁguration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favorably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.
Minsley, B.J.
2011-01-01
A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, 'best' model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequency-domain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favourably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment. ?? 2011. Geophysical Journal International ?? 2011 RAS.
Unsupervised SAR images change detection with hidden Markov chains on a sliding window
NASA Astrophysics Data System (ADS)
Bouyahia, Zied; Benyoussef, Lamia; Derrode, Stéphane
2007-10-01
This work deals with unsupervised change detection in bi-date Synthetic Aperture Radar (SAR) images. Whatever the indicator of change used, e.g. log-ratio or Kullback-Leibler divergence, we have observed poor quality change maps for some events when using the Hidden Markov Chain (HMC) model we focus on in this work. The main reason comes from the stationary assumption involved in this model - and in most Markovian models such as Hidden Markov Random Fields-, which can not be justified in most observed scenes: changed areas are not necessarily stationary in the image. Besides the few non stationary Markov models proposed in the literature, the aim of this paper is to describe a pragmatic solution to tackle stationarity by using a sliding window strategy. In this algorithm, the criterion image is scanned pixel by pixel, and a classical HMC model is applied only on neighboring pixels. By moving the window through the image, the process is able to produce a change map which can better exhibit non stationary changes than the classical HMC applied directly on the whole criterion image. Special care is devoted to the estimation of the number of classes in each window, which can vary from one (no change) to three (positive change, negative change and no change) by using the corrected Akaike Information Criterion (AICc) suited to small samples. The quality assessment of the proposed approach is achieved with speckle-simulated images in which simulated changes is introduced. The windowed strategy is also evaluated with a pair of RADARSAT images bracketing the Nyiragongo volcano eruption event in January 2002. The available ground truth confirms the effectiveness of the proposed approach compared to a classical HMC-based strategy.
Combined survival analysis of cardiac patients by a Cox PH model and a Markov chain.
Shauly, Michal; Rabinowitz, Gad; Gilutz, Harel; Parmet, Yisrael
2011-10-01
The control and treatment of dyslipidemia is a major public health challenge, particularly for patients with coronary heart diseases. In this paper we propose a framework for survival analysis of patients who had a major cardiac event, focusing on assessment of the effect of changing LDL-cholesterol level and statins consumption on survival. This framework includes a Cox PH model and a Markov chain, and combines their results into reinforced conclusions regarding the factors that affect survival time. We prospectively studied 2,277 cardiac patients, and the results show high congruence between the Markov model and the PH model; both evidence that diabetes, history of stroke, peripheral vascular disease and smoking significantly increase hazard rate and reduce survival time. On the other hand, statin consumption is correlated with a lower hazard rate and longer survival time in both models. The role of such a framework in understanding the therapeutic behavior of patients and implementing effective secondary and primary prevention of heart diseases is discussed here. PMID:21735134
A Markov chain analysis of fish movements to determine entrainment zones
Johnson, Gary E.; Hedgepeth, J.; Skalski, John R.; Giorgi, Albert E.
2004-06-01
The extent of the biological zone of influence (BZI) of a water withdrawal port, such as a cooling water intake or a smolt bypass, directly reflects its local effect on fish. This study produced a new technique to determine the BZI, defined as the region immediately upstream of a portal where the probability of fish movement toward the portal is greater than 90%. We developed and applied the technique at The Dalles Dam on the Columbia River, where the ice/trash sluiceway functions as a surface flow smolt bypass. To map the BZI, we applied a Markov-Chain analysis to smolt movement data collected with an active fish tracking sonar system. Probabilities of fish movement from cell to cell in the sample volume, calculated from tracked fish data, formed a Markov transition matrix. Multiplying this matrix by itself many times with absorption at the boundaries produced estimates of probability of passage out each side of the sample volume from the cells within. The BZI of a sluiceway entrance at The Dalles Dam was approximately 5 m across and extended 6-8 m out from the face of the dam in the surface layer 2-3 m deep. BZI mapping is applicable to many bioengineering efforts to protect fish populations.
Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain
Dai, Yonghui; Han, Dongmei; Dai, Weihui
2014-01-01
The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP) neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market. PMID:24782659
Pasyanos, M E; Franz, G A; Ramirez, A L
2004-08-30
In an effort to build seismic models that are most consistent with multiple data sets, we have applied a new probabilistic inverse technique. This method uses a Markov Chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over a single deterministic model, notably the reconciliation of different data types that constrain the model, the proper handling of uncertainties, and the ability to include prior information. We also benefit from the advantage of forward modeling rather than inverting the data. Here, we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula (YSKP) region. We discuss the data sets, parameterization and starting model, outline the technique and its implementation, observe the behavior of the inversion, and demonstrate some of the advantages of this approach.
Markov Chain Monte Carlo estimation for Bayesian approach based on right censored data
NASA Astrophysics Data System (ADS)
Ahmed, Alomari Mohammed
2014-06-01
This study consider the estimation of Maximum Likelihood Estimator and the Bayesian Estimator using Jeffreys prior and extension of Jeffreys prior information of the Weibull distribution with right censored data. The shape parametric estimation by maximum likelihood method is not available in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions can not be solved analytically. Hence Markov Chain Monte Carlo method is used, where the full conditional distribution for the scale and shape parameters are obtained via Gibbs sampling and Metropolis-Hastings algorithm followed by the survival and hazard functions estimates. The methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the best method in parameters, the survival and the hazard functions.
3D+t brain MRI segmentation using robust 4D Hidden Markov Chain.
Lavigne, François; Collet, Christophe; Armspach, Jean-Paul
2014-01-01
In recent years many automatic methods have been developed to help physicians diagnose brain disorders, but the problem remains complex. In this paper we propose a method to segment brain structures on two 3D multi-modal MR images taken at different times (longitudinal acquisition). A bias field correction is performed with an adaptation of the Hidden Markov Chain (HMC) allowing us to take into account the temporal correlation in addition to spatial neighbourhood information. To improve the robustness of the segmentation of the principal brain structures and to detect Multiple Sclerosis Lesions as outliers the Trimmed Likelihood Estimator (TLE) is used during the process. The method is validated on 3D+t brain MR images. PMID:25571045
Estimation of the transition matrix of a discrete-time Markov chain.
Craig, Bruce A; Sendi, Peter P
2002-01-01
Discrete-time Markov chains have been successfully used to investigate treatment programs and health care protocols for chronic diseases. In these situations, the transition matrix, which describes the natural progression of the disease, is often estimated from a cohort observed at common intervals. Estimation of the matrix, however, is often complicated by the complex relationship among transition probabilities. This paper summarizes methods to obtain the maximum likelihood estimate of the transition matrix when the cycle length of the model coincides with the observation interval, the cycle length does not coincide with the observation interval, and when the observation intervals are unequal in length. In addition, the bootstrap is discussed as a method to assess the uncertainty of the maximum likelihood estimate and to construct confidence intervals for functions of the transition matrix such as expected survival. PMID:11788980
A methodology for stochastic analysis of share prices as Markov chains with finite states.
Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey
2014-01-01
Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data. PMID:25520904
Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques
NASA Astrophysics Data System (ADS)
Kupinski, Matthew A.; Hoppin, John W.; Clarkson, Eric; Barrett, Harrison H.
2003-03-01
The ideal observer sets an upper limit on the performance of an observer on a detection or classification task. The performance of the ideal observer can be used to optimize hardware components of imaging systems and also to determine another observer's relative performance in comparison with the best possible observer. The ideal observer employs complete knowledge of the statistics of the imaging system, including the noise and object variability. Thus computing the ideal observer for images (large-dimensional vectors) is burdensome without severely restricting the randomness in the imaging system, e.g., assuming a flat object. We present a method for computing the ideal-observer test statistic and performance by using Markov-chain Monte Carlo techniques when we have a well-characterized imaging system, knowledge of the noise statistics, and a stochastic object model. We demonstrate the method by comparing three different parallel-hole collimator imaging systems in simulation.
Study of behavior and determination of customer lifetime value(CLV) using Markov chain model
NASA Astrophysics Data System (ADS)
Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.
2014-03-01
Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.
Assessing confidence in phylogenetic trees : bootstrap versus Markov chain Monte Carlo
Burr, Tom; Doak, J. E.; Gattiker, J. R.; Stanbro, W. D.
2002-01-01
Recent implementations of Bayesian approaches are one of the largest advances in phylogenetic tree estimation in the last 10 years. Markov chain Monte Carlo (MCMC) is used in these new approaches to estimate the Bayesian posterior probability for each tree topology of interest. Our goal is to assess the confidence in the estimated tree (particularly in whether prespecified groups are monophyletic) using MCMC and to compare the Bayesian estimate of confidence to a bootstrap-based estimate of confidence. We compare the Bayesian posterior probability to the bootstrap probability for specified groups in two real sets of influenza sequences and two sets of simulated sequences for our comparison. We conclude that the bootstrap estimate is adequate compared to the MCMC estimate except perhaps if the number of DNA sites is small.
Markov Chain Monte Carlo Sampling Methods for 1D Seismic and EM Data Inversion
2008-09-22
This software provides several Markov chain Monte Carlo sampling methods for the Bayesian model developed for inverting 1D marine seismic and controlled source electromagnetic (CSEM) data. The current software can be used for individual inversion of seismic AVO and CSEM data and for joint inversion of both seismic and EM data sets. The structure of the software is very general and flexible, and it allows users to incorporate their own forward simulation codes and rockmore » physics model codes easily into this software. Although the softwae was developed using C and C++ computer languages, the user-supplied codes can be written in C, C++, or various versions of Fortran languages. The software provides clear interfaces for users to plug in their own codes. The output of this software is in the format that the R free software CODA can directly read to build MCMC objects.« less
Projection of postgraduate students flow with a smoothing matrix transition diagram of Markov chain
NASA Astrophysics Data System (ADS)
Rahim, Rahela; Ibrahim, Haslinda; Adnan, Farah Adibah
2013-04-01
This paper presents a case study of modeling postgraduate students flow at the College of Art and Sciences, Universiti Utara Malaysia. First, full time postgraduate students and the semester they were in are identified. Then administrative data were used to estimate the transitions between these semesters for the year 2001-2005 periods. Markov chain model is developed to calculate the -5 and -10 years projection of postgraduate students flow at the college. The optimization question addressed in this study is 'Which transitions would sustain the desired structure in the dynamic situation such as trend towards graduation?' The smoothed transition probabilities are proposed to estimate the transition probabilities matrix of 16 × 16. The results shows that using smoothed transition probabilities, the projection number of postgraduate students enrolled in the respective semesters are closer to actual than using the conventional steady states transition probabilities.
Study of behavior and determination of customer lifetime value(CLV) using Markov chain model
Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.
2014-03-24
Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.
Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains.
Dans, Silvana Laura; Degrati, Mariana; Pedraza, Susana Noemí; Crespo, Enrique Alberto
2012-08-01
In Patagonia, Argentina, watching dolphins, especially dusky dolphins (Lagenorhynchus obscurus), is a new tourist activity. Feeding time decreases and time to return to feeding after feeding is abandoned and time it takes a group of dolphins to feed increase in the presence of boats. Such effects on feeding behavior may exert energetic costs on dolphins and thus reduce an individual's survival and reproductive capacity or maybe associated with shifts in distribution. We sought to predict which behavioral changes modify the activity pattern of dolphins the most. We modeled behavioral sequences of dusky dolphins with Markov chains. We calculated transition probabilities from one activity to another and arranged them in a stochastic matrix model. The proportion of time dolphins dedicated to a given activity (activity budget) and the time it took a dolphin to resume that activity after it had been abandoned (recurrence time) were calculated. We used a sensitivity analysis of Markov chains to calculate the sensitivity of the time budget and the activity-resumption time to changes in behavioral transition probabilities. Feeding-time budget was most sensitive to changes in the probability of dolphins switching from traveling to feeding behavior and of maintaining feeding behavior. Thus, an increase in these probabilities would be associated with the largest reduction in the time dedicated to feeding. A reduction in the probability of changing from traveling to feeding would also be associated with the largest increases in the time it takes dolphins to resume feeding. To approach dolphins when they are traveling would not affect behavior less because presence of the boat may keep dolphins from returning to feeding. Our results may help operators of dolphin-watching vessels minimize negative effects on dolphins. PMID:22624561
A stochastic Markov chain model to describe lung cancer growth and metastasis.
Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter
2012-01-01
A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.
A stochastic Markov chain model to describe lung cancer growth and metastasis.
Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter
2012-01-01
A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model. PMID:22558094
A Markov Chain Model for Changes in Users’ Assessment of Search Results
Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark
2016-01-01
Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results. PMID:27171426
A Markov Chain Model for Changes in Users' Assessment of Search Results.
Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark
2016-01-01
Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same"coarse" relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users' judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results.
Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution
Djordjevic, Ivan B.
2015-01-01
Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually
Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.
Djordjevic, Ivan B
2015-08-24
Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually
Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET
NASA Astrophysics Data System (ADS)
Hatt, M.; Lamare, F.; Boussion, N.; Turzo, A.; Collet, C.; Salzenstein, F.; Roux, C.; Jarritt, P.; Carson, K.; Cheze-LeRest, C.; Visvikis, D.
2007-07-01
Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm3 and 64 mm3). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The analysis of both
ERIC Educational Resources Information Center
Nicholls, Miles G.
2007-01-01
In this paper, absorbing markov chains are used to analyse the flows of higher degree by research candidates (doctoral and master) within an Australian faculty of business. The candidates are analysed according to whether they are full time or part time. The need for such analysis stemmed from what appeared to be a rather poor completion rate (as…
ERIC Educational Resources Information Center
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
Fiske, Ian J.; Royle, J. Andrew; Gross, Kevin
2014-01-01
Ecologists and wildlife biologists increasingly use latent variable models to study patterns of species occurrence when detection is imperfect. These models have recently been generalized to accommodate both a more expansive description of state than simple presence or absence, and Markovian dynamics in the latent state over successive sampling seasons. In this paper, we write these multi-season, multi-state models as hidden Markov models to find both maximum likelihood estimates of model parameters and finite-sample estimators of the trajectory of the latent state over time. These estimators are especially useful for characterizing population trends in species of conservation concern. We also develop parametric bootstrap procedures that allow formal inference about latent trend. We examine model behavior through simulation, and we apply the model to data from the North American Amphibian Monitoring Program.
A Markov Random Field Framework for Protein Side-Chain Resonance Assignment
NASA Astrophysics Data System (ADS)
Zeng, Jianyang; Zhou, Pei; Donald, Bruce Randall
Nuclear magnetic resonance (NMR) spectroscopy plays a critical role in structural genomics, and serves as a primary tool for determining protein structures, dynamics and interactions in physiologically-relevant solution conditions. The current speed of protein structure determination via NMR is limited by the lengthy time required in resonance assignment, which maps spectral peaks to specific atoms and residues in the primary sequence. Although numerous algorithms have been developed to address the backbone resonance assignment problem [68,2,10,37,14,64,1,31,60], little work has been done to automate side-chain resonance assignment [43, 48, 5]. Most previous attempts in assigning side-chain resonances depend on a set of NMR experiments that record through-bond interactions with side-chain protons for each residue. Unfortunately, these NMR experiments have low sensitivity and limited performance on large proteins, which makes it difficult to obtain enough side-chain resonance assignments. On the other hand, it is essential to obtain almost all of the side-chain resonance assignments as a prerequisite for high-resolution structure determination. To overcome this deficiency, we present a novel side-chain resonance assignment algorithm based on alternative NMR experiments measuring through-space interactions between protons in the protein, which also provide crucial distance restraints and are normally required in high-resolution structure determination. We cast the side-chain resonance assignment problem into a Markov Random Field (MRF) framework, and extend and apply combinatorial protein design algorithms to compute the optimal solution that best interprets the NMR data. Our MRF framework captures the contact map information of the protein derived from NMR spectra, and exploits the structural information available from the backbone conformations determined by orientational restraints and a set of discretized side-chain conformations (i.e., rotamers). A Hausdorff
Bayesian inference of local trees along chromosomes by the sequential Markov coalescent.
Zheng, Chaozhi; Kuhner, Mary K; Thompson, Elizabeth A
2014-05-01
We propose a genealogy-sampling algorithm, Sequential Markov Ancestral Recombination Tree (SMARTree), that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, Genetics 7:16, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in 10 DNA sequences over 50 kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al. Genetics 156:1393-1401, 2000a), a sampler which uses the full model. PMID:24817610
Multi-Physics Markov Chain Monte Carlo Methods for Subsurface Flows
NASA Astrophysics Data System (ADS)
Rigelo, J.; Ginting, V.; Rahunanthan, A.; Pereira, F.
2014-12-01
For CO2 sequestration in deep saline aquifers, contaminant transport in subsurface, and oil or gas recovery, we often need to forecast flow patterns. Subsurface characterization is a critical and challenging step in flow forecasting. To characterize subsurface properties we establish a statistical description of the subsurface properties that are conditioned to existing dynamic and static data. A Markov Chain Monte Carlo (MCMC) algorithm is used in a Bayesian statistical description to reconstruct the spatial distribution of rock permeability and porosity. The MCMC algorithm requires repeatedly solving a set of nonlinear partial differential equations describing displacement of fluids in porous media for different values of permeability and porosity. The time needed for the generation of a reliable MCMC chain using the algorithm can be too long to be practical for flow forecasting. In this work we develop fast and effective computational methods for generating MCMC chains in the Bayesian framework for the subsurface characterization. Our strategy consists of constructing a family of computationally inexpensive preconditioners based on simpler physics as well as on surrogate models such that the number of fine-grid simulations is drastically reduced in the generated MCMC chains. In particular, we introduce a huff-puff technique as screening step in a three-stage multi-physics MCMC algorithm to reduce the number of expensive final stage simulations. The huff-puff technique in the algorithm enables a better characterization of subsurface near wells. We assess the quality of the proposed multi-physics MCMC methods by considering Monte Carlo simulations for forecasting oil production in an oil reservoir.
Efficient variants of the minimal diffusion formulation of Markov chain ensembles
NASA Astrophysics Data System (ADS)
Güler, Marifi
2016-02-01
This study is concerned with ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. In this context, our prior work [Phys. Rev. E 91, 062116 (2015), 10.1103/PhysRevE.91.062116] has formulated an approximation scheme, called the minimal diffusion formulation, to deduce how the number of chains in a prescribed relevant state evolves in time. The formulation consists of two specifically coupled Ornstein-Uhlenbeck processes in a stochastic differential equation representation; it is minimal in the sense that its structure does not change with the state space size or the transition matrix density, and it requires no matrix square-root operations. In the present study, we first calculate the autocorrelation function of the relevant state density in the minimal diffusion formulation, which is fundamental to the identification of the ensemble dynamics. The obtained autocorrelation function is then employed to develop two diffusion formulations that reduce the structural complexity of the minimal diffusion formulation without significant loss of accuracy in the dynamics. One of these variant formulations includes one less noise term than the minimal diffusion formulation and still satisfies the above-mentioned autocorrelation function in its dynamics. The second variant is in the form of a one-dimensional Langevin equation, therefore it is the simplest possible diffusion formulation one can obtain for the problem, yet its autocorrelation function is first-order accurate in time gap. Numerical simulations supporting the theoretical analysis are delivered.
Efficient variants of the minimal diffusion formulation of Markov chain ensembles.
Güler, Marifi
2016-02-01
This study is concerned with ensembles of continuous-time Markov chains evolving independently under a common transition rate matrix in some finite state space. In this context, our prior work [Phys. Rev. E 91, 062116 (2015)] has formulated an approximation scheme, called the minimal diffusion formulation, to deduce how the number of chains in a prescribed relevant state evolves in time. The formulation consists of two specifically coupled Ornstein-Uhlenbeck processes in a stochastic differential equation representation; it is minimal in the sense that its structure does not change with the state space size or the transition matrix density, and it requires no matrix square-root operations. In the present study, we first calculate the autocorrelation function of the relevant state density in the minimal diffusion formulation, which is fundamental to the identification of the ensemble dynamics. The obtained autocorrelation function is then employed to develop two diffusion formulations that reduce the structural complexity of the minimal diffusion formulation without significant loss of accuracy in the dynamics. One of these variant formulations includes one less noise term than the minimal diffusion formulation and still satisfies the above-mentioned autocorrelation function in its dynamics. The second variant is in the form of a one-dimensional Langevin equation, therefore it is the simplest possible diffusion formulation one can obtain for the problem, yet its autocorrelation function is first-order accurate in time gap. Numerical simulations supporting the theoretical analysis are delivered. PMID:26986304
Statistical Inference in Hidden Markov Models Using k-Segment Constraints
Titsias, Michalis K.; Holmes, Christopher C.; Yau, Christopher
2016-01-01
Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online. PMID:27226674
NASA Astrophysics Data System (ADS)
Feroz, F.; Hobson, M. P.
2008-02-01
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation
Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET
Hatt, Mathieu; Lamare, Frédéric; Boussion, Nicolas; Roux, Christian; Turzo, Alexandre; Cheze-Lerest, Catherine; Jarritt, Peter; Carson, Kathryn; Salzenstein, Fabien; Collet, Christophe; Visvikis, Dimitris
2007-01-01
Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the Fuzzy Hidden Markov Chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical Hidden Markov Chain (HMC) algorithm, FHMC takes into account noise, voxel’s intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the “fuzzy” nature of the object on interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8mm3 and 64mm3). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The analysis of both
NASA Astrophysics Data System (ADS)
Zhang, Hua; Harter, Thomas; Sivakumar, Bellie
2006-06-01
Facies-based geostatistical models have become important tools for analyzing flow and mass transport processes in heterogeneous aquifers. Yet little is known about the relationship between these latter processes and the parameters of facies-based geostatistical models. In this study, we examine the transport of a nonpoint source solute normal (perpendicular) to the major bedding plane of an alluvial aquifer medium that contains multiple geologic facies, including interconnected, high-conductivity (coarse textured) facies. We also evaluate the dependence of the transport behavior on the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system's hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute traveltime probability density function (pdf) for solute flux from the water table to the bottom boundary (the production horizon) of the aquifer. The cases examined include two-, three-, and four-facies models, with mean length anisotropy ratios for horizontal to vertical facies, ek, from 25:1 to 300:1 and with a wide range of facies volume proportions (e.g., from 5 to 95% coarse-textured facies). Predictions of traveltime pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer. Those predictions of traveltime pdfs also are affected by the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and, to a lesser degree, the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, traveltime is not lognormally distributed as is often assumed. Also, macrodispersive behavior (variance of the traveltime) is found not to be a unique function of the conductivity variance. For the parameter range
Fitting complex population models by combining particle filters with Markov chain Monte Carlo.
Knape, Jonas; de Valpine, Perry
2012-02-01
We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.
Markov-chain approach to the distribution of ancestors in species of biparental reproduction.
Caruso, M; Jarne, C
2014-08-01
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This presents huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values with respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under a gauge (local) group of dilations. These ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provides some elements that can be used to improve models of animal reproduction.
CIGALEMC: GALAXY PARAMETER ESTIMATION USING A MARKOV CHAIN MONTE CARLO APPROACH WITH CIGALE
Serra, Paolo; Amblard, Alexandre; Temi, Pasquale; Im, Stephen; Noll, Stefan
2011-10-10
We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code Code Investigating GALaxy Emission (CIGALE). The original CIGALE builds a grid of theoretical spectral energy distribution (SED) models and fits to photometric fluxes from ultraviolet to infrared to put constraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. MCMC methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well-known and -studied Spitzer Infrared Nearby Galaxy Survey sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
Accelerating Markov chain Monte Carlo simulation through sequential updating and parallel computing
NASA Astrophysics Data System (ADS)
Ren, Ruichao
Monte Carlo simulation is a statistical sampling method used in studies of physical systems with properties that cannot be easily obtained analytically. The phase behavior of the Restricted Primitive Model of electrolyte solutions on the simple cubic lattice is studied using grand canonical Monte Carlo simulations and finite-size scaling techniques. The transition between disordered and ordered, NaCl-like structures is continuous, second-order at high temperatures and discrete, first-order at low temperatures. The line of continuous transitions meets the line of first-order transitions at a tricritical point. A new algorithm-Random Skipping Sequential (RSS) Monte Carl---is proposed, justified and shown analytically to have better mobility over the phase space than the conventional Metropolis algorithm satisfying strict detailed balance. The new algorithm employs sequential updating, and yields greatly enhanced sampling statistics than the Metropolis algorithm with random updating. A parallel version of Markov chain theory is introduced and applied in accelerating Monte Carlo simulation via cluster computing. It is shown that sequential updating is the key to reduce the inter-processor communication or synchronization which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time by the new method for systems of large and moderate sizes.
Markov-chain approach to the distribution of ancestors in species of biparental reproduction
NASA Astrophysics Data System (ADS)
Caruso, M.; Jarne, C.
2014-08-01
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This presents huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values with respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under a gauge (local) group of dilations. These ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provides some elements that can be used to improve models of animal reproduction.
Improving Markov Chain Monte Carlo algorithms in LISA Pathfinder Data Analysis
NASA Astrophysics Data System (ADS)
Karnesis, N.; Nofrarias, M.; Sopuerta, C. F.; Lobo, A.
2012-06-01
The LISA Pathfinder mission (LPF) aims to test key technologies for the future LISA mission. The LISA Technology Package (LTP) on-board LPF will consist of an exhaustive suite of experiments and its outcome will be crucial for the future detection of gravitational waves. In order to achieve maximum sensitivity, we need to have an understanding of every instrument on-board and parametrize the properties of the underlying noise models. The Data Analysis team has developed algorithms for parameter estimation of the system. A very promising one implemented for LISA Pathfinder data analysis is the Markov Chain Monte Carlo. A series of experiments are going to take place during flight operations and each experiment is going to provide us with essential information for the next in the sequence. Therefore, it is a priority to optimize and improve our tools available for data analysis during the mission. Using a Bayesian framework analysis allows us to apply prior knowledge for each experiment, which means that we can efficiently use our prior estimates for the parameters, making the method more accurate and significantly faster. This, together with other algorithm improvements, will lead us to our main goal, which is no other than creating a robust and reliable tool for parameter estimation during the LPF mission.
Yoo, Chulsang; Lee, Jinwook; Ro, Yonghun
2016-01-01
This paper evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO_{2}) and 2x CO_{2}conditions. As a result of this study, the increase or decrease in the mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.
Yoo, Chulsang; Lee, Jinwook; Ro, Yonghun
2016-01-01
This paper evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO2) and 2x CO2conditions. As a result of this study, the increase or decrease in themore » mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.« less
Two-state Markov-chain Poisson nature of individual cellphone call statistics
NASA Astrophysics Data System (ADS)
Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier
2016-07-01
Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.
Study on the calculation models of bus delay at bays using queueing theory and Markov chain.
Sun, Feng; Sun, Li; Sun, Shao-Wei; Wang, Dian-Hai
2015-01-01
Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays.
Fitting complex population models by combining particle filters with Markov chain Monte Carlo.
Knape, Jonas; de Valpine, Perry
2012-02-01
We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm. PMID:22624307
Evaluation of screening for nasopharyngeal carcinoma: trial design using Markov chain models.
Chen, H H; Prevost, T C; Duffy, S W
1999-04-01
In this paper, we develop a Markov chain model to estimate parameters pertaining to the natural history of nasopharyngeal carcinoma (NPC). The model is of progression from no disease to Epstein-Barr virus (EBV) infection, preclinical screen-detectable tumour and clinical tumour. We derive tentative estimates of the parameters of the model, based on limited published data, to assess the efficacy of serum screening in conjunction with clinical assessment (indirect mirror examination for NPC), for example the average duration of the preclinical screen-detectable phase is estimated as 3.1 years. We further apply these parameters to a hypothetical screening trial in the Hong Kong population to assess the efficacy of serum screening with clinical assessment by different combinations of screening regime. Results suggest: (1) there is no substantial difference between 3-yearly and 6-yearly serum screening; and (2) within the same serum screening regime annual and 3-yearly clinical assessment can prevent 33% and 28% of deaths from NPC respectively. Prediction of deaths and surrogate end points can be used to estimate the required sample size and duration for designing a randomized trial of screening for NPC. Based on these findings and power projections, we suggest a design for a randomized trial in a high incidence area such as Hong Kong. PMID:10206310
A Markov chain model for image ranking system in social networks
NASA Astrophysics Data System (ADS)
Zin, Thi Thi; Tin, Pyke; Toriu, Takashi; Hama, Hiromitsu
2014-03-01
In today world, different kinds of networks such as social, technological, business and etc. exist. All of the networks are similar in terms of distributions, continuously growing and expanding in large scale. Among them, many social networks such as Facebook, Twitter, Flickr and many others provides a powerful abstraction of the structure and dynamics of diverse kinds of inter personal connection and interaction. Generally, the social network contents are created and consumed by the influences of all different social navigation paths that lead to the contents. Therefore, identifying important and user relevant refined structures such as visual information or communities become major factors in modern decision making world. Moreover, the traditional method of information ranking systems cannot be successful due to their lack of taking into account the properties of navigation paths driven by social connections. In this paper, we propose a novel image ranking system in social networks by using the social data relational graphs from social media platform jointly with visual data to improve the relevance between returned images and user intentions (i.e., social relevance). Specifically, we propose a Markov chain based Social-Visual Ranking algorithm by taking social relevance into account. By using some extensive experiments, we demonstrated the significant and effectiveness of the proposed social-visual ranking method.
NASA Astrophysics Data System (ADS)
Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji
2015-12-01
Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.
Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-05-01
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.
Improving Hydrologic Data Assimilation by a Multivariate Particle Filter-Markov Chain Monte Carlo
NASA Astrophysics Data System (ADS)
Yan, H.; DeChant, C. M.; Moradkhani, H.
2014-12-01
Data assimilation (DA) is a popular method for merging information from multiple sources (i.e. models and remotely sensing), leading to improved hydrologic prediction. With the increasing availability of satellite observations (such as soil moisture) in recent years, DA is emerging in operational forecast systems. Although these techniques have seen widespread application, developmental research has continued to further refine their effectiveness. This presentation will examine potential improvements to the Particle Filter (PF) through the inclusion of multivariate correlation structures. Applications of the PF typically rely on univariate DA schemes (such as assimilating the outlet observed discharge), and multivariate schemes generally ignore the spatial correlation of the observations. In this study, a multivariate DA scheme is proposed by introducing geostatistics into the newly developed particle filter with Markov chain Monte Carlo (PF-MCMC) method. This new method is assessed by a case study over one of the basin with natural hydrologic process in Model Parameter Estimation Experiment (MOPEX), located in Arizona. The multivariate PF-MCMC method is used to assimilate the Advanced Scatterometer (ASCAT) grid (12.5 km) soil moisture retrievals and the observed streamflow in five gages (four inlet and one outlet gages) into the Sacramento Soil Moisture Accounting (SAC-SMA) model for the same scale (12.5 km), leading to greater skill in hydrologic predictions.
Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems
NASA Astrophysics Data System (ADS)
Suwa, Hidemaro
2013-03-01
We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad
Smart pilot points using reversible-jump Markov-chain Monte Carlo
NASA Astrophysics Data System (ADS)
Jiménez, S.; Mariethoz, G.; Brauchler, R.; Bayer, P.
2016-05-01
Pilot points are typical means for calibration of highly parameterized numerical models. We propose a novel procedure based on estimating not only the pilot point values, but also their number and suitable locations. This is accomplished by a trans-dimensional Bayesian inversion procedure that also allows for uncertainty quantification. The utilized algorithm, reversible-jump Markov-Chain Monte Carlo (RJ-MCMC), is computationally demanding and this challenges the application for model calibration. We present a solution for fast, approximate simulation through the application of a Bayesian inversion. A fast pathfinding algorithm is used to estimate tracer travel times instead of doing a full transport simulation. This approach extracts the information from measured breakthrough curves, which is crucial for the reconstruction of aquifer heterogeneity. As a result, the "smart pilot points" can be tuned during thousands of rapid model evaluations. This is demonstrated for both a synthetic and a field application. For the selected synthetic layered aquifer, two different hydrofacies are reconstructed. For the field investigation, multiple fluorescent tracers were injected in different well screens in a shallow alluvial aquifer and monitored in a tomographic source-receiver configuration. With the new inversion procedure, a sand layer was identified and reconstructed with a high spatial resolution in 3-D. The sand layer was successfully validated through additional slug tests at the site. The promising results encourage further applications in hydrogeological model calibration, especially for cases with simulation of transport.
Search process evaluation for a hierarchical menu system by Markov chains
NASA Astrophysics Data System (ADS)
Takagi, Hideaki; Kitajima, Muneo; Yamamoto, Tetsuo; Zhang, Yongbing
2001-07-01
When computers are used to execute tasks, it is often necessary for the user to locate a target item in a menu or a list. For example, users of word processors and spreadsheet applications select appropriate commands in a hierarchical menu to display dialog boxes and edit file or table attributes. To locate the desired information on the World Wide Web, users select the most appropriate candidate out of those presented by a search engine, and proceed through a series of hyperlinks that appear to be related to the task. This paper applies a cognitive model of the user's item selection process to the task of target search in a hierarchical menu system that contains one or more of the following four operations: (1) item selection on the basis of similarity to the task, (2) consideration in various ways of the selection history when making the next selection, (3) backtracking when an appropriate item is not present among those selectable at a given point in time, and (4) abandoning the task unachieved. We model this selection process with Markov chains. We calculate the probability that task goals are achieved and the average number of selections to make until the task goals are achieved. Finally we use these results to propose a method of evaluating the structures of hierarchical menus and links on a website.
Sanov and central limit theorems for output statistics of quantum Markov chains
Horssen, Merlijn van; Guţă, Mădălin
2015-02-15
In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.
NASA Astrophysics Data System (ADS)
Jokar Arsanjani, Jamal; Helbich, Marco; Kainz, Wolfgang; Darvishi Boloorani, Ali
2013-04-01
This research analyses the suburban expansion in the metropolitan area of Tehran, Iran. A hybrid model consisting of logistic regression model, Markov chain (MC), and cellular automata (CA) was designed to improve the performance of the standard logistic regression model. Environmental and socio-economic variables dealing with urban sprawl were operationalised to create a probability surface of spatiotemporal states of built-up land use for the years 2006, 2016, and 2026. For validation, the model was evaluated by means of relative operating characteristic values for different sets of variables. The approach was calibrated for 2006 by cross comparing of actual and simulated land use maps. The achieved outcomes represent a match of 89% between simulated and actual maps of 2006, which was satisfactory to approve the calibration process. Thereafter, the calibrated hybrid approach was implemented for forthcoming years. Finally, future land use maps for 2016 and 2026 were predicted by means of this hybrid approach. The simulated maps illustrate a new wave of suburban development in the vicinity of Tehran at the western border of the metropolis during the next decades.
Study on the calculation models of bus delay at bays using queueing theory and Markov chain.
Sun, Feng; Sun, Li; Sun, Shao-Wei; Wang, Dian-Hai
2015-01-01
Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays. PMID:25759720
Markov chain Monte Carlo analysis to constrain dark matter properties with directional detection
Billard, J.; Mayet, F.; Santos, D.
2011-04-01
Directional detection is a promising dark matter search strategy. Indeed, weakly interacting massive particle (WIMP)-induced recoils would present a direction dependence toward the Cygnus constellation, while background-induced recoils exhibit an isotropic distribution in the Galactic rest frame. Taking advantage of these characteristic features, and even in the presence of a sizeable background, it has recently been shown that data from forthcoming directional detectors could lead either to a competitive exclusion or to a conclusive discovery, depending on the value of the WIMP-nucleon cross section. However, it is possible to further exploit these upcoming data by using the strong dependence of the WIMP signal with: the WIMP mass and the local WIMP velocity distribution. Using a Markov chain Monte Carlo analysis of recoil events, we show for the first time the possibility to constrain the unknown WIMP parameters, both from particle physics (mass and cross section) and Galactic halo (velocity dispersion along the three axis), leading to an identification of non-baryonic dark matter.
Mapping systematic errors in helium abundance determinations using Markov Chain Monte Carlo
Aver, Erik; Olive, Keith A.; Skillman, Evan D. E-mail: olive@umn.edu
2011-03-01
Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H II regions. The helium abundance is sensitive to several physical parameters associated with the H II region. In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He I emission lines. We demonstrate that introducing the electron temperature derived from the [O III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. We perform a frequentist analysis on data from several ''high quality'' systems. Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.
NASA Astrophysics Data System (ADS)
Xu, Feng; Davis, Anthony B.; Diner, David J.
2016-11-01
A Markov chain formalism is developed for computing the transport of polarized radiation according to Generalized Radiative Transfer (GRT) theory, which was developed recently to account for unresolved random fluctuations of scattering particle density and can also be applied to unresolved spectral variability of gaseous absorption as an improvement over the standard correlated-k method. Using Gamma distribution to describe the probability density function of the extinction or absorption coefficient, a shape parameter a that quantifies the variability is introduced, defined as the mean extinction or absorption coefficient squared divided by its variance. It controls the decay rate of a power-law transmission that replaces the usual exponential Beer-Lambert-Bouguer law. Exponential transmission, hence classic RT, is recovered when a→∞. The new approach is verified to high accuracy against numerical benchmark results obtained with a custom Monte Carlo method. For a<∞, angular reciprocity is violated to a degree that increases with the spatial variability, as observed for finite portions of real-world cloudy scenes. While the degree of linear polarization in liquid water cloudbows, supernumerary bows, and glories is affected by spatial heterogeneity, the positions in scattering angle of these features are relatively unchanged. As a result, a single-scattering model based on the assumption of subpixel homogeneity can still be used to derive droplet size distributions from polarimetric measurements of extended stratocumulus clouds.
Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences.
Schbath, S; Prum, B; de Turckheim, E
1995-01-01
Identifying exceptional motifs is often used for extracting information from long DNA sequences. The two difficulties of the method are the choice of the model that defines the expected frequencies of words and the approximation of the variance of the difference T(W) between the number of occurrences of a word W and its estimation. We consider here different Markov chain models, either with stationary or periodic transition probabilities. We estimate the variance of the difference T(W) by the conditional variance of the number of occurrences of W given the oligonucleotides counts that define the model. Two applications show how to use asymptotically standard normal statistics associated with the counts to describe a given sequence in terms of its outlying words. Sequences of Escherichia coli and of Bacillus subtilis are compared with respect to their exceptional tri- and tetranucleotides. For both bacteria, exceptional 3-words are mainly found in the coding frame. E. coli palindrome counts are analyzed in different models, showing that many overabundant words are one-letter mutations of avoided palindromes. PMID:8521272
NASA Astrophysics Data System (ADS)
Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.
2016-06-01
We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.
NASA Astrophysics Data System (ADS)
Yoo, Jiyoung; Kwon, Hyun-Han; So, Byung-Jin; Rajagopalan, Balaji; Kim, Tae-Woong
2015-04-01
This study proposed a hidden Markov chain model-based drought analysis (HMM-DA) tool to understand the beginning and ending of meteorological drought and to further characterize typhoon-induced drought busters (TDB) by exploring spatiotemporal drought patterns in South Korea. It was found that typhoons have played a dominant role in ending drought events (EDE) during the typhoon season (July-September) over the last four decades (1974-2013). The percentage of EDEs terminated by TDBs was about 43-90% mainly along coastal regions in South Korea. Furthermore, the TDBs, mainly during summer, have a positive role in managing extreme droughts during the subsequent autumn and spring seasons. The HMM-DA models the temporal dependencies between drought states using Markov chain, consequently capturing the dependencies between droughts and typhoons well, thus, enabling a better performance in modeling spatiotemporal drought attributes compared to traditional methods.
Xu, Feng; Davis, Anthony B; West, Robert A; Esposito, Larry W
2011-01-17
Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.
NASA Astrophysics Data System (ADS)
Kamal Chowdhury, AFM; Lockart, Natalie; Willgoose, Garry; Kuczera, George
2015-04-01
One of the overriding issues in the rainfall simulation is the underestimation of observed rainfall variability in longer timescales (e.g. monthly, annual and multi-year), which usually results into under-estimation of reservoir reliability in urban water planning. This study has developed a Compound Distribution Markov Chain (CDMC) model for stochastic generation of daily rainfall. We used two parameters of Markov Chain process (transition probabilities of wet-to-wet and dry-to-dry days) for simulating rainfall occurrence and two parameters of gamma distribution (calculated from mean and standard deviation of wet-day rainfall) for simulating wet-day rainfall amounts. While two models with deterministic parameters underestimated long term variability, our investigation found that the long term variability of rainfall in the model is predominantly governed by the long term variability of gamma parameters, rather than the variability of Markov Chain parameters. Therefore, in the third approach, we developed the CDMC model with deterministic parameters of Markov Chain process, but stochastic parameters of gamma distribution by sampling the mean and standard deviation of wet-day rainfall from their log-normal and bivariate-normal distribution. We have found that the CDMC is able to replicate both short term and long term rainfall variability, when we calibrated the model at two sites in east coast of Australia using three types of daily rainfall data - (1) dynamically downscaled, 10 km resolution gridded data produced by NSW/ACT Regional Climate Modelling project, (2) 5 km resolution gridded data by Australian Water Availability Project and (3) point scale raingauge stations data by Bureau of Meteorology, Australia. We also examined the spatial variability of parameters and their link with local orography at our field site. The suitability of the model in runoff generation and urban reservoir-water simulation will be discussed.
Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.
Trägårdh, Magnus; Chappell, Michael J; Ahnmark, Andrea; Lindén, Daniel; Evans, Neil D; Gennemark, Peter
2016-04-01
Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery. PMID:26932466
Discovering beaten paths in collaborative ontology-engineering projects using Markov chains.
Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A; Noy, Natalya F
2014-10-01
Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50,000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology
Discovering Beaten Paths in Collaborative Ontology-Engineering Projects using Markov Chains
Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A.; Noy, Natalya F.
2014-01-01
Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50, 000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology
NASA Astrophysics Data System (ADS)
Wirth, Erin A.; Long, Maureen D.; Moriarty, John C.
2016-10-01
Teleseismic receiver functions contain information regarding Earth structure beneath a seismic station. P-to-SV converted phases are often used to characterize crustal and upper mantle discontinuities and isotropic velocity structures. More recently, P-to-SH converted energy has been used to interrogate the orientation of anisotropy at depth, as well as the geometry of dipping interfaces. Many studies use a trial-and-error forward modeling approach to the interpretation of receiver functions, generating synthetic receiver functions from a user-defined input model of Earth structure and amending this model until it matches major features in the actual data. While often successful, such an approach makes it impossible to explore model space in a systematic and robust manner, which is especially important given that solutions are likely non-unique. Here, we present a Markov chain Monte Carlo algorithm with Gibbs sampling for the interpretation of anisotropic receiver functions. Synthetic examples are used to test the viability of the algorithm, suggesting that it works well for models with a reasonable number of free parameters (< ˜20). Additionally, the synthetic tests illustrate that certain parameters are well constrained by receiver function data, while others are subject to severe tradeoffs - an important implication for studies that attempt to interpret Earth structure based on receiver function data. Finally, we apply our algorithm to receiver function data from station WCI in the central United States. We find evidence for a change in anisotropic structure at mid-lithospheric depths, consistent with previous work that used a grid search approach to model receiver function data at this station. Forward modeling of receiver functions using model space search algorithms, such as the one presented here, provide a meaningful framework for interrogating Earth structure from receiver function data.
A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection
Apenteng, Ofosuhene O.; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
BENCHMARK TESTS FOR MARKOV CHAIN MONTE CARLO FITTING OF EXOPLANET ECLIPSE OBSERVATIONS
Rogers, Justin; Lopez-Morales, Mercedes; Apai, Daniel; Adams, Elisabeth
2013-04-10
Ground-based observations of exoplanet eclipses provide important clues to the planets' atmospheric physics, yet systematics in light curve analyses are not fully understood. It is unknown if measurements suggesting near-infrared flux densities brighter than models predict are real, or artifacts of the analysis processes. We created a large suite of model light curves, using both synthetic and real noise, and tested the common process of light curve modeling and parameter optimization with a Markov Chain Monte Carlo algorithm. With synthetic white noise models, we find that input eclipse signals are generally recovered within 10% accuracy for eclipse depths greater than the noise amplitude, and to smaller depths for higher sampling rates and longer baselines. Red noise models see greater discrepancies between input and measured eclipse signals, often biased in one direction. Finally, we find that in real data, systematic biases result even with a complex model to account for trends, and significant false eclipse signals may appear in a non-Gaussian distribution. To quantify the bias and validate an eclipse measurement, we compare both the planet-hosting star and several of its neighbors to a separately chosen control sample of field stars. Re-examining the Rogers et al. Ks-band measurement of CoRoT-1b finds an eclipse 3190{sup +370}{sub -440} ppm deep centered at {phi}{sub me} = 0.50418{sup +0.00197}{sub -0.00203}. Finally, we provide and recommend the use of selected data sets we generated as a benchmark test for eclipse modeling and analysis routines, and propose criteria to verify eclipse detections.
A Markov Chain Monte Carlo Approach to Estimate AIDS after HIV Infection.
Apenteng, Ofosuhene O; Ismail, Noor Azina
2015-01-01
The spread of human immunodeficiency virus (HIV) infection and the resulting acquired immune deficiency syndrome (AIDS) is a major health concern in many parts of the world, and mathematical models are commonly applied to understand the spread of the HIV epidemic. To understand the spread of HIV and AIDS cases and their parameters in a given population, it is necessary to develop a theoretical framework that takes into account realistic factors. The current study used this framework to assess the interaction between individuals who developed AIDS after HIV infection and individuals who did not develop AIDS after HIV infection (pre-AIDS). We first investigated how probabilistic parameters affect the model in terms of the HIV and AIDS population over a period of time. We observed that there is a critical threshold parameter, R0, which determines the behavior of the model. If R0 ≤ 1, there is a unique disease-free equilibrium; if R0 < 1, the disease dies out; and if R0 > 1, the disease-free equilibrium is unstable. We also show how a Markov chain Monte Carlo (MCMC) approach could be used as a supplement to forecast the numbers of reported HIV and AIDS cases. An approach using a Monte Carlo analysis is illustrated to understand the impact of model-based predictions in light of uncertain parameters on the spread of HIV. Finally, to examine this framework and demonstrate how it works, a case study was performed of reported HIV and AIDS cases from an annual data set in Malaysia, and then we compared how these approaches complement each other. We conclude that HIV disease in Malaysia shows epidemic behavior, especially in the context of understanding and predicting emerging cases of HIV and AIDS. PMID:26147199
Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach
Xu, Lixin; Lu, Jianbo E-mail: lvjianbo819@163.com
2010-03-01
We use the Markov Chain Monte Carlo method to investigate a global constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Constitution dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a non-flat universe, the constraint results for GCG model are, Ω{sub b}h{sup 2} = 0.0235{sup +0.0021}{sub −0.0018} (1σ) {sup +0.0028}{sub −0.0022} (2σ), Ω{sub k} = 0.0035{sup +0.0172}{sub −0.0182} (1σ) {sup +0.0226}{sub −0.0204} (2σ), A{sub s} = 0.753{sup +0.037}{sub −0.035} (1σ) {sup +0.045}{sub −0.044} (2σ), α = 0.043{sup +0.102}{sub −0.106} (1σ) {sup +0.134}{sub −0.117} (2σ), and H{sub 0} = 70.00{sup +3.25}{sub −2.92} (1σ) {sup +3.77}{sub −3.67} (2σ), which is more stringent than the previous results for constraint on GCG model parameters. Furthermore, according to the information criterion, it seems that the current observations much support ΛCDM model relative to the GCG model.
NASA Astrophysics Data System (ADS)
Freiberger, Manuel; Laurain, Antoine; Hintermüller, Michael; Köstinger, Alice; Scharfetter, Hermann
2011-07-01
Fluorescence tomography aims at the reconstruction of the concentration and life-time of fluorescent inclusions from boundary measurements of light emitted. The underlying ill-posed problem is often solved with gradient descent of Gauss-Newton methods, for example. Unfortunately, these approaches don't allow to assess the quality of the reconstruction (e.g. the variance and covariance of the parameters) and also require the tuning of regularization parameters. We intend to mitigate this drawback by the application of topological derivatives and Markov-chain Monte-Carlo (MCMC) methods for solving the inverse problem. This submission focuses on the topological derivative, which is used for the initialization of the MCMC code. The basic idea is to probe every location inside the domain with an infinitely small fluorescent ball and to estimate the effect of such a perturbation on the residual, which is the difference of the theoretically predicted data to the true measurement. Obviously, the reconstructed inclusions should be placed at locations for which the topological derivative is significantly negative, i.e. where the residual decreases. Previous results show that usual first-order approximations deteriorates for probe inclusions close to the boundary. This seems to be a particular feature of certain inverse problems such as fluorescence tomography or electrical impedance tomography. Fortunately this flaw may be corrected using a few higher-order terms which may be explicitly determined With this extension the topological derivative can be utilized as a one-step method for the determination of the number of inclusions and their approximate locations. This outcome is used as initialization for the MCMC algorithm.
Transition probability/Markov chain analyses of DNAPL source zones and plumes.
Maji, R; Sudicky, E A; Panday, S; Teutsch, G
2006-01-01
At sites where a dense nonaqueous phase liquid (DNAPL) was spilled or released into the subsurface, estimates of the mass of DNAPL contained in the subsurface from core or monitoring well data, either in the nonaqueous or aqueous phase, can be highly uncertain because of the erratic distribution of the DNAPL due to geologic heterogeneity. In this paper, a multiphase compositional model is applied to simulate, in detail, the DNAPL saturations and aqueous-phase plume migration in a highly characterized, heterogeneous glaciofluvial aquifer, the permeability and porosity data of which were collected by researchers at the University of Tübingen, Germany. The DNAPL saturation distribution and the aqueous-phase contaminant mole fractions are then reconstructed by sampling the data from the forward simulation results using two alternate approaches, each with different degrees of sampling conditioning. To reconstruct the DNAPL source zone architecture, the aqueous-phase plume configuration, and the contaminant mass in each phase, one method employs the novel transition probability/Markov chain approach (TP/MC), while the other involves a traditional variogram analysis of the sampled data followed by ordinary kriging. The TP/MC method is typically used for facies and/or hydraulic conductivity reconstruction, but here we explore the applicability of the TP/MC method for the reconstruction of DNAPL source zones and aqueous-phase plumes. The reconstructed geometry of the DNAPL source zone, the dissolved contaminant plume, and the estimated mass in each phase are compared using the two different geostatistical modeling approaches and for various degrees of data sampling from the results of the forward simulation. It is demonstrated that the TP/MC modeling technique is robust and accurate and is a preferable alternative compared to ordinary kriging for the reconstruction of DNAPL saturation patterns and dissolved-phase contaminant plumes.
Discovering beaten paths in collaborative ontology-engineering projects using Markov chains.
Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A; Noy, Natalya F
2014-10-01
Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50,000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology
Han, Chao; Chen, Jian; Wu, Qingyao; Mu, Shuai; Min, Huaqing
2015-10-01
Automated assignment of protein function has received considerable attention in recent years for genome-wide study. With the rapid accumulation of genome sequencing data produced by high-throughput experimental techniques, the process of manually predicting functional properties of proteins has become increasingly cumbersome. Such large genomics data sets can only be annotated computationally. However, automated assignment of functions to unknown protein is challenging due to its inherent difficulty and complexity. Previous studies have revealed that solving problems involving complicated objects with multiple semantic meanings using the multi-instance multi-label (MIML) framework is effective. For the protein function prediction problems, each protein object in nature may associate with distinct structural units (instances) and multiple functional properties (class labels) where each unit is described by an instance and each functional property is considered as a class label. Thus, it is convenient and natural to tackle the protein function prediction problem by using the MIML framework. In this paper, we propose a sparse Markov chain-based semi-supervised MIML method, called Sparse-Markov. A sparse transductive probability graph is constructed to encode the affinity information of the data based on ensemble of Hausdorff distance metrics. Our goal is to exploit the affinity between protein objects in the sparse transductive probability graph to seek a sparse steady state probability of the Markov chain model to do protein function prediction, such that two proteins are given similar functional labels if they are close to each other in terms of an ensemble Hausdorff distance in the graph. Experimental results on seven real-world organism data sets covering three biological domains show that our proposed Sparse-Markov method is able to achieve better performance than four state-of-the-art MIML learning algorithms.
Luo, Yuqun; Lin, Shili
2003-07-01
Genetic data from founder populations are advantageous for studies of complex traits that are often plagued by the problem of genetic heterogeneity. However, the desire to analyze large and complex pedigrees that often arise from such populations, coupled with the need to handle many linked and highly polymorphic loci simultaneously, poses challenges to current standard approaches. A viable alternative to solving such problems is via Markov chain Monte Carlo (MCMC) procedures, where a Markov chain, defined on the state space of a latent variable (e.g., genotypic configuration or inheritance vector), is constructed. However, finding starting points for the Markov chains is a difficult problem when the pedigree is not single-locus peelable; methods proposed in the literature have not yielded completely satisfactory solutions. We propose a generalization of the heated Gibbs sampler with relaxed penetrances (HGRP) of Lin et al., ([1993] IMA J. Math. Appl. Med. Biol. 10:1-17) to search for starting points. HGRP guarantees that a starting point will be found if there is no error in the data, but the chain usually needs to be run for a long time if the pedigree is extremely large and complex. By introducing a forcing step, the current algorithm substantially reduces the state space, and hence effectively speeds up the process of finding a starting point. Our algorithm also has a built-in preprocessing procedure for Mendelian error detection. The algorithm has been applied to both simulated and real data on two large and complex Hutterite pedigrees under many settings, and good results are obtained. The algorithm has been implemented in a user-friendly package called START. PMID:12813723
Sargeant, G.A.; Sovada, M.A.; Slivinski, C.C.; Johnson, D.H.
2005-01-01
Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997-1999, we searched 355 townships (ca. 93 km2) 1-3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of ?? = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ???1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between
Sargeant, Glen A.; Sovada, Marsha A.; Slivinski, Christiane C.; Johnson, Douglas H.
2005-01-01
Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997–1999, we searched 355 townships (ca. 93 km) 1–3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ≥1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between
Naruse, Yasushi; Takiyama, Ken; Okada, Masato; Murata, Tsutomu
2010-07-01
Alpha rhythm is a major component of spontaneous electroencephalographic (EEG) data. We develop a novel method that can be used to estimate the instantaneous phases and amplitudes of the alpha rhythm with high accuracy by modeling the alpha rhythm phase and amplitude as Markov random field (MRF) models. By using a belief propagation technique, we construct an exact-inference algorithm that can be used to estimate instantaneous phases and amplitudes and calculate the marginal likelihood. Maximizing the marginal likelihood enables us to estimate the hyperparameters on the basis of type-II maximum likelihood estimation. We prove that the instantaneous phase and amplitude estimation by our method is consistent with that by the Hilbert transform, which has been commonly used to estimate instantaneous phases and amplitudes, of a signal filtered from observed data in the limited case that the observed data consist of only one frequency signal whose amplitude is constant and a Gaussian noise. Comparison of the performances of observation noise reduction by our method and by a Gaussian MRF model of alpha rhythm signal indicates that our method reduces observation noise more efficiently. Moreover, the instantaneous phase and amplitude estimates obtained using our method are more accurate than those obtained by the Hilbert transform. Application of our method to experimental EEG data also demonstrates that the relationship between the alpha rhythm phase and the reaction time emerges more clearly by using our method than the Hilbert transform. This indicates our method's practical usefulness. Therefore, applying our method to experimental EEG data will enable us to estimate the instantaneous phases and amplitudes of the alpha rhythm more precisely.
NASA Astrophysics Data System (ADS)
Naruse, Yasushi; Takiyama, Ken; Okada, Masato; Murata, Tsutomu
2010-07-01
Alpha rhythm is a major component of spontaneous electroencephalographic (EEG) data. We develop a novel method that can be used to estimate the instantaneous phases and amplitudes of the alpha rhythm with high accuracy by modeling the alpha rhythm phase and amplitude as Markov random field (MRF) models. By using a belief propagation technique, we construct an exact-inference algorithm that can be used to estimate instantaneous phases and amplitudes and calculate the marginal likelihood. Maximizing the marginal likelihood enables us to estimate the hyperparameters on the basis of type-II maximum likelihood estimation. We prove that the instantaneous phase and amplitude estimation by our method is consistent with that by the Hilbert transform, which has been commonly used to estimate instantaneous phases and amplitudes, of a signal filtered from observed data in the limited case that the observed data consist of only one frequency signal whose amplitude is constant and a Gaussian noise. Comparison of the performances of observation noise reduction by our method and by a Gaussian MRF model of alpha rhythm signal indicates that our method reduces observation noise more efficiently. Moreover, the instantaneous phase and amplitude estimates obtained using our method are more accurate than those obtained by the Hilbert transform. Application of our method to experimental EEG data also demonstrates that the relationship between the alpha rhythm phase and the reaction time emerges more clearly by using our method than the Hilbert transform. This indicates our method’s practical usefulness. Therefore, applying our method to experimental EEG data will enable us to estimate the instantaneous phases and amplitudes of the alpha rhythm more precisely.
NASA Astrophysics Data System (ADS)
Yang, P.; Ng, T. L.; Yang, W.
2015-12-01
Effective water resources management depends on the reliable estimation of the uncertainty of drought events. Confidence intervals (CIs) are commonly applied to quantify this uncertainty. A CI seeks to be at the minimal length necessary to cover the true value of the estimated variable with the desired probability. In drought analysis where two or more variables (e.g., duration and severity) are often used to describe a drought, copulas have been found suitable for representing the joint probability behavior of these variables. However, the comprehensive assessment of the parameter uncertainties of copulas of droughts has been largely ignored, and the few studies that have recognized this issue have not explicitly compared the various methods to produce the best CIs. Thus, the objective of this study to compare the CIs generated using two widely applied uncertainty estimation methods, bootstrapping and Markov Chain Monte Carlo (MCMC). To achieve this objective, (1) the marginal distributions lognormal, Gamma, and Generalized Extreme Value, and the copula functions Clayton, Frank, and Plackett are selected to construct joint probability functions of two drought related variables. (2) The resulting joint functions are then fitted to 200 sets of simulated realizations of drought events with known distribution and extreme parameters and (3) from there, using bootstrapping and MCMC, CIs of the parameters are generated and compared. The effect of an informative prior on the CIs generated by MCMC is also evaluated. CIs are produced for different sample sizes (50, 100, and 200) of the simulated drought events for fitting the joint probability functions. Preliminary results assuming lognormal marginal distributions and the Clayton copula function suggest that for cases with small or medium sample sizes (~50-100), MCMC to be superior method if an informative prior exists. Where an informative prior is unavailable, for small sample sizes (~50), both bootstrapping and MCMC
Multiple-Event Location Using the Markov-Chain Monte Carlo Technique
Myers, S C; Johannesson, G; Hanley, W
2005-07-13
The goal of next-generation seismic location is to ascertain a consistent set of event locations and travel-time corrections through simultaneous analysis of all relevant data. Towards that end, we are developing a new multiple-event location algorithm that utilizes the Markov-Chain Monte Carlo (MCMC) method for solving large, non-linear event inverse problems. Unlike most inverse methods, the MCMC approach produces a suite of solutions, each of which is consistent with seismic and other observations, as well as prior estimates of data and model uncertainties. In the MCMC multiple-event locator (MCMCloc), the model uncertainties consist of prior estimates on the accuracy of each input event location, travel-time prediction uncertainties, phase measurement uncertainties, and assessments of phase identification. The prior uncertainty estimates include correlations between travel-time predictions, correlations between measurement errors, and the probability of misidentifying one phase for another (or bogus picks). The implementation of prior constraints on location accuracy allows the direct utilization of ground-truth events in the location algorithm. This is a significant improvement over most other multiple-event locators (GMEL is an exception), for which location accuracy is achieved through post-processing comparisons with ground-truth information. Like the double-difference algorithm, the implementation of a correlation structure for travel-time predictions allows MCMCloc to operate over arbitrarily large geographic areas. MCMCloc can accommodate non-Gaussian and multi-modal pick distributions, which can enhance application to poorly recorded events. Further, MCMCloc allows for ambiguous determination of phase assignments, and the solution includes the probability that phases are properly assigned. The probabilities that phase assignments are correct are propagated to the estimates of all other model parameters. Posteriori estimates of event locations, path
NASA Astrophysics Data System (ADS)
Farr, Benjamin; Kalogera, Vicky; Luijten, Erik
2014-07-01
We introduce a new Markov-chain Monte Carlo (MCMC) approach designed for the efficient sampling of highly correlated and multimodal posteriors. Parallel tempering, though effective, is a costly technique for sampling such posteriors. Our approach minimizes the use of parallel tempering, only applying it for a short time to build a proposal distribution that is based upon estimation of the kernel density and tuned to the target posterior. This proposal makes subsequent use of parallel tempering unnecessary, allowing all chains to be cooled to sample the target distribution. Gains in efficiency are found to increase with increasing posterior complexity, ranging from tens of percent in the simplest cases to over a factor of 10 for the more complex cases. Our approach is particularly useful in the context of parameter estimation of gravitational-wave signals measured by ground-based detectors, which is currently done through Bayesian inference with MCMC, one of the leading sampling methods. Posteriors for these signals are typically multimodal with strong nonlinear correlations, making sampling difficult. As we enter the advanced-detector era, improved sensitivities and wider bandwidths will drastically increase the computational cost of analyses, demanding more efficient search algorithms to meet these challenges.
NASA Astrophysics Data System (ADS)
Borka, Szabolcs
2016-01-01
The aim of this study was to examine the relationship between structural elements and the so-called genetic lithofacies in a clastic deep-water depositional system. Process-sedimentology has recently been gaining importance in the characterization of these systems. This way the recognized facies attributes can be associated with the depositional processes establishing the genetic lithofacies. In this paper this approach was presented through a case study of a Tertiary deep-water sequence of the Pannonian-basin. Of course it was necessary to interpret the stratigraphy of the sequences in terms of "general" sedimentology, focusing on the structural elements. For this purpose, well-logs and standard deep-water models were applied. The cyclicity of sedimentary sequences can be easily revealed by using Markov chains. Though Markov chain analysis has broad application in mainly fluvial depositional environments, its utilization is uncommon in deep-water systems. In this context genetic lithofacies was determined and analysed by embedded Markov chains. The randomness in the presence of a lithofacies within a cycle was estimated by entropy tests (entropy after depositional, before depositional, for the whole system). Subsequently the relationships between lithofacies were revealed and a depositional model (i.e. modal cycle) was produced with 90% confidence level of stationarity. The non-randomness of the latter was tested by chi-square test. The consequences coming from the comparison of "general" sequences (composed of architectural elements), the genetic-based sequences (showing the distributions of the genetic lithofacies) and the lithofacies relationships were discussed in details. This way main depositional channel has the best, channelized lobes have good potential hydrocarbon reservoir attributes, with symmetric alternation of persistent fine-grained sandstone (Facies D) and muddy fine-grained sandstone with traction structures (Facies F)
NASA Astrophysics Data System (ADS)
Lalande, Jean-Marie; Waxler, Roger; Velea, Doru
2016-04-01
As infrasonic waves propagate at long ranges through atmospheric ducts it has been suggested that observations of such waves can be used as a remote sensing techniques in order to update properties such as temperature and wind speed. In this study we investigate a new inverse approach based on Markov Chain Monte Carlo methods. This approach as the advantage of searching for the full Probability Density Function in the parameter space at a lower computational cost than extensive parameters search performed by the standard Monte Carlo approach. We apply this inverse methods to observations from the Humming Roadrunner experiment (New Mexico) and discuss implications for atmospheric updates, explosion characterization, localization and yield estimation.
Sieh, Weiva; Basu, Saonli; Fu, Audrey Q; Rothstein, Joseph H; Scheet, Paul A; Stewart, William CL; Sung, Yun J; Thompson, Elizabeth A; Wijsman, Ellen M
2005-01-01
We performed multipoint linkage analysis of the electrophysiological trait ECB21 on chromosome 4 in the full pedigrees provided by the Collaborative Study on the Genetics of Alcoholism (COGA). Three Markov chain Monte Carlo (MCMC)-based approaches were applied to the provided and re-estimated genetic maps and to five different marker panels consisting of microsatellite (STRP) and/or SNP markers at various densities. We found evidence of linkage near the GABRB1 STRP using all methods, maps, and marker panels. Difficulties encountered with SNP panels included convergence problems and demanding computations. PMID:16451566
Obesity status transitions across the elementary years: Use of Markov chain modeling
Technology Transfer Automated Retrieval System (TEKTRAN)
Overweight and obesity status transition probabilities using first-order Markov transition models applied to elementary school children were assessed. Complete longitudinal data across eleven assessments were available from 1,494 elementary school children (from 7,599 students in 41 out of 45 school...
Schofield, Jeremy Bayat, Hanif
2014-09-07
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains
NASA Astrophysics Data System (ADS)
Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo
2016-09-01
The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.
Nortey, Ezekiel N N; Ansah-Narh, Theophilus; Asah-Asante, Richard; Minkah, Richard
2015-01-01
Although, there exists numerous literature on the procedure for forecasting or predicting election results, in Ghana only opinion poll strategies have been used. To fill this gap, the paper develops Markov chain models for forecasting the 2016 presidential election results at the Regional, Zonal (i.e. Savannah, Coastal and Forest) and the National levels using past presidential election results of Ghana. The methodology develops a model for prediction of the 2016 presidential election results in Ghana using the Markov chains Monte Carlo (MCMC) methodology with bootstrap estimates. The results were that the ruling NDC may marginally win the 2016 Presidential Elections but would not obtain the more than 50 % votes to be declared an outright winner. This means that there is going to be a run-off election between the two giant political parties: the ruling NDC and the major opposition party, NPP. The prediction for the 2016 Presidential run-off election between the NDC and the NPP was rather in favour of the major opposition party, the NPP with a little over the 50 % votes obtained. PMID:26435890
Nortey, Ezekiel N N; Ansah-Narh, Theophilus; Asah-Asante, Richard; Minkah, Richard
2015-01-01
Although, there exists numerous literature on the procedure for forecasting or predicting election results, in Ghana only opinion poll strategies have been used. To fill this gap, the paper develops Markov chain models for forecasting the 2016 presidential election results at the Regional, Zonal (i.e. Savannah, Coastal and Forest) and the National levels using past presidential election results of Ghana. The methodology develops a model for prediction of the 2016 presidential election results in Ghana using the Markov chains Monte Carlo (MCMC) methodology with bootstrap estimates. The results were that the ruling NDC may marginally win the 2016 Presidential Elections but would not obtain the more than 50 % votes to be declared an outright winner. This means that there is going to be a run-off election between the two giant political parties: the ruling NDC and the major opposition party, NPP. The prediction for the 2016 Presidential run-off election between the NDC and the NPP was rather in favour of the major opposition party, the NPP with a little over the 50 % votes obtained.
Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carlo Methods
NASA Astrophysics Data System (ADS)
Chen, J.; Hubbard, S.; Rubin, Y.; Murray, C.; Roden, E.; Majer, E.
2002-12-01
if they were available from direct measurements or as variables otherwise. To estimate the geochemical parameters, we first assigned a prior model for each variable and a likelihood model for each type of data, which together define posterior probability distributions for each variable on the domain. Since the posterior probability distribution may involve hundreds of variables, we used a Markov Chain Monte Carlo (MCMC) method to explore each variable by generating and subsequently evaluating hundreds of realizations. Results from this case study showed that although geophysical attributes are not necessarily directly related to geochemical parameters, geophysical data could be very useful for providing accurate and high-resolution information about geochemical parameter distribution through their joint and indirect connections with hydrogeological properties such as lithofacies. This case study also demonstrated that MCMC methods were particularly useful for geochemical parameter estimation using geophysical data because they allow incorporation into the procedure of spatial correlation information, measurement errors, and cross correlations among different types of parameters.
NASA Astrophysics Data System (ADS)
Julie, Hongki; Pasaribu, Udjianna S.; Pancoro, Adi
2015-12-01
This paper will allow Markov Chain's application in genome shared identical by descent by two individual at full sibs model. The full sibs model was a continuous time Markov Chain with three state. In the full sibs model, we look for the cumulative distribution function of the number of sub segment which have 2 IBD haplotypes from a segment of the chromosome which the length is t Morgan and the cumulative distribution function of the number of sub segment which have at least 1 IBD haplotypes from a segment of the chromosome which the length is t Morgan. This cumulative distribution function will be developed by the moment generating function.
NASA Astrophysics Data System (ADS)
Oware, E. K.
2015-12-01
Modeling aquifer heterogeneities (AH) is a complex, multidimensional problem that mostly requires stochastic imaging strategies for tractability. While the traditional Bayesian Markov chain Monte Carlo (McMC) provides a powerful framework to model AH, the generic McMC is computationally prohibitive and, thus, unappealing for large-scale problems. An innovative variant of the McMC scheme that imposes priori spatial statistical constraints on model parameter updates, for improved characterization in a computationally efficient manner is proposed. The proposed algorithm (PA) is based on Markov random field (MRF) modeling, which is an image processing technique that infers the global behavior of a random field from its local properties, making the MRF approach well suited for imaging AH. MRF-based modeling leverages the equivalence of Gibbs (or Boltzmann) distribution (GD) and MRF to identify the local properties of an MRF in terms of the easily quantifiable Gibbs energy. The PA employs the two-step approach to model the lithological structure of the aquifer and the hydraulic properties within the identified lithologies simultaneously. It performs local Gibbs energy minimizations along a random path, which requires parameters of the GD (spatial statistics) to be specified. A PA that implicitly infers site-specific GD parameters within a Bayesian framework is also presented. The PA is illustrated with a synthetic binary facies aquifer with a lognormal heterogeneity simulated within each facies. GD parameters of 2.6, 1.2, -0.4, and -0.2 were estimated for the horizontal, vertical, NESW, and NWSE directions, respectively. Most of the high hydraulic conductivity zones (facies 2) were fairly resolved (see results below) with facies identification accuracy rate of 81%, 89%, and 90% for the inversions conditioned on concentration (R1), resistivity (R2), and joint (R3), respectively. The incorporation of the conditioning datasets improved on the root mean square error (RMSE
NASA Technical Reports Server (NTRS)
Graves, M. E.; Perlmutter, M.
1974-01-01
To aid the planning of the Apollo Soyuz Test Program (ASTP), certain natural environment statistical relationships are presented, based on Markov theory and empirical counts. The practical results are in terms of conditional probability of favorable and unfavorable launch conditions at Kennedy Space Center (KSC). They are based upon 15 years of recorded weather data which are analyzed under a set of natural environmental launch constraints. Three specific forecasting problems were treated: (1) the length of record of past weather which is useful to a prediction; (2) the effect of persistence in runs of favorable and unfavorable conditions; and (3) the forecasting of future weather in probabilistic terms.
Fellows, Kelly; Rodriguez-Cruz, Vivian; Covelli, Jenna; Droopad, Alyssa; Alexander, Sheril; Ramanathan, Murali
2015-03-01
Lack of adherence is a frequent cause of hospitalizations, but its effects on dosing patterns have not been extensively investigated. The purpose of this work was to critically evaluate a novel pharmacometric model for deriving the relationships of adherence to dosing patterns and the dosing interval distribution. The hybrid, stochastic model combines a Markov chain process with the von Mises distribution. The model was challenged with electronic medication monitoring data from 207 hypertension patients and against 5-year persistence data. The model estimates distributions of dosing runs, drug holidays, and dosing intervals. Drug holidays, which can vary between individuals with the same adherence, were characterized by the patient cooperativity index parameter. The drug holiday and dosing run distributions deviate markedly from normality. The dosing interval distribution exhibits complex patterns of multimodality and can be long-tailed. Dosing patterns are an important but under recognized covariate for explaining within-individual variance in drug concentrations. PMID:25609224
Shaw, Milton Sam; Coe, Joshua D; Sewell, Thomas D
2009-01-01
An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The 'full' system of interest is calculated using density functional theory (DFT) with a 6-31 G* basis set for the configurational energies. The 'reference' system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric-isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P's and T's of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.
Snipas, Mindaugas; Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Paulauskas, Nerijus; Bukauskas, Feliksas F
2015-01-01
The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times. PMID:25705700
NASA Astrophysics Data System (ADS)
Lunt, Mark F.; Rigby, Matt; Ganesan, Anita L.; Manning, Alistair J.
2016-09-01
Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.
ERIC Educational Resources Information Center
Lichtenberg, James W.; Hummel, Thomas J.
This investigation tested the hypothesis that the probabilistic structure underlying psychotherapy interviews is Markovian. The "goodness of fit" of a first-order Markov chain model to actual therapy interviews was assessed using a x squared test of homogeneity, and by generating by Monte Carlo methods empirical sampling distributions of selected…
Application of Markov chain model to daily maximum temperature for thermal comfort in Malaysia
Nordin, Muhamad Asyraf bin Che; Hassan, Husna
2015-10-22
The Markov chain’s first order principle has been widely used to model various meteorological fields, for prediction purposes. In this study, a 14-year (2000-2013) data of daily maximum temperatures in Bayan Lepas were used. Earlier studies showed that the outdoor thermal comfort range based on physiologically equivalent temperature (PET) index in Malaysia is less than 34°C, thus the data obtained were classified into two state: normal state (within thermal comfort range) and hot state (above thermal comfort range). The long-run results show the probability of daily temperature exceed TCR will be only 2.2%. On the other hand, the probability daily temperature within TCR will be 97.8%.
Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
NASA Astrophysics Data System (ADS)
Allefeld, Carsten; Bialonski, Stephan
2007-12-01
Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.
Monaco, James Peter; Madabhushi, Anant
2011-07-01
The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate.
Markov Chain Modelling Analysis of HIV/AIDS Progression: A Race-based Forecast in the United States.
Lee, S; Ko, J; Tan, Xi; Patel, Isha; Balkrishnan, R; Chang, J
2014-03-01
HIV/AIDS has reached a pandemic level across the world with more than 33 million people who are living with HIV. In the United States, more than half a million people have been victims of AIDS. This study investigates the most vulnerable racial minority population (the African Americans) in the United States and the second least affected (the Caucasians) in order to predict the trends of the epidemic. A Markov chain analysis was used to model the progression of the disease among vulnerable people, infective people and AIDS cases for the two races separately, based on the 2009 Centers of Disease Control and Prevention HIV/AIDS Surveillance Report. Based on the Markov model, our study predicts that the number of African American people living with AIDS diagnosis and HIV infection and dead due to HIV/AIDS will be 662.2, 1225.3 and 62.9 in 2015 and 794.9, 1566.5 and 79.2 in 2030, respectively. The number of Caucasian people living with AIDS diagnosis and HIV infection and dead due to HIV/AIDS will be 96.4, 160 and 6.5 in 2015 and 118.6, 206.9 and 8.3 in 2030, respectively. The numbers of deaths due to HIV/AIDS are quite stable over the years in both the races. There is an increasing trend in the number of people living with HIV infection and AIDS diagnosis in Caucasians compared with African Americans. The absolute number of Caucasians living with AIDS diagnosis and HIV infection is quite smaller compared with African Americans. The results reveal discrepancy in HIV infection, AIDS diagnosis and deaths due to HIV/AIDS among the African Americans and the Caucasians races. There is a need for interventions focusing on HIV/AIDS prevention and management, optimum resource allocation and development of antiAIDS campaigns to reduce the infection rate. PMID:24843183
Markov chain Monte Carlo study on dark matter property related to the cosmic e{sup {+-}}excesses
Liu Jie; Yuan Qiang; Bi Xiaojun; Li Hong; Zhang Xinmin
2010-01-15
In this paper we develop a Markov chain Monte Carlo code to study the dark matter properties in frameworks to interpret the recent observations of cosmic ray electron/positron excesses. We assume that the dark matter particles couple dominantly to leptons and consider two cases, annihilating or decaying into lepton pairs, respectively. The constraint on the central density profile from the H.E.S.S. observation of diffuse {gamma} rays around the Galactic center is also included in the Markov chain Monte Carlo code self-consistently. In the numerical study, we have considered two cases of the background: fixed e{sup +}e{sup -} background and the relaxed one. Two data sets of electrons/positrons, i.e. PAMELA+ATIC (Data set I) and PAMELA+Fermi-LAT+H.E.S.S. (Data set II), are fitted independently, considering the current inconsistence between the observational data. We find that for Data set I, dark matter with m{sub {chi}{approx_equal}0}.70 TeV for annihilation (or 1.4 TeV for decay) and a non-negligible branching ratio to e{sup +}e{sup -} channel is favored; while for Data set II, m{sub {chi}{approx_equal}2}.2 TeV for annihilation (or 4.5 TeV for decay) and the combination of {mu}{sup +{mu}-} and {tau}{sup +{tau}-} final states can best fit the data. We also show that the background of electrons and positrons actually will significantly affect the branching ratios. The H.E.S.S. observation of {gamma} rays in the Galactic center ridge puts a strong constraint on the central density profile of the dark matter halo for the annihilation dark matter scenario. In this case the Navarro-Frenk-White profile, which is regarded as the typical predication from the cold dark matter scenario, is excluded with a high significance (>3{sigma}). For the decaying dark matter scenario, the constraint is much weaker.
NASA Astrophysics Data System (ADS)
Pan, J.; Durand, M. T.; Vanderjagt, B. J.
2014-12-01
The Markov chain Monte Carlo (MCMC) method had been proved to be successful in snow water equivalent retrieval based on synthetic point-scale passive microwave brightness temperature (TB) observations. This method needs only general prior information about distribution of snow parameters, and could estimate layered snow properties, including the thickness, temperature, density and snow grain size (or exponential correlation length) of each layer. In this study, the multi-layer HUT (Helsinki University of Technology) model and the MEMLS (Microwave Emission Model of Layered Snowpacks) will be used as observation models to assimilate the observed TB into snow parameter prediction. Previous studies had shown that the multi-layer HUT model tends to underestimate TB at 37 GHz for deep snow, while the MEMLS does not show sensitivity of model bias to snow depth. Therefore, results using HUT model and MEMLS will be compared to see how the observation model will influence the retrieval of snow parameters. The radiometric measurements at 10.65, 18.7, 36.5 and 90 GHz at Sodankyla, Finland will be used as MCMC input, and the statistics of all snow property measurement will be used to calculate the prior information. 43 dry snowpits with complete measurements of all snow parameters will be used for validation. The entire dataset are from NorSREx (Nordic Snow Radar Experiment) experiments carried out by Juha Lemmetyinen, Anna Kontu and Jouni Pulliainen in FMI in 2009-2011 winters, and continued two more winters from 2011 to Spring of 2013. Besides the snow thickness and snow density that are directly related to snow water equivalent, other parameters will be compared with observations, too. For thin snow, the previous studies showed that influence of underlying soil is considerable, especially when the soil is half frozen with part of unfrozen liquid water and part of ice. Therefore, this study will also try to employ a simple frozen soil permittivity model to improve the
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. PMID:26584064
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis.
Jewell, J. B.; O'Dwyer, I. J.; Huey, Greg; Gorski, K. M.; Eriksen, H. K.; Wandelt, B. D. E-mail: h.k.k.eriksen@astro.uio.no
2009-05-20
We present a new Markov Chain Monte Carlo (MCMC) algorithm for cosmic microwave background (CMB) analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C {sub l}, followed by a particular deterministic rescaling operation of the sky signal, s. The acceptance probability for this joint move depends on the sky map only through the difference of {chi}{sup 2} between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.
NASA Astrophysics Data System (ADS)
Tang, Qunshu; Hobbs, Richard; Zheng, Chan; Biescas, Berta; Caiado, Camila
2016-06-01
Marine seismic reflection technique is used to observe the strong ocean dynamic process of nonlinear internal solitary waves (ISWs or solitons) in the near-surface water. Analysis of ISWs is problematical because of their transient nature and limitations of classical physical oceanography methods. This work explores a Markov Chain Monte Carlo (MCMC) approach to recover the temperature and salinity of ISW field using the seismic reflectivity data and in situ hydrographic data. The MCMC approach is designed to directly sample the posterior probability distributions of temperature and salinity which are the solutions of the system under investigation. The principle improvement is the capability of incorporating uncertainties in observations and prior models which then provide quantified uncertainties in the output model parameters. We tested the MCMC approach on two acoustic reflectivity data sets one synthesized from a CTD cast and the other derived from multichannel seismic reflections. This method finds the solutions faithfully within the significantly narrowed confidence intervals from the provided priors. Combined with a low frequency initial model interpreted from seismic horizons of ISWs, the MCMC method is used to compute the finescale temperature, salinity, acoustic velocity, and density of ISW field. The statistically derived results are equivalent to the conventional linearized inversion method. However, the former provides us the quantified uncertainties of the temperature and salinity along the whole section whilst the latter does not. These results are the first time ISWs have been mapped with sufficient detail for further analysis of their dynamic properties.
Menezes, Amor A; Kabamba, Pierre T
2016-06-01
Motivated by the desire to study evolutionary responsiveness in fluctuating environments, and by the current interest in analyses of evolution that merge notions of fitness maximization with dynamical systems concepts such as Lyapunov functions, this paper models natural evolution with a simple stochastic dynamical system that can be represented as a Markov chain. The process maximizes fitness globally via search and has links to information and entropy. These links suggest that a possible rationale for evolution with the exponential fitness functions observed in nature is that of optimally-efficient search in a dynamic environment, which represents the quickest trade-off of prior information about the genotype search space for search effort savings after an environment perturbation. A Lyapunov function is also provided that relates the stochastic dynamical system model with search information, and the model shows that evolution is not gradient-based but dwells longer on more fit outcomes. The model further indicates that tuning the amount of selection trades off environment responsiveness with the time to reach fit outcomes, and that excessive selection causes a loss of responsiveness, a result that is validated by the literature and impacts efforts in directed evolution.
Choi, Cheuk Wai; Lee, Michael C H; Ng, Wai Tong; Law, Lai Yau; Yau, Tsz Kok; Lee, Anne W M
2011-03-01
Treatment of nasopharyngeal carcinoma (NPC) can be improved by early detection of the disease as treatment outcome worsens with disease's progression. This can be achieved with a mass screening program using Epstein Barr virus (EBV) serology and nasopharyngoscopy. The efficacy of any screening strategy should be evaluated before putting it into practice. Such evaluation is ideally performed with simulation as time and cost often preclude the evaluation by randomized trial. This study simulated and compared the outcomes of 4 screening strategies over a period of 12 years: (A) Annual screening, (B) biennial screening, (C) triennial screening, and (D) triennial screening for participants tested EBV negative and annual screening once the participants are tested EBV positive. Progression of the disease was divided into 4 phases and calculated by applying Markov chain model. Parameters of the transition matrix and probabilities were estimated using data from previous screening results of 1,072 family members of NPC patients. The early detection rates with strategies A, B, C and D are 88, 79, 71 and 87% respectively. The 5-year overall survival with screening is 10-12% higher than that without and is the highest with strategies A and D. Strategy D, however, requires only 64% screening tests compared with strategy A and has almost identical resultant disease stage distribution to strategy A. We concluded that strategy D offered the highest efficacy for NPC screening of family members of NPC patients among the four strategies studied. PMID:21052850
Charitos, Theodore; de Waal, Peter R; van der Gaag, Linda C
2008-03-15
Markov chains constitute a common way of modelling the progression of a chronic disease through various severity states. For these models, a transition matrix with the probabilities of moving from one state to another for a specific time interval is usually estimated from cohort data. Quite often, however, the cohort is observed at specific times with intervals that may be greater than the interval of interest. The transition matrix computed then needs to be decomposed in order to estimate the desired interval transition matrix suited to the model. Although simple to implement, this method of matrix decomposition can yet result in an invalid short-interval transition matrix with negative or complex entries. In this paper, we present a method for computing short-interval transition matrices that is based on regularization techniques. Our method operates separately on each row of the invalid short-interval transition matrix aiming to minimize an appropriate distance measure. We test our method on various matrix structures and sizes, and evaluate its performance on a real-life transition model for HIV-infected individuals. PMID:17579926
Liu, Ruimin; Men, Cong; Wang, Xiujuan; Xu, Fei; Yu, Wenwen
2016-01-01
Soil and water conservation in the Three Gorges Reservoir Area of China is important, and soil erosion is a significant issue. In the present study, spatial Markov chains were applied to explore the impacts of the regional context on soil erosion in the Xiangxi River watershed, and Thematic Mapper remote sensing data from 1999 and 2007 were employed. The results indicated that the observed changes in soil erosion were closely related to the soil erosion levels of the surrounding areas. When neighboring regions were not considered, the probability that moderate erosion transformed into slight and severe erosion was 0.8330 and 0.0049, respectively. However, when neighboring regions that displayed intensive erosion were considered, the probabilities were 0.2454 and 0.7513, respectively. Moreover, the different levels of soil erosion in neighboring regions played different roles in soil erosion. If the erosion levels in the neighboring region were lower, the probability of a high erosion class transferring to a lower level was relatively high. In contrast, if erosion levels in the neighboring region were higher, the probability was lower. The results of the present study provide important information for the planning and implementation of soil conservation measures in the study area. PMID:27642824
Sweeney, Lisa M.; Parker, Ann; Haber, Lynne T.; Tran, C. Lang; Kuempel, Eileen D.
2015-01-01
A biomathematical model was previously developed to describe the long-term clearance and retention of particles in the lungs of coal miners. The model structure was evaluated and parameters were estimated in two data sets, one from the United States and one from the United Kingdom. The three-compartment model structure consists of deposition of inhaled particles in the alveolar region, competing processes of either clearance from the alveolar region or translocation to the lung interstitial region, and very slow, irreversible sequestration of interstitialized material in the lung-associated lymph nodes. Point estimates of model parameter values were estimated separately for the two data sets. In the current effort, Bayesian population analysis using Markov chain Monte Carlo simulation was used to recalibrate the model while improving assessments of parameter variability and uncertainty. When model parameters were calibrated simultaneously to the two data sets, agreement between the derived parameters for the two groups was very good, and the central tendency values were similar to those derived from the deterministic approach. These findings are relevant to the proposed update of the ICRP human respiratory tract model with revisions to the alveolar-interstitial region based on this long-term particle clearance and retention model. PMID:23454101
Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores
2015-01-01
One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914
NASA Astrophysics Data System (ADS)
Moradkhani, Hamid; Dechant, Caleb M.; Sorooshian, Soroosh
2012-12-01
Particle filters (PFs) have become popular for assimilation of a wide range of hydrologic variables in recent years. With this increased use, it has become necessary to increase the applicability of this technique for use in complex hydrologic/land surface models and to make these methods more viable for operational probabilistic prediction. To make the PF a more suitable option in these scenarios, it is necessary to improve the reliability of these techniques. Improved reliability in the PF is achieved in this work through an improved parameter search, with the use of variable variance multipliers and Markov Chain Monte Carlo methods. Application of these methods to the PF allows for greater search of the posterior distribution, leading to more complete characterization of the posterior distribution and reducing risk of sample impoverishment. This leads to a PF that is more efficient and provides more reliable predictions. This study introduces the theory behind the proposed algorithm, with application on a hydrologic model. Results from both real and synthetic studies suggest that the proposed filter significantly increases the effectiveness of the PF, with marginal increase in the computational demand for hydrologic prediction.
NASA Astrophysics Data System (ADS)
Rey, Sergio J.; Kang, Wei; Wolf, Levi
2016-10-01
Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series.
Liu, Ruimin; Men, Cong; Wang, Xiujuan; Xu, Fei; Yu, Wenwen
2016-01-01
Soil and water conservation in the Three Gorges Reservoir Area of China is important, and soil erosion is a significant issue. In the present study, spatial Markov chains were applied to explore the impacts of the regional context on soil erosion in the Xiangxi River watershed, and Thematic Mapper remote sensing data from 1999 and 2007 were employed. The results indicated that the observed changes in soil erosion were closely related to the soil erosion levels of the surrounding areas. When neighboring regions were not considered, the probability that moderate erosion transformed into slight and severe erosion was 0.8330 and 0.0049, respectively. However, when neighboring regions that displayed intensive erosion were considered, the probabilities were 0.2454 and 0.7513, respectively. Moreover, the different levels of soil erosion in neighboring regions played different roles in soil erosion. If the erosion levels in the neighboring region were lower, the probability of a high erosion class transferring to a lower level was relatively high. In contrast, if erosion levels in the neighboring region were higher, the probability was lower. The results of the present study provide important information for the planning and implementation of soil conservation measures in the study area.
NASA Technical Reports Server (NTRS)
Bonamente, Massimillano; Joy, Marshall K.; Carlstrom, John E.; Reese, Erik D.; LaRoque, Samuel J.
2004-01-01
X-ray and Sunyaev-Zel'dovich effect data can be combined to determine the distance to galaxy clusters. High-resolution X-ray data are now available from Chandra, which provides both spatial and spectral information, and Sunyaev-Zel'dovich effect data were obtained from the BIMA and Owens Valley Radio Observatory (OVRO) arrays. We introduce a Markov Chain Monte Carlo procedure for the joint analysis of X-ray and Sunyaev- Zel'dovich effect data. The advantages of this method are the high computational efficiency and the ability to measure simultaneously the probability distribution of all parameters of interest, such as the spatial and spectral properties of the cluster gas and also for derivative quantities such as the distance to the cluster. We demonstrate this technique by applying it to the Chandra X-ray data and the OVRO radio data for the galaxy cluster A611. Comparisons with traditional likelihood ratio methods reveal the robustness of the method. This method will be used in follow-up paper to determine the distances to a large sample of galaxy cluster.
NASA Astrophysics Data System (ADS)
Pan, J.; Durand, M. T.; Vanderjagt, B. J.
2015-12-01
Markov Chain Monte Carlo (MCMC) method is a retrieval algorithm based on Bayes' rule, which starts from an initial state of snow/soil parameters, and updates it to a series of new states by comparing the posterior probability of simulated snow microwave signals before and after each time of random walk. It is a realization of the Bayes' rule, which gives an approximation to the probability of the snow/soil parameters in condition of the measured microwave TB signals at different bands. Although this method could solve all snow parameters including depth, density, snow grain size and temperature at the same time, it still needs prior information of these parameters for posterior probability calculation. How the priors will influence the SWE retrieval is a big concern. Therefore, in this paper at first, a sensitivity test will be carried out to study how accurate the snow emission models and how explicit the snow priors need to be to maintain the SWE error within certain amount. The synthetic TB simulated from the measured snow properties plus a 2-K observation error will be used for this purpose. It aims to provide a guidance on the MCMC application under different circumstances. Later, the method will be used for the snowpits at different sites, including Sodankyla, Finland, Churchill, Canada and Colorado, USA, using the measured TB from ground-based radiometers at different bands. Based on the previous work, the error in these practical cases will be studied, and the error sources will be separated and quantified.
Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores
2015-01-01
One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914
Johannesson, G; Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2005-02-07
Estimating unknown system configurations/parameters by combining system knowledge gained from a computer simulation model on one hand and from observed data on the other hand is challenging. An example of such inverse problem is detecting and localizing potential flaws or changes in a structure by using a finite-element model and measured vibration/displacement data. We propose a probabilistic approach based on Bayesian methodology. This approach does not only yield a single best-guess solution, but a posterior probability distribution over the parameter space. In addition, the Bayesian approach provides a natural framework to accommodate prior knowledge. A Markov chain Monte Carlo (MCMC) procedure is proposed to generate samples from the posterior distribution (an ensemble of likely system configurations given the data). The MCMC procedure proposed explores the parameter space at different resolutions (scales), resulting in a more robust and efficient procedure. The large-scale exploration steps are carried out using coarser-resolution finite-element models, yielding a considerable decrease in computational time, which can be a crucial for large finite-element models. An application is given using synthetic displacement data from a simple cantilever beam with MCMC exploration carried out at three different resolutions.
NASA Astrophysics Data System (ADS)
LIU, B.; Liang, Y.
2015-12-01
Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications, such as nuclear physics, computational biology, financial engineering, among others. In Earth sciences applications of MCMC are primarily in the field of geophysics [1]. The purpose of this study is to introduce MCMC to geochemical inverse problems related to trace element fractionation during concurrent melting, melt transport and melt-rock reaction in the mantle. MCMC method has several advantages over linearized least squares methods in inverting trace element patterns in basalts and mantle rocks. First, MCMC can handle equations that have no explicit analytical solutions which are required by linearized least squares methods for gradient calculation. Second, MCMC converges to global minimum while linearized least squares methods may be stuck at a local minimum or converge slowly due to nonlinearity. Furthermore, MCMC can provide insight into uncertainties of model parameters with non-normal trade-off. We use MCMC to invert for extent of melting, amount of trapped melt, and extent of chemical disequilibrium between the melt and residual solid from REE data in abyssal peridotites from Central Indian Ridge and Mid-Atlantic Ridge. In the first step, we conduct forward calculation of REE evolution with melting models in a reasonable model space. We then build up a chain of melting models according to Metropolis-Hastings algorithm to represent the probability of specific model. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites. In the future, MCMC will be applied to more realistic but also more complicated melting models in which partition coefficients, diffusion coefficients, as well as melting and melt suction rates vary as functions of temperature, pressure and mineral compositions. [1]. Sambridge & Mosegarrd [2002] Rev. Geophys.
Comen, E; Mason, J; Kuhn, P; Nieva, J; Newton, P; Norton, L; Venkatappa, N; Jochelson, M
2014-06-01
Purpose: Traditionally, breast cancer metastasis is described as a process wherein cancer cells spread from the breast to multiple organ systems via hematogenous and lymphatic routes. Mapping organ specific patterns of cancer spread over time is essential to understanding metastatic progression. In order to better predict sites of metastases, here we demonstrate modeling of the patterned migration of metastasis. Methods: We reviewed the clinical history of 453 breast cancer patients from Memorial Sloan Kettering Cancer Center who were non-metastatic at diagnosis but developed metastasis over time. We used the variables of organ site of metastases as well as time to create a Markov chain model of metastasis. We illustrate the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Results: Based on the clinical histories of 453 breast cancer patients who developed metastasis, we have learned (i) how to create the Markov transition matrix governing the probabilities of cancer progression from site to site; (ii) how to create a systemic network diagram governing disease progression modeled as a random walk on a directed graph; (iii) how to classify metastatic sites as ‘sponges’ that tend to only receive cancer cells or ‘spreaders’ that receive and release them; (iv) how to model the time-scales of disease progression as a Weibull probability distribution function; (v) how to perform Monte Carlo simulations of disease progression; and (vi) how to interpret disease progression as an entropy-increasing stochastic process. Conclusion: Based on our modeling, metastatic spread may follow predictable pathways. Mapping metastasis not simply by organ site, but by function as either a ‘spreader’ or ‘sponge’ fundamentally reframes our understanding of metastatic processes. This model serves as a novel platform from which we may integrate the evolving genomic landscape that drives cancer
NASA Astrophysics Data System (ADS)
Pham, Tuan D.; Salvetti, Federica; Wang, Bing; Diani, Marco; Heindel, Walter; Knecht, Stefan; Wersching, Heike; Baune, Bernhard T.; Berger, Klaus
2011-02-01
Rating and quantification of cerebral white matter hyperintensities on magnetic resonance imaging (MRI) are important tasks in various clinical and scientific settings. As manual evaluation is time consuming and imprecise, much effort has been made to automate the quantification of white matter hyperintensities. There is rarely any report that attempts to study the similarity/dissimilarity of white matter hyperintensity patterns that have different sizes, shapes and spatial localizations on the MRI. This paper proposes an original computational neuroscience framework for such a conceptual study with a standpoint that the prior knowledge about white matter hyperintensities can be accumulated and utilized to enable a reliable inference of the rating of a new white matter hyperintensity observation. This computational approach for rating inference of white matter hyperintensities, which appears to be the first study, can be utilized as a computerized rating-assisting tool and can be very economical for diagnostic evaluation of brain tissue lesions.
Adibuzzaman, Mohammad; Kramer, George C; Galeotti, Loriano; Merrill, Stephen J; Strauss, David G; Scully, Christopher G
2014-01-01
Identifying the need for interventions during hemorrhage is complicated due to physiological compensation mechanisms that can stabilize vital signs until a significant amount of blood loss. Physiological systems providing compensation during hemorrhage affect the arterial blood pressure waveform through changes in dynamics and waveform morphology. We investigated the use of Markov chain analysis of the arterial blood pressure waveform to monitor physiological systems changes during hemorrhage. Continuous arterial blood pressure recordings were made on anesthetized swine (N=7) during a 5 min baseline period and during a slow hemorrhage (10 ml/kg over 30 min). Markov chain analysis was applied to 20 sec arterial blood pressure waveform segments with a sliding window. 20 ranges of arterial blood pressure were defined as states and empirical transition probability matrices were determined for each 20 sec segment. The mixing rate (2(nd) largest eigenvalue of the transition probability matrix) was determined for all segments. A change in the mixing rate from baseline estimates was identified during hemorrhage for each animal (median time of 13 min, ~10% estimated blood volume, with minimum and maximum times of 2 and 33 min, respectively). The mixing rate was found to have an inverse correlation with shock index for all 7 animals (median correlation coefficient of -0.95 with minimum and maximum of -0.98 and -0.58, respectively). The Markov chain mixing rate of arterial blood pressure recordings is a novel potential biomarker for monitoring and understanding physiological systems during hemorrhage. PMID:25570688
Welton, Nicky J; Ades, A E
2005-01-01
Markov transition models are frequently used to model disease progression. The authors show how the solution to Kolmogorov's forward equations can be exploited to map between transition rates and probabilities from probability data in multistate models. They provide a uniform, Bayesian treatment of estimation and propagation of uncertainty of transition rates and probabilities when 1) observations are available on all transitions and exact time at risk in each state (fully observed data) and 2) observations are on initial state and final state after a fixed interval of time but not on the sequence of transitions (partially observed data). The authors show how underlying transition rates can be recovered from partially observed data using Markov chain Monte Carlo methods in WinBUGS, and they suggest diagnostics to investigate inconsistencies between evidence from different starting states. An illustrative example for a 3-state model is given, which shows how the methods extend to more complex Markov models using the software WBDiff to compute solutions. Finally, the authors illustrate how to statistically combine data from multiple sources, including partially observed data at several follow-up times and also how to calibrate a Markov model to be consistent with data from one specific study. PMID:16282214
Lin, Chin; Chu, Chi-Ming; Su, Sui-Lung
2016-01-01
Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The "missing heritability" has been suggested to be due to lack of studies focused on epistasis, also called gene-gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called "Epistasis Test in Meta-Analysis" (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene-gene interactions in the renin-angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html]. PMID:27045371
Mukhopadhyay, Anirban; Mondal, Parimal; Barik, Jyotiskona; Chowdhury, S M; Ghosh, Tuhin; Hazra, Sugata
2015-06-01
The composition and assemblage of mangroves in the Bangladesh Sundarbans are changing systematically in response to several environmental factors. In order to understand the impact of the changing environmental conditions on the mangrove forest, species composition maps for the years 1985, 1995 and 2005 were studied. In the present study, 1985 and 1995 species zonation maps were considered as base data and the cellular automata-Markov chain model was run to predict the species zonation for the year 2005. The model output was validated against the actual dataset for 2005 and calibrated. Finally, using the model, mangrove species zonation maps for the years 2025, 2055 and 2105 have been prepared. The model was run with the assumption that the continuation of the current tempo and mode of drivers of environmental factors (temperature, rainfall, salinity change) of the last two decades will remain the same in the next few decades. Present findings show that the area distribution of the following species assemblages like Goran (Ceriops), Sundari (Heritiera), Passur (Xylocarpus), and Baen (Avicennia) would decrease in the descending order, whereas the area distribution of Gewa (Excoecaria), Keora (Sonneratia) and Kankra (Bruguiera) dominated assemblages would increase. The spatial distribution of projected mangrove species assemblages shows that more salt tolerant species will dominate in the future; which may be used as a proxy to predict the increase of salinity and its spatial variation in Sundarbans. Considering the present rate of loss of forest land, 17% of the total mangrove cover is predicted to be lost by the year 2105 with a significant loss of fresh water loving mangroves and related ecosystem services. This paper describes a unique approach to assess future changes in species composition and future forest zonation in mangroves under the 'business as usual' scenario of climate change. PMID:25719448
Lin, Chin; Chu, Chi-Ming; Su, Sui-Lung
2016-01-01
Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The “missing heritability” has been suggested to be due to lack of studies focused on epistasis, also called gene–gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called “Epistasis Test in Meta-Analysis” (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene–gene interactions in the renin–angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html]. PMID:27045371
NASA Astrophysics Data System (ADS)
Li, Jun; Calo, Victor M.
2013-09-01
We present a single-particle Lennard-Jones (L-J) model for CO2 and N2. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed using the proposed single-particle models for CO2 and N2 agree well with experimental data over a wide range of temperatures. These diagrams are computed using the Markov Chain Monte Carlo method based on the Gibbs-NVT ensemble. This good agreement validates the proposed simplified models. That is, with properly selected parameters, the single-particle models have similar accuracy in predicting gas-phase properties as more complex, state-of-the-art molecular models. To further test these single-particle models, three binary mixtures of CH4, CO2 and N2 are studied using a Gibbs-NPT ensemble. These results are compared against experimental data over a wide range of pressures. The single-particle model has similar accuracy in the gas phase as traditional models although its deviation in the liquid phase is greater. Since the single-particle model reduces the particle number and avoids the time-consuming Ewald summation used to evaluate Coulomb interactions, the proposed model improves the computational efficiency significantly, particularly in the case of high liquid density where the acceptance rate of the particle-swap trial move increases. We compare, at constant temperature and pressure, the Gibbs-NPT and Gibbs-NVT ensembles to analyze their performance differences and results consistency. As theoretically predicted, the agreement between the simulations implies that Gibbs-NVT can be used to validate Gibbs-NPT predictions when experimental data is not available.
NASA Astrophysics Data System (ADS)
Xu, F.; Diner, D. J.; Seidel, F. C.; Dubovik, O.; Zhai, P.
2014-12-01
A vector Markov chain radiative transfer method was developed for forward modeling of radiance and polarization fields in a coupled atmosphere-ocean system. The method was benchmarked against an independent Successive Orders of Scattering code and linearized through the use of Jacobians. Incorporated with the multi-patch optimization algorithm and look-up-table method, simultaneous aerosol and ocean color retrievals were performed using imagery acquired by the Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) when it was operated in step-and-stare mode with 9 viewing angles ranging between ±67°. Data from channels near 355, 380, 445, 470*, 555, 660*, and 865* nm were used in the retrievals, where the asterisk denotes the polarimetric bands. Retrievals were run for AirMSPI overflights over Southern California and Monterey Bay, CA. For the relatively high aerosol optical depth (AOD) case (~0.28 at 550 nm), the retrieved aerosol concentration, size distribution, water-leaving radiance, and chlorophyll concentration were compared to those reported by the USC SeaPRISM AERONET-OC site off the coast of Southern California on 6 February 2013. For the relatively low AOD case (~0.08 at 550 nm), the retrieved aerosol concentration and size distribution were compared to those reported by the Monterey Bay AERONET site on 28 April 2014. Further, we evaluate the benefits of multi-angle and polarimetric observations by performing the retrievals using (a) all view angles and channels; (b) all view angles but radiances only (no polarization); (c) the nadir view angle only with both radiance and polarization; and (d) the nadir view angle without polarization. Optimized retrievals using different initial guesses were performed to provide a measure of retrieval uncertainty. Removal of multi-angular or polarimetric information resulted in increases in both parameter uncertainty and systematic bias. Potential accuracy improvements afforded by applying constraints on the surface
Hoad, K A; van't Hoog, A H; Rosen, D; Marston, B; Nyabiage, L; Williams, B G; Dye, C; Cheng, R C H
2009-04-01
For some diseases, the transmission of infection can cause spatial clustering of disease cases. This clustering has an impact on how one estimates the rate of the spread of the disease and on the design of control strategies. It is, however, difficult to assess such clustering, (local effects on transmission), using traditional statistical methods. A stochastic Markov-chain model that takes into account possible local or more dispersed global effects on the risk of contracting disease is introduced in the context of the transmission dynamics of tuberculosis. The model is used to analyse TB notifications collected in the Asembo and Gem Divisions of Nyanza Province in western Kenya by the Kenya Ministry of Health/National Leprosy and Tuberculosis Program and the Centers for Disease Control and Prevention. The model shows evidence of a pronounced local effect that is significantly greater than the global effect. We discuss a number of variations of the model which identify how this local effect depends on factors such as age and gender. Zoning/clustering of villages is used to identify the influence that zone size has on the model's ability to distinguish local and global effects. An important possible use of the model is in the design of a community randomised trial where geographical clusters of people are divided into two groups and the effectiveness of an intervention policy is assessed by applying it to one group but not the other. Here the model can be used to take the effect of case clustering into consideration in calculating the minimum difference in an outcome variable (e.g. disease prevalence) that can be detected with statistical significance. It thereby gauges the potential effectiveness of such a trial. Such a possible application is illustrated with the given time/spatial TB data set.
NASA Astrophysics Data System (ADS)
Jadoon, K. Z.; Altaf, M. U.; McCabe, M. F.; Hoteit, I.; Moghadas, D.
2014-12-01
In arid and semi-arid regions, soil salinity has a major impact on agro-ecosystems, agricultural productivity, environment and sustainability. High levels of soil salinity adversely affect plant growth and productivity, soil and water quality, and may eventually result in soil erosion and land degradation. Being essentially a hazard, it's important to monitor and map soil salinity at an early stage to effectively use soil resources and maintain soil salinity level below the salt tolerance of crops. In this respect, low frequency electromagnetic induction (EMI) systems can be used as a noninvasive method to map the distribution of soil salinity at the field scale and at a high spatial resolution. In this contribution, an EMI system (the CMD Mini-Explorer) is used to estimate soil salinity using a Bayesian approach implemented via a Markov chain Monte Carlo (MCMC) sampling for inversion of multi-configuration EMI measurements. In-situ and EMI measurements were conducted across a farm where Acacia trees are irrigated with brackish water using a drip irrigation system. The electromagnetic forward model is based on the full solution of Maxwell's equation, and the subsurface is considered as a three-layer problem. In total, five parameters (electrical conductivity of three layers and thickness of top two layers) were inverted and modeled electrical conductivities were converted into the universal standard of soil salinity measurement (i.e. using the method of electrical conductivity of a saturated soil paste extract). Simulation results demonstrate that the proposed scheme successfully recovers soil salinity and reduces the uncertainties in the prior estimate. Analysis of the resulting posterior distribution of parameters indicates that electrical conductivity of the top two layers and the thickness of the first layer are well constrained by the EMI measurements. The proposed approach allows for quantitative mapping and monitoring of the spatial electrical conductivity
Mukhopadhyay, Anirban; Mondal, Parimal; Barik, Jyotiskona; Chowdhury, S M; Ghosh, Tuhin; Hazra, Sugata
2015-06-01
The composition and assemblage of mangroves in the Bangladesh Sundarbans are changing systematically in response to several environmental factors. In order to understand the impact of the changing environmental conditions on the mangrove forest, species composition maps for the years 1985, 1995 and 2005 were studied. In the present study, 1985 and 1995 species zonation maps were considered as base data and the cellular automata-Markov chain model was run to predict the species zonation for the year 2005. The model output was validated against the actual dataset for 2005 and calibrated. Finally, using the model, mangrove species zonation maps for the years 2025, 2055 and 2105 have been prepared. The model was run with the assumption that the continuation of the current tempo and mode of drivers of environmental factors (temperature, rainfall, salinity change) of the last two decades will remain the same in the next few decades. Present findings show that the area distribution of the following species assemblages like Goran (Ceriops), Sundari (Heritiera), Passur (Xylocarpus), and Baen (Avicennia) would decrease in the descending order, whereas the area distribution of Gewa (Excoecaria), Keora (Sonneratia) and Kankra (Bruguiera) dominated assemblages would increase. The spatial distribution of projected mangrove species assemblages shows that more salt tolerant species will dominate in the future; which may be used as a proxy to predict the increase of salinity and its spatial variation in Sundarbans. Considering the present rate of loss of forest land, 17% of the total mangrove cover is predicted to be lost by the year 2105 with a significant loss of fresh water loving mangroves and related ecosystem services. This paper describes a unique approach to assess future changes in species composition and future forest zonation in mangroves under the 'business as usual' scenario of climate change.
Lin, Chin; Chu, Chi-Ming; Su, Sui-Lung
2016-01-01
Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The "missing heritability" has been suggested to be due to lack of studies focused on epistasis, also called gene-gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called "Epistasis Test in Meta-Analysis" (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene-gene interactions in the renin-angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html].
NASA Astrophysics Data System (ADS)
Mandal, K. G.; Padhi, J.; Kumar, A.; Ghosh, S.; Panda, D. K.; Mohanty, R. K.; Raychaudhuri, M.
2015-08-01
Rainfed agriculture plays and will continue to play a dominant role in providing food and livelihoods for an increasing world population. Rainfall analyses are helpful for proper crop planning under changing environment in any region. Therefore, in this paper, an attempt has been made to analyse 16 years of rainfall (1995-2010) at the Daspalla region in Odisha, eastern India for prediction using six probability distribution functions, forecasting the probable date of onset and withdrawal of monsoon, occurrence of dry spells by using Markov chain model and finally crop planning for the region. For prediction of monsoon and post-monsoon rainfall, log Pearson type III and Gumbel distribution were the best-fit probability distribution functions. The earliest and most delayed week of the onset of rainy season was the 20th standard meteorological week (SMW) (14th-20th May) and 25th SMW (18th-24th June), respectively. Similarly, the earliest and most delayed week of withdrawal of rainfall was the 39th SMW (24th-30th September) and 47th SMW (19th-25th November), respectively. The longest and shortest length of rainy season was 26 and 17 weeks, respectively. The chances of occurrence of dry spells are high from the 1st-22nd SMW and again the 42nd SMW to the end of the year. The probability of weeks (23rd-40th SMW) remaining wet varies between 62 and 100 % for the region. Results obtained through this analysis would be utilised for agricultural planning and mitigation of dry spells at the Daspalla region in Odisha, India.
2010-01-01
Background The Medium-chain Dehydrogenases/Reductases (MDR) form a protein superfamily whose size and complexity defeats traditional means of subclassification; it currently has over 15000 members in the databases, the pairwise sequence identity is typically around 25%, there are members from all kingdoms of life, the chain-lengths vary as does the oligomericity, and the members are partaking in a multitude of biological processes. There are profile hidden Markov models (HMMs) available for detecting MDR superfamily members, but none for determining which MDR family each protein belongs to. The current torrential influx of new sequence data enables elucidation of more and more protein families, and at an increasingly fine granularity. However, gathering good quality training data usually requires manual attention by experts and has therefore been the rate limiting step for expanding the number of available models. Results We have developed an automated algorithm for HMM refinement that produces stable and reliable models for protein families. This algorithm uses relationships found in data to generate confident seed sets. Using this algorithm we have produced HMMs for 86 distinct MDR families and 34 of their subfamilies which can be used in automated annotation of new sequences. We find that MDR forms with 2 Zn2+ ions in general are dehydrogenases, while MDR forms with no Zn2+ in general are reductases. Furthermore, in Bacteria MDRs without Zn2+ are more frequent than those with Zn2+, while the opposite is true for eukaryotic MDRs, indicating that Zn2+ has been recruited into the MDR superfamily after the initial life kingdom separations. We have also developed a web site http://mdr-enzymes.org that provides textual and numeric search against various characterised MDR family properties, as well as sequence scan functions for reliable classification of novel MDR sequences. Conclusions Our method of refinement can be readily applied to create stable and reliable HMMs
Utilizing Gaussian Markov random field properties of Bayesian animal models.
Steinsland, Ingelin; Jensen, Henrik
2010-09-01
In this article, we demonstrate how Gaussian Markov random field properties give large computational benefits and new opportunities for the Bayesian animal model. We make inference by computing the posteriors for important quantitative genetic variables. For the single-trait animal model, a nonsampling-based approximation is presented. For the multitrait model, we set up a robust and fast Markov chain Monte Carlo algorithm. The proposed methodology was used to analyze quantitative genetic properties of morphological traits of a wild house sparrow population. Results for single- and multitrait models were compared.
NASA Astrophysics Data System (ADS)
Olivares, G.; Teferle, F. N.
2013-12-01
Geodetic time series provide information which helps to constrain theoretical models of geophysical processes. It is well established that such time series, for example from GPS, superconducting gravity or mean sea level (MSL), contain time-correlated noise which is usually assumed to be a combination of a long-term stochastic process (characterized by a power-law spectrum) and random noise. Therefore, when fitting a model to geodetic time series it is essential to also estimate the stochastic parameters beside the deterministic ones. Often the stochastic parameters include the power amplitudes of both time-correlated and random noise, as well as, the spectral index of the power-law process. To date, the most widely used method for obtaining these parameter estimates is based on maximum likelihood estimation (MLE). We present an integration method, the Bayesian Monte Carlo Markov Chain (MCMC) method, which, by using Markov chains, provides a sample of the posteriori distribution of all parameters and, thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. This algorithm automatically optimizes the Markov chain step size and estimates the convergence state by spectral analysis of the chain. We assess the MCMC method through comparison with MLE, using the recently released GPS position time series from JPL and apply it also to the MSL time series from the Revised Local Reference data base of the PSMSL. Although the parameter estimates for both methods are fairly equivalent, they suggest that the MCMC method has some advantages over MLE, for example, without further computations it provides the spectral index uncertainty, is computationally stable and detects multimodality.
Bayesian Inference in Probabilistic Risk Assessment -- The Current State of the Art
Dana L. Kelly; Curtis L. Smith
2009-02-01
Markov chain Monte Carlo approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via Markov chain Monte Carlo sampling to a variety of important problems.
Lu, Yan; Burykin, Anton; Deem, Michael W; Buchman, Timothy G
2009-09-01
Analysis of heart rate (HR) dynamics before, during, and after a physiologic stress has clinical importance. For example, the celerity of heart rate recovery (HRR) after a cardiac stress test (eg, treadmill exercise test) has been shown to be an independent predictor of all-cause mortality. Heart rate dynamics are modulated, in part, by the autonomic nervous system. These dynamics are commonly abstracted using metrics of heart rate variability (HRV), which are known to be sensitive to the influence of the autonomic nervous system on HR. The patient-specific modulators of HR should be reflected both in the response to stress as well as in the recovery from stress. We therefore hypothesized that the patient-specific HR response to stress could be used to predict the HRR after the stress. We devised a Markov chain model to predict the poststress HRR dynamics using the parameters (transition matrix) calculated from HR data during the stress. The model correctly predicts the exponential shape of poststress HRR. This model features a simple analytical relationship linking poststress HRR time constant (T(off)) with a standard measure of HRV, namely the correlation coefficient of the Poincaré plot (first return map) of the HR recorded during the stress. A corresponding relationship exists between the time constant (T(on)) of R-R interval decrease at the onset of stress and the correlation coefficient of the Poincaré plot of prestress R-R intervals. Consequently, the model can be used for the prediction of poststress HRR using the HRV measured during the stress. This direct relationship between the event-to-event microscopic fluctuations (HRV) during the stress and the macroscopic response (HRR) after the stress terminates can be interpreted as an instance of a fluctuation-dissipation relationship. We have thus applied the fluctuation-dissipation theorem to the analysis of heart rate dynamics. The approach is specific neither to cardiac physiology nor to transitions
Audren, Benjamin; Lesgourgues, Julien; Bird, Simeon; Haehnelt, Martin G.; Viel, Matteo E-mail: julien.lesgourgues@cern.ch E-mail: haehnelt@ast.cam.ac.uk
2013-01-01
We present forecasts for the accuracy of determining the parameters of a minimal cosmological model and the total neutrino mass based on combined mock data for a future Euclid-like galaxy survey and Planck. We consider two different galaxy surveys: a spectroscopic redshift survey and a cosmic shear survey. We make use of the Monte Carlo Markov Chains (MCMC) technique and assume two sets of theoretical errors. The first error is meant to account for uncertainties in the modelling of the effect of neutrinos on the non-linear galaxy power spectrum and we assume this error to be fully correlated in Fourier space. The second error is meant to parametrize the overall residual uncertainties in modelling the non-linear galaxy power spectrum at small scales, and is conservatively assumed to be uncorrelated and to increase with the ratio of a given scale to the scale of non-linearity. It hence increases with wavenumber and decreases with redshift. With these two assumptions for the errors and assuming further conservatively that the uncorrelated error rises above 2% at k = 0.4 h/Mpc and z = 0.5, we find that a future Euclid-like cosmic shear/galaxy survey achieves a 1-σ error on M{sub ν} close to 32 meV/25 meV, sufficient for detecting the total neutrino mass with good significance. If the residual uncorrelated errors indeed rises rapidly towards smaller scales in the non-linear regime as we have assumed here then the data on non-linear scales does not increase the sensitivity to the total neutrino mass. Assuming instead a ten times smaller theoretical error with the same scale dependence, the error on the total neutrino mass decreases moderately from σ(M{sub ν}) = 18 meV to 14 meV when mildly non-linear scales with 0.1 h/Mpc < k < 0.6 h/Mpc are included in the analysis of the galaxy survey data.
Tani, Yuji
2016-01-01
Background Consistent with the “attention, interest, desire, memory, action” (AIDMA) model of consumer behavior, patients collect information about available medical institutions using the Internet to select information for their particular needs. Studies of consumer behavior may be found in areas other than medical institution websites. Such research uses Web access logs for visitor search behavior. At this time, research applying the patient searching behavior model to medical institution website visitors is lacking. Objective We have developed a hospital website search behavior model using a Bayesian approach to clarify the behavior of medical institution website visitors and determine the probability of their visits, classified by search keyword. Methods We used the website data access log of a clinic of internal medicine and gastroenterology in the Sapporo suburbs, collecting data from January 1 through June 31, 2011. The contents of the 6 website pages included the following: home, news, content introduction for medical examinations, mammography screening, holiday person-on-duty information, and other. The search keywords we identified as best expressing website visitor needs were listed as the top 4 headings from the access log: clinic name, clinic name + regional name, clinic name + medical examination, and mammography screening. Using the search keywords as the explaining variable, we built a binomial probit model that allows inspection of the contents of each purpose variable. Using this model, we determined a beta value and generated a posterior distribution. We performed the simulation using Markov Chain Monte Carlo methods with a noninformation prior distribution for this model and determined the visit probability classified by keyword for each category. Results In the case of the keyword “clinic name,” the visit probability to the website, repeated visit to the website, and contents page for medical examination was positive. In the case of the
Destri, C.; Vega, H. J. de; Sanchez, N. G.
2008-07-15
Generically, the classical evolution of the inflaton has a brief fast-roll stage that precedes the slow-roll regime. The fast-roll stage leads to a purely attractive potential in the wave equations of curvature and tensor perturbations (while the potential is purely repulsive in the slow-roll stage). This attractive potential leads to a depression of the CMB quadrupole moment for the curvature and B-mode angular power spectra. A single new parameter emerges in this way in the early universe model: the comoving wave number k{sub 1} characteristic scale of this attractive potential. This mode k{sub 1} happens to exit the horizon precisely at the transition from the fast-roll to the slow-roll stage. The fast-roll stage dynamically modifies the initial power spectrum by a transfer function D(k). We compute D(k) by solving the inflaton evolution equations. D(k) effectively suppresses the primordial power for k
Duffy, S W; Chen, H H; Tabar, L; Day, N E
1995-07-30
The sojourn time, time spent in the preclinical detectable phase (PCDP) for chronic diseases, for example, breast cancer, plays an important role in the design and assessment of screening programmes. Traditional methods to estimate it usually assume a uniform incidence rate of preclinical disease from a randomized control group or historical data. In this paper, a two-parameter Markov chain model is proposed and developed to explicitly estimate the preclinical incidence rate (lambda 1) and the rate of transition from preclinical to clinical state (lambda 2, equivalent to the inverse of mean sojourn time) without using control data. A new estimate of sensitivity is proposed, based on the estimated parameters of the Markov process. When this method is applied to the data from the Swedish two-county study of breast cancer screening in the age group 70-74, the estimate of MST is 2.3 with 95 per cent CI ranging from 2.1 to 2.5, which is close to the result based on the traditional method but the 95 per cent CI is narrower using the Markov model. The reason for the greater precision of the latter is the fuller use of all temporal data, since the continuous exact times to events are used in our method instead of grouping them as in the traditional method. Ongoing and future researches should extend this model to include, for example, the tumour size, nodal status and malignancy grade, along with methods of simultaneously estimating sensitivity and the transition rates in the Markov process.
King, Martin D; Crowder, Martin J; Hand, David J; Harris, Neil G; Williams, Stephen R; Obrenovitch, Tihomir P; Gadian, David G
2003-06-01
Markov chain Monte Carlo simulation was used in a reanalysis of the longitudinal data obtained by Harris et al. (J Cereb Blood Flow Metab 20:28-36) in a study of the direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischemia. The main purpose was to provide a formal analysis of the temporal relationship between the ADC and DC responses, to explore the possible involvement of a common latent (driving) process. A Bayesian nonlinear hierarchical random coefficients model was adopted. DC and ADC transition parameter posterior probability distributions were generated using three parallel Markov chains created using the Metropolis algorithm. Particular attention was paid to the within-subject differences between the DC and ADC time course characteristics. The results show that the DC response is biphasic, whereas the ADC exhibits monophasic behavior, and that the two DC components are each distinguishable from the ADC response in their time dependencies. The DC and ADC changes are not, therefore, driven by a common latent process. This work demonstrates a general analytical approach to the multivariate, longitudinal data-processing problem that commonly arises in stroke and other biomedical research. PMID:12796716
NASA Astrophysics Data System (ADS)
Jalayer, Fatemeh; Ebrahimian, Hossein
2014-05-01
Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the
NASA Astrophysics Data System (ADS)
Määttänen, Anni; Douspis, Marian
2015-04-01
In the last years several datasets on deposition mode ice nucleation in Martian conditions have showed that the effectiveness of mineral dust as a condensation nucleus decreases with temperature (Iraci et al., 2010; Phebus et al., 2011; Trainer et al., 2009). Previously, nucleation modelling in Martian conditions used only constant values of this so-called contact parameter, provided by the few studies previously published on the topic. The new studies paved the way for possibly more realistic way of predicting ice crystal formation in the Martian environment. However, the caveat of these studies (Iraci et al., 2010; Phebus et al., 2011) was the limited temperature range that inhibits using the provided (linear) equations for the contact parameter temperature dependence in all conditions of cloud formation on Mars. One wide temperature range deposition mode nucleation dataset exists (Trainer et al., 2009), but the used substrate was silicon, which cannot imitate realistically the most abundant ice nucleus on Mars, mineral dust. Nevertheless, this dataset revealed, thanks to measurements spanning from 150 to 240 K, that the behaviour of the contact parameter as a function of temperature was exponential rather than linear as suggested by previous work. We have tried to combine the previous findings to provide realistic and practical formulae for application in nucleation and atmospheric models. We have analysed the three cited datasets using a Monte Carlo Markov Chain (MCMC) method. The used method allows us to test and evaluate different functional forms for the temperature dependence of the contact parameter. We perform a data inversion by finding the best fit to the measured data simultaneously at all points for different functional forms of the temperature dependence of the contact angle m(T). The method uses a full nucleation model (Määttänen et al., 2005; Vehkamäki et al., 2007) to calculate the observables at each data point. We suggest one new and test
Pickling Peridotites in the IBM Mantle Wedge: Inferences from the Guguan Cross-Chain, Mariana Arc
NASA Astrophysics Data System (ADS)
Stern, R. J.; Bloomer, S. H.; Leybourne, M.; Miller, N. R.; Hargrove, U. S.; Griffin, W. R.; Fouch, M.; Kohut, E.; Vervoort, J.; Prytulak, J.
2003-12-01
MTSB mantle source. Ba/La vs. La/Yb systematics show that magmatic front lavas plot near the fluid-dominated endmember whereas Guguan II plots along the trends inferred for sediment melts. Similarly, Th/U doubles across the cross-chain, from ~1.5-2.0 along the magmatic front (consistent with U-rich fluids from altered oceanic crust, AOC) to ~2.5-3.0, similar to that of MTSB and approaching values for sediment melts. On a plot of Zr/Nb vs. Th/Nb, lavas from along the magmatic front (esp. Guguan) show the high Zr/Nb expected for depleted mantle that is fluxed by hydrous fluids. W. Guguan and Guguan II show lower Zr/Nb and Th/Nb that trend towards sediment and MTSB. Surprisingly, there is little systematic variation in Sr/Nd and Pb/Ce across the chain. There is no systematic variation in Pb isotopic compositions across the arc. There is a marked gradient in 87Sr/86Sr, decreasing from ~0.7035 along the magmatic front to 0.7032 for W. Guguan and 0.70317 for Guguan II. These values approach the mean of 0.70291+/-0.00015 found for MTSB. 143Nd/144Nd also decreases slightly, but 176Hf/177Hf decreases slightly from the magmatic front to the rear. Coupled isotopic and trace element variations are difficult to reconcile with suggestions that cross-arc variations result from increasing participation of sediment melt with distance from the magmatic front.
Inference and Hierarchical Modeling in the Social Sciences.
ERIC Educational Resources Information Center
Draper, David
1995-01-01
The use of hierarchical models in social science research is discussed, with emphasis on causal inference and consideration of the limitations of hierarchical models. The increased use of Gibbs sampling and other Markov-chain Monte Carlo methods in the application of hierarchical models is recommended. (SLD)
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data for yearling and subyearling Chinook salmon and juvenile steelhead were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the information collected at McNary Dam was in the form of three-dimensional tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and test configurations of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting three-dimensional results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we investigated the feasibility of using a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis is one way that can be used to summarize numerically the behavior of fish in the forebay. Numerically summarizing the behavior of juvenile salmonids in the forebay of McNary Dam using the Markov chain analysis allowed us to confirm what had been previously summarized using visualization software. For example, proportions of yearling and subyearling Chinook salmon passing the three powerhouse areas was often greater in the southern and middle areas, compared to the northern area. The opposite generally was observed for steelhead. Results of this analysis also allowed us to confirm and quantify the extent of milling behavior that had been observed for steelhead. For fish that were first detected in the powerhouse region, less than 0.10 of the steelhead, on average, passed within each of the powerhouse areas. Instead, steelhead transitioned to adjoining areas in the
Metrics for Labeled Markov Systems
NASA Technical Reports Server (NTRS)
Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash
1999-01-01
Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.
Lie Markov models with purine/pyrimidine symmetry.
Fernández-Sánchez, Jesús; Sumner, Jeremy G; Jarvis, Peter D; Woodhams, Michael D
2015-03-01
Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with time-dependent rates satisfying the same constraints. It is then useful to require that, under some time restrictions, there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models" which, as we will show, are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines-that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra.
Kim, Jaiseung
2011-04-01
We have made a Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f{sub NL}) using the WMAP bispectrum and power spectrum. In our analysis, we have simultaneously constrained f{sub NL} and cosmological parameters so that the uncertainties of cosmological parameters can properly propagate into the f{sub NL} estimation. Investigating the parameter likelihoods deduced from MCMC samples, we find slight deviation from Gaussian shape, which makes a Fisher matrix estimation less accurate. Therefore, we have estimated the confidence interval of f{sub NL} by exploring the parameter likelihood without using the Fisher matrix. We find that the best-fit values of our analysis make a good agreement with other results, but the confidence interval is slightly different.
NASA Astrophysics Data System (ADS)
Saika, Yohei
2008-02-01
On the basis of statistical mechanics of the Q-Ising model we formulate the problem of inverse-halftoning for the halftone image which is obtained by the error diffusion method using the Floyd-Steinburg and two weight kernels. Then using the Markov-Chain Monte Carlo simulation both for a set of the snapshots of the Q-Ising model and a gray-level standard image, we estimate the performance of our method based on the mean square error and the edge structures observed both in the halftone image and reconstructed images, such as the edge length and the gradient of the gray-level. We clarify that our method reconstructs the gray-level image from the halftone image by suppressing the gradient of the gray-level on the edges embedded in the halftone image and by removing a part of the edges if we appropriately set parameters of our model.
2012-01-01
Background GEE and mixed models are powerful tools to compare treatment effects in longitudinal smoking cessation trials. However, they are not capable of assessing the relapse (from abstinent back to smoking) simultaneously with cessation, which can be studied by transition models. Methods We apply a first-order Markov chain model to analyze the transition of smoking status measured every 6 months in a 2-year randomized smoking cessation trial, and to identify what factors are associated with the transition from smoking to abstinent and from abstinent to smoking. Missing values due to non-response are assumed non-ignorable and handled by the selection modeling approach. Results Smokers receiving high-intensity disease management (HDM), of male gender, lower daily cigarette consumption, higher motivation and confidence to quit, and having serious attempts to quit were more likely to become abstinent (OR = 1.48, 1.66, 1.03, 1.15, 1.09 and 1.34, respectively) in the next 6 months. Among those who were abstinent, lower income and stronger nicotine dependence (OR = 1.72 for ≤ vs. > 40 K and OR = 1.75 for first cigarette ≤ vs. > 5 min) were more likely to have relapse in the next 6 months. Conclusions Markov chain models allow investigation of dynamic smoking-abstinence behavior and suggest that relapse is influenced by different factors than cessation. The knowledge of treatments and covariates in transitions in both directions may provide guidance for designing more effective interventions on smoking cessation and relapse prevention. Trial Registration clinicaltrials.gov identifier: NCT00440115 PMID:22770436
Twelve years of succession on sandy substrates in a post-mining landscape: a Markov chain analysis.
Baasch, Annett; Tischew, Sabine; Bruelheide, Helge
2010-06-01
Knowledge of succession rates and pathways is crucial for devising restoration strategies for highly disturbed ecosystems such as surface-mined land. As these processes have often only been described in qualitative terms, we used Markov models to quantify transitions between successional stages. However, Markov models are often considered not attractive for some reasons, such as model assumptions (e.g., stationarity in space and time, or the high expenditure of time required to estimate successional transitions in the field). Here we present a solution for converting multivariate ecological time series into transition matrices and demonstrate the applicability of this approach for a data set that resulted from monitoring the succession of sandy dry grassland in a post-mining landscape. We analyzed five transition matrices, four one-step matrices referring to specific periods of transition (1995-1998, 1998-2001, 2001-2004, 2004-2007), and one matrix for the whole study period (stationary model, 1995-2007). Finally, the stationary model was enhanced to a partly time-variable model. Applying the stationary and the time-variable models, we started a prediction well outside our calibration period, beginning with 100% bare soil in 1974 as the known start of the succession, and generated the coverage of 12 predefined vegetation types in three-year intervals. Transitions among vegetation types changed significantly in space and over time. While the probability of colonization was almost constant over time, the replacement rate tended to increase, indicating that the speed of succession accelerated with time or fluctuations became stronger. The predictions of both models agreed surprisingly well with the vegetation data observed more than two decades later. This shows that our dry grassland succession in a post-mining landscape can be adequately described by comparably simple types of Markov models, although some model assumptions have not been fulfilled and within
Twelve years of succession on sandy substrates in a post-mining landscape: a Markov chain analysis.
Baasch, Annett; Tischew, Sabine; Bruelheide, Helge
2010-06-01
Knowledge of succession rates and pathways is crucial for devising restoration strategies for highly disturbed ecosystems such as surface-mined land. As these processes have often only been described in qualitative terms, we used Markov models to quantify transitions between successional stages. However, Markov models are often considered not attractive for some reasons, such as model assumptions (e.g., stationarity in space and time, or the high expenditure of time required to estimate successional transitions in the field). Here we present a solution for converting multivariate ecological time series into transition matrices and demonstrate the applicability of this approach for a data set that resulted from monitoring the succession of sandy dry grassland in a post-mining landscape. We analyzed five transition matrices, four one-step matrices referring to specific periods of transition (1995-1998, 1998-2001, 2001-2004, 2004-2007), and one matrix for the whole study period (stationary model, 1995-2007). Finally, the stationary model was enhanced to a partly time-variable model. Applying the stationary and the time-variable models, we started a prediction well outside our calibration period, beginning with 100% bare soil in 1974 as the known start of the succession, and generated the coverage of 12 predefined vegetation types in three-year intervals. Transitions among vegetation types changed significantly in space and over time. While the probability of colonization was almost constant over time, the replacement rate tended to increase, indicating that the speed of succession accelerated with time or fluctuations became stronger. The predictions of both models agreed surprisingly well with the vegetation data observed more than two decades later. This shows that our dry grassland succession in a post-mining landscape can be adequately described by comparably simple types of Markov models, although some model assumptions have not been fulfilled and within
Forward-Chaining Versus A Graph Approach As The Inference Engine In Expert Systems
NASA Astrophysics Data System (ADS)
Neapolitan, Richard E.
1986-03-01
Rule-based expert systems are those in which a certain number of IF-THEN rules are assumed to be true. Based on the verity of some assertions, the rules deduce as many new conclusions as possible. A standard technique used to make these deductions is forward-chaining. In forward-chaining, the program or 'inference engine' cycles through the rules. At each rule, the premises for the rule are checked against the current true assertions. If all the premises are found, the conclusion is added to the list of true assertions. At that point it is necessary to start over at the first rule, since the new conclusion may be a premise in a rule already checked. Therefore, each time a new conclusion is deduced it is necessary to start the rule checking procedure over. This process continues until no new conclusions are added and the end of the list of rules is reached. The above process, although quite costly in terms of CPU cycles due to the necessity of repeatedly starting the process over, is necessary if the rules contain 'pattern variables'. An example of such a rule is, 'IF X IS A BACTERIA, THEN X CAN BE TREATED WITH ANTIBIOTICS'. Since the rule can lead to conclusions for many values of X, it is necessary to check each premise in the rule against every true assertion producing an association list to be used in the checking of the next premise. However, if the rule does not contain variable data, as is the case in many current expert systems, then a rule can lead to only one conclusion. In this case, the rules can be stored in a graph, and the true assertions in an assertion list. The assertion list is traversed only once; at each assertion a premise is triggered in all the rules which have that assertion as a premise. When all premises for a rule trigger, the rule's conclusion is added to the END of the list of assertions. It must be added at the end so that it will eventually be used to make further deductions. In the current paper, the two methods are described in
Raberto, Marco; Rapallo, Fabio; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the valuable information collected at McNary Dam was in the form of three-dimensional (hereafter referred to as 3-D) tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and testing of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting 3-D results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we used a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis allowed us to numerically summarize the behavior of fish in the forebay. This report is the second report published in 2012 that uses this analytical method. The first report included only fish released as part of the annual studies conducted at McNary Dam. This second report includes sockeye salmon that were released as part of studies conducted by the Chelan and Grant County Public Utility Districts at mid-Columbia River dams. The studies conducted in the mid-Columbia used the same transmitters as were used for McNary Dam studies, but transmitter pulse width was different between studies. Additionally, no passive integrated transponder tags were implanted in sockeye salmon. Differences in transmitter pulse width resulted in lower detection probabilities for sockeye salmon at McNary Dam. The absence of passive integrated transponder tags prevented us from determining if fish passed the powerhouse through the juvenile bypass system (JBS) or turbines. To
The infinite hidden Markov random field model.
Chatzis, Sotirios P; Tsechpenakis, Gabriel
2010-06-01
Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.
Hiebeler, David E; Millett, Nicholas E
2011-06-21
We investigate a spatial lattice model of a population employing dispersal to nearest and second-nearest neighbors, as well as long-distance dispersal across the landscape. The model is studied via stochastic spatial simulations, ordinary pair approximation, and triplet approximation. The latter method, which uses the probabilities of state configurations of contiguous blocks of three sites as its state variables, is demonstrated to be greatly superior to pair approximations for estimating spatial correlation information at various scales. Correlations between pairs of sites separated by arbitrary distances are estimated by constructing spatial Markov processes using the information from both approximations. These correlations demonstrate why pair approximation misses basic qualitative features of the model, such as decreasing population density as a large proportion of offspring are dropped on second-nearest neighbors, and why triplet approximation is able to include them. Analytical and numerical results show that, excluding long-distance dispersal, the initial growth rate of an invading population is maximized and the equilibrium population density is also roughly maximized when the population spreads its offspring evenly over nearest and second-nearest neighboring sites.
Sacks-Davis, Rachel; McBryde, Emma; Grebely, Jason; Hellard, Margaret; Vickerman, Peter
2015-03-01
Hepatitis C virus (HCV) reinfection rates are probably underestimated due to reinfection episodes occurring between study visits. A Markov model of HCV reinfection and spontaneous clearance was fitted to empirical data. Bayesian post-estimation was used to project reinfection rates, reinfection spontaneous clearance probability and duration of reinfection. Uniform prior probability distributions were assumed for reinfection rate (more than 0), spontaneous clearance probability (0-1) and duration (0.25-6.00 months). Model estimates were 104 per 100 person-years (95% CrI: 21-344), 0.84 (95% CrI: 0.59-0.98) and 1.3 months (95% CrI: 0.3-4.1) for reinfection rate, spontaneous clearance probability and duration, respectively. Simulation studies were used to assess model validity, demonstrating that the Bayesian model estimates provided useful information about the possible sources and magnitude of bias in epidemiological estimates of reinfection rates, probability of reinfection clearance and duration or reinfection. The quality of the Bayesian estimates improved for larger samples and shorter test intervals. Uncertainty in model estimates notwithstanding, findings suggest that HCV reinfections frequently and quickly result in spontaneous clearance, with many reinfection events going unobserved. PMID:25589564
Sacks-Davis, Rachel; McBryde, Emma; Grebely, Jason; Hellard, Margaret; Vickerman, Peter
2015-01-01
Hepatitis C virus (HCV) reinfection rates are probably underestimated due to reinfection episodes occurring between study visits. A Markov model of HCV reinfection and spontaneous clearance was fitted to empirical data. Bayesian post-estimation was used to project reinfection rates, reinfection spontaneous clearance probability and duration of reinfection. Uniform prior probability distributions were assumed for reinfection rate (more than 0), spontaneous clearance probability (0–1) and duration (0.25–6.00 months). Model estimates were 104 per 100 person-years (95% CrI: 21–344), 0.84 (95% CrI: 0.59–0.98) and 1.3 months (95% CrI: 0.3–4.1) for reinfection rate, spontaneous clearance probability and duration, respectively. Simulation studies were used to assess model validity, demonstrating that the Bayesian model estimates provided useful information about the possible sources and magnitude of bias in epidemiological estimates of reinfection rates, probability of reinfection clearance and duration or reinfection. The quality of the Bayesian estimates improved for larger samples and shorter test intervals. Uncertainty in model estimates notwithstanding, findings suggest that HCV reinfections frequently and quickly result in spontaneous clearance, with many reinfection events going unobserved. PMID:25589564
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data for yearling and subyearling Chinook salmon and juvenile steelhead were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the information collected at McNary Dam was in the form of three-dimensional tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and test configurations of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting three-dimensional results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we investigated the feasibility of using a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis is one way that can be used to summarize numerically the behavior of fish in the forebay. Numerically summarizing the behavior of juvenile salmonids in the forebay of McNary Dam using the Markov chain analysis allowed us to confirm what had been previously summarized using visualization software. For example, proportions of yearling and subyearling Chinook salmon passing the three powerhouse areas was often greater in the southern and middle areas, compared to the northern area. The opposite generally was observed for steelhead. Results of this analysis also allowed us to confirm and quantify the extent of milling behavior that had been observed for steelhead. For fish that were first detected in the powerhouse region, less than 0.10 of the steelhead, on average, passed within each of the powerhouse areas. Instead, steelhead transitioned to adjoining areas in the
NASA Astrophysics Data System (ADS)
Hasimoto Fengler, Felipe; Leite de Moraes, Jener Fernando; Irio Ribeiro, Admilson; Peche Filho, Afonso; Araujo de Medeiros, Gerson; Baldin Damame, Desirée; Márcia Longo, Regina
2015-04-01
In Brazil is common practice the concurrency of large urban centers water catchment in distant sites. There's no policy to preserve strategic springs in the urban territory. Thus, rural areas, located in the surrounds of municipals, usually provide water and others environment services to the population that reside on cities. The Jundiaí-Mirim river basin, located in the most urbanized state in Brazil, São Paulo, composes an interesting example of this situation. It is located in a rural area near large urban centers, with large industrial parks, near the capital of state. As result of expansion of the cities on its surrounds their lands have had a historic of monetary valorization, making its territories attractive to the housing market. Consequently, the region has an intense process of urbanization that resulted in an increasing environmental disturbance in the areas of natural vegetation. In the other hand, the watershed is the principal water supplier of Jundiaí city, and houses forest remaining of an important Biome in Brazil, the Atlantic Rain Forest. Given the need to preserve its water production capacity and the forest remnants there, this study modeled the environmental quality of forest fragments through indicators of disturbance and evaluated the changes that occur between 1972 and 2013 using the Markov Chain model. The environment quality was determined by nine indicators of environmental disturbance (distance of urban areas, roads, edge land use, size, distance of others forest fragments, land capacity of use, watershed forest cover, number of forest fragments in the watersheds, shape of the forest fragment), obtained by techniques of Geoprocessing, and integrated by Multicriteria Analysis. The Markov Chain model showed a constant tendency of deteriorating in natural vegetation environmental quality, attributed to the intense process of occupation of the river basin. The results showed a historical trend of transformation in forest fragments with
NASA Technical Reports Server (NTRS)
Panday, Prajjwal K.; Williams, Christopher A.; Frey, Karen E.; Brown, Molly E.
2013-01-01
Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree
Decentralized learning in Markov games.
Vrancx, Peter; Verbeeck, Katja; Nowé, Ann
2008-08-01
Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.
Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.
2008-05-15
We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive global information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.
Stroeer, Alexander; Veitch, John
2009-09-15
The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme-mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals ''out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.
Begun, Alexander; Morbach, Stephan; Rümenapf, Gerhard; Icks, Andrea
2016-01-01
The diabetic foot is a lifelong disease. The longer patients with diabetes and foot ulcers are observed, the higher the likelihood that they will develop comorbidities that adversely influence ulcer recurrence, amputation and survival (for example peripheral arterial disease, renal failure or ischaemic heart disease). The purpose of our study was to quantify person and limb-related disease progression and the time-dependent influence of any associated factors (present at baseline or appearing during observation) based on which effective prevention and/or treatment strategies could be developed. Using a nine-state continuous-time Markov chain model with time-dependent risk factors, all living patients were divided into eight groups based on their ulceration (previous or current) and previous amputation (none, minor or major) status. State nine is an absorbing state (death). If all transitions are fully observable, this model can be decomposed into eight submodels, which can be analyzed using the methods of survival analysis for competing risks. The dependencies of the risk factors (covariates) were included in the submodels using Cox-like regression. The transition intensities and relative risks for covariates were calculated from long-term data of patients with diabetic foot ulcers collected in a single specialized center in North-Rhine Westphalia (Germany). The detected estimates were in line with previously published, but scarce, data. Together with the interesting new results obtained, this indicates that the proposed model may be useful for studying disease progression in larger samples of patients with diabetic foot ulcers.
Chen, Jinsong; Hubbard, Susan; Rubin, Yoram; Murray, Christopher J.; Roden, Eric E.; Majer, Ernest L.
2004-12-22
The paper demonstrates the use of ground-penetrating radar (GPR) tomographic data for estimating extractable Fe(II) and Fe(III) concentrations using a Markov chain Monte Carlo (MCMC) approach, based on data collected at the DOE South Oyster Bacterial Transport Site in Virginia. Analysis of multidimensional data including physical, geophysical, geochemical, and hydrogeological measurements collected at the site shows that GPR attenuation and lithofacies are most informative for the estimation. A statistical model is developed for integrating the GPR attenuation and lithofacies data. In the model, lithofacies is considered as a spatially correlated random variable and petrophysical models for linking GPR attenuation to geochemical parameters were derived from data at and near boreholes. Extractable Fe(II) and Fe(III) concentrations at each pixel between boreholes are estimated by conditioning to the co-located GPR data and the lithofacies measurements along boreholes through spatial correlation. Cross-validation results show that geophysical data, constrained by lithofacies, provided information about extractable Fe(II) and Fe(III) concentration in a minimally invasive manner and with a resolution unparalleled by other geochemical characterization methods. The developed model is effective and flexible, and should be applicable for estimating other geochemical parameters at other sites.
Chen, Jinsong; Hubbard, Susan; Rubin, Yoram; Murray, Chris; Roden, Eric; Majer, Ernest
2003-11-18
The spatial distribution of field-scale geochemical parameters, such as extractable Fe(II) and Fe(III), influences microbial processes and thus the efficacy of bioremediation. Because traditional characterization of those parameters is invasive and laborious, it is rarely performed sufficiently at the field-scale. Since both geochemical and geophysical parameters often correlate to some common physical properties (such as lithofacies), we investigated the utility of tomographic radar attenuation data for improving estimation of geochemical parameters using a Markov Chain Monte Carlo (MCMC) approach. The data used in this study included physical, geophysical, and geochemical measurements collected in and between several boreholes at the DOE South Oyster Bacterial Transport Site in Virginia. Results show that geophysical data, constrained by physical data, provided field-scale information about extractable Fe(II) and Fe(III) in a minimally invasive manner and with a resolution unparalleled by other geochemical characterization methods. This study presents our estimation framework for estimating Fe(II) and Fe(III), and its application to a specific site. Our hypothesis--that geochemical parameters and geophysical attributes can be linked through their mutual dependence on physical properties--should be applicable for estimating other geochemical parameters at other sites.
NASA Astrophysics Data System (ADS)
Bacani, Vitor Matheus; Sakamoto, Arnaldo Yoso; Quénol, Hervé; Vannier, Clémence; Corgne, Samuel
2016-01-01
The dynamics of land use/land cover change in the Lower Nhecolândia wetland are marked by deforestation for pasture expansion, resulting in a real threat to the ecological stability. The aim of our work was to analyze the spatial distribution of land cover changes in the Lower Nhecolândia from 1985 to 2013 and to predict changes in trends for 2040. The mapping of land cover changes was developed using Landsat satellite images of 1985, 1999, 2007, and 2013, based on geographic object-based image analysis approach. This study uses integrated Markov chains and cellular automata modeling and multicriteria evaluation techniques to produce transition probability maps and describe the trajectory analysis methodology to construct a continuity of spatial and temporal changes for the wetland. The results of the multitemporal change detection classification show that, from 1985 to 2013, the forest woodland decreased by 6.89% and the grassland class increased by 18.29%. On the other hand, all water bodies showed a reducing trend, while the bare soil class increased compared to 1985, but did not present a regular trend of increase or decrease. From the present day, the trend for the future is a reduction of almost 6.4% by 2040. We found that deforestation actions will be concentrated in the areas with the highest concentration of saline lakes, constituting a serious threat to the natural functioning of this environmental system.
Ma, Junsheng; Chan, Wenyaw; Tsai, Chu-Lin; Xiong, Momiao; Tilley, Barbara C
2015-11-30
Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. PMID:26123093
Kadoura, Ahmad; Sun, Shuyu Salama, Amgad
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.
NASA Astrophysics Data System (ADS)
Berradja, Khadidja; Boughanmi, Nabil
2016-09-01
In dynamic cardiac PET FDG studies the assessment of myocardial metabolic rate of glucose (MMRG) requires the knowledge of the blood input function (IF). IF can be obtained by manual or automatic blood sampling and cross calibrated with PET. These procedures are cumbersome, invasive and generate uncertainties. The IF is contaminated by spillover of radioactivity from the adjacent myocardium and this could cause important error in the estimated MMRG. In this study, we show that the IF can be extracted from the images in a rat heart study with 18F-fluorodeoxyglucose (18F-FDG) by means of Independent Component Analysis (ICA) based on Bayesian theory and Markov Chain Monte Carlo (MCMC) sampling method (BICA). Images of the heart from rats were acquired with the Sherbrooke small animal PET scanner. A region of interest (ROI) was drawn around the rat image and decomposed into blood and tissue using BICA. The Statistical study showed that there is a significant difference (p < 0.05) between MMRG obtained with IF extracted by BICA with respect to IF extracted from measured images corrupted with spillover.
Spahn, Philipp N.; Hansen, Anders H.; Hansen, Henning G.; Arnsdorf, Johnny; Kildegaard, Helene F.; Lewis, Nathan E.
2016-01-01
Glycosylation is a critical quality attribute of most recombinant biotherapeutics. Consequently, drug development requires careful control of glycoforms to meet bioactivity and biosafety requirements. However, glycoengineering can be extraordinarily difficult given the complex reaction networks underlying glycosylation and the vast number of different glycans that can be synthesized in a host cell. Computational modeling offers an intriguing option to rationally guide glycoengineering, but the high parametric demands of current modeling approaches pose challenges to their application. Here we present a novel low-parameter approach to describe glycosylation using flux-balance and Markov chain modeling. The model recapitulates the biological complexity of glycosylation, but does not require user-provided kinetic information. We use this method to predict and experimentally validate glycoprofiles on EPO, IgG as well as the endogenous secretome following glycosyltransferase knock-out in different Chinese hamster ovary (CHO) cell lines. Our approach offers a flexible and user-friendly platform that can serve as a basis for powerful computational engineering efforts in mammalian cell factories for biopharmaceutical production. PMID:26537759
Adams, Noah S.; Hatton, Tyson W.
2012-01-01
Passage and survival data were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the valuable information collected at McNary Dam was in the form of three-dimensional (hereafter referred to as 3-D) tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and testing of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting 3-D results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we used a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis allowed us to numerically summarize the behavior of fish in the forebay. This report is the second report published in 2012 that uses this analytical method. The first report included only fish released as part of the annual studies conducted at McNary Dam. This second report includes sockeye salmon that were released as part of studies conducted by the Chelan and Grant County Public Utility Districts at mid-Columbia River dams. The studies conducted in the mid-Columbia used the same transmitters as were used for McNary Dam studies, but transmitter pulse width was different between studies. Additionally, no passive integrated transponder tags were implanted in sockeye salmon. Differences in transmitter pulse width resulted in lower detection probabilities for sockeye salmon at McNary Dam. The absence of passive integrated transponder tags prevented us from determining if fish passed the powerhouse through the juvenile bypass system (JBS) or turbines. To
NASA Astrophysics Data System (ADS)
Peng, C.; Zhou, X.
2015-12-01
To reduce simulation uncertainties due to inaccurate model parameters, the Markov Chain Monte Carlo (MCMC) method was applied in this study to improve the estimations of four key parameters used in the process-based ecosystem model of TRIPLEX-FLUX. These four key parameters include a maximum photosynthetic carboxylation rate of 25°C (Vcmax), an electron transport (Jmax) light-saturated rate within the photosynthetic carbon reduction cycle of leaves, a coefficient of stomatal conductance (m), and a reference respiration rate of 10ºC (R10). Seven forest flux tower sites located across North America were used to investigate and facilitate understanding of the daily variation in model parameters for three deciduous forests, three evergreen temperate forests, and one evergreen boreal forest. Eddy covariance CO2 exchange measurements were assimilated to optimize the parameters in the year 2006. After parameter optimization and adjustment took place, net ecosystem production prediction significantly improved (by approximately 25%) compared to the CO2 flux measurements taken at the seven forest ecosystem sites.
Karalidi, Theodora; Apai, Dániel; Schneider, Glenn; Hanson, Jake R.; Pasachoff, Jay M.
2015-11-20
Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of a giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR.
Infinite Factorial Unbounded-State Hidden Markov Model.
Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando
2016-09-01
There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markovmodels (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem. PMID:26571511
Zipf exponent of trajectory distribution in the hidden Markov model
NASA Astrophysics Data System (ADS)
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Stochastic algorithms for Markov models estimation with intermittent missing data.
Deltour, I; Richardson, S; Le Hesran, J Y
1999-06-01
Multistate Markov models are frequently used to characterize disease processes, but their estimation from longitudinal data is often hampered by complex patterns of incompleteness. Two algorithms for estimating Markov chain models in the case of intermittent missing data in longitudinal studies, a stochastic EM algorithm and the Gibbs sampler, are described. The first can be viewed as a random perturbation of the EM algorithm and is appropriate when the M step is straightforward but the E step is computationally burdensome. It leads to a good approximation of the maximum likelihood estimates. The Gibbs sampler is used for a full Bayesian inference. The performances of the two algorithms are illustrated on two simulated data sets. A motivating example concerned with the modelling of the evolution of parasitemia by Plasmodium falciparum (malaria) in a cohort of 105 young children in Cameroon is described and briefly analyzed.
Aberer, Andre J; Stamatakis, Alexandros; Ronquist, Fredrik
2016-01-01
Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a [Formula: see text] distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes. PMID:26231183
NASA Technical Reports Server (NTRS)
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
BIE: Bayesian Inference Engine
NASA Astrophysics Data System (ADS)
Weinberg, Martin D.
2013-12-01
The Bayesian Inference Engine (BIE) is an object-oriented library of tools written in C++ designed explicitly to enable Bayesian update and model comparison for astronomical problems. To facilitate "what if" exploration, BIE provides a command line interface (written with Bison and Flex) to run input scripts. The output of the code is a simulation of the Bayesian posterior distribution from which summary statistics e.g. by taking moments, or determine confidence intervals and so forth, can be determined. All of these quantities are fundamentally integrals and the Markov Chain approach produces variates heta distributed according to P( heta|D) so moments are trivially obtained by summing of the ensemble of variates.
Begun, Alexander; Morbach, Stephan; Rümenapf, Gerhard; Icks, Andrea
2016-01-01
The diabetic foot is a lifelong disease. The longer patients with diabetes and foot ulcers are observed, the higher the likelihood that they will develop comorbidities that adversely influence ulcer recurrence, amputation and survival (for example peripheral arterial disease, renal failure or ischaemic heart disease). The purpose of our study was to quantify person and limb-related disease progression and the time-dependent influence of any associated factors (present at baseline or appearing during observation) based on which effective prevention and/or treatment strategies could be developed. Using a nine-state continuous-time Markov chain model with time-dependent risk factors, all living patients were divided into eight groups based on their ulceration (previous or current) and previous amputation (none, minor or major) status. State nine is an absorbing state (death). If all transitions are fully observable, this model can be decomposed into eight submodels, which can be analyzed using the methods of survival analysis for competing risks. The dependencies of the risk factors (covariates) were included in the submodels using Cox-like regression. The transition intensities and relative risks for covariates were calculated from long-term data of patients with diabetic foot ulcers collected in a single specialized center in North-Rhine Westphalia (Germany). The detected estimates were in line with previously published, but scarce, data. Together with the interesting new results obtained, this indicates that the proposed model may be useful for studying disease progression in larger samples of patients with diabetic foot ulcers. PMID:26814723
Begun, Alexander; Morbach, Stephan; Rümenapf, Gerhard; Icks, Andrea
2016-01-01
The diabetic foot is a lifelong disease. The longer patients with diabetes and foot ulcers are observed, the higher the likelihood that they will develop comorbidities that adversely influence ulcer recurrence, amputation and survival (for example peripheral arterial disease, renal failure or ischaemic heart disease). The purpose of our study was to quantify person and limb-related disease progression and the time-dependent influence of any associated factors (present at baseline or appearing during observation) based on which effective prevention and/or treatment strategies could be developed. Using a nine-state continuous-time Markov chain model with time-dependent risk factors, all living patients were divided into eight groups based on their ulceration (previous or current) and previous amputation (none, minor or major) status. State nine is an absorbing state (death). If all transitions are fully observable, this model can be decomposed into eight submodels, which can be analyzed using the methods of survival analysis for competing risks. The dependencies of the risk factors (covariates) were included in the submodels using Cox-like regression. The transition intensities and relative risks for covariates were calculated from long-term data of patients with diabetic foot ulcers collected in a single specialized center in North-Rhine Westphalia (Germany). The detected estimates were in line with previously published, but scarce, data. Together with the interesting new results obtained, this indicates that the proposed model may be useful for studying disease progression in larger samples of patients with diabetic foot ulcers. PMID:26814723
Wang, Huiyuan; Mo, H. J.; Yang, Xiaohu; Lin, W. P.; Jing, Y. P.
2014-10-10
Simulating the evolution of the local universe is important for studying galaxies and the intergalactic medium in a way free of cosmic variance. Here we present a method to reconstruct the initial linear density field from an input nonlinear density field, employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics. The HMC+PM method is applied to cosmological simulations, and the reconstructed linear density fields are then evolved to the present day with N-body simulations. These constrained simulations accurately reproduce both the amplitudes and phases of the input simulations at various z. Using a PM model with a grid cell size of 0.75 h {sup –1} Mpc and 40 time steps in the HMC can recover more than half of the phase information down to a scale k ∼ 0.85 h Mpc{sup –1} at high z and to k ∼ 3.4 h Mpc{sup –1} at z = 0, which represents a significant improvement over similar reconstruction models in the literature, and indicates that our model can reconstruct the formation histories of cosmic structures over a large dynamical range. Adopting PM models with higher spatial and temporal resolutions yields even better reconstructions, suggesting that our method is limited more by the availability of computer resource than by principle. Dynamic models of structure evolution adopted in many earlier investigations can induce non-Gaussianity in the reconstructed linear density field, which in turn can cause large systematic deviations in the predicted halo mass function. Such deviations are greatly reduced or absent in our reconstruction.
NASA Astrophysics Data System (ADS)
Chaudhuri, Sutapa; Goswami, Sayantika; Das, Debanjana; Middey, Anirban
2014-05-01
Forecasting summer monsoon rainfall with precision becomes crucial for the farmers to plan for harvesting in a country like India where the national economy is mostly based on regional agriculture. The forecast of monsoon rainfall based on artificial neural network is a well-researched problem. In the present study, the meta-heuristic ant colony optimization (ACO) technique is implemented to forecast the amount of summer monsoon rainfall for the next day over Kolkata (22.6°N, 88.4°E), India. The ACO technique belongs to swarm intelligence and simulates the decision-making processes of ant colony similar to other adaptive learning techniques. ACO technique takes inspiration from the foraging behaviour of some ant species. The ants deposit pheromone on the ground in order to mark a favourable path that should be followed by other members of the colony. A range of rainfall amount replicating the pheromone concentration is evaluated during the summer monsoon season. The maximum amount of rainfall during summer monsoon season (June—September) is observed to be within the range of 7.5-35 mm during the period from 1998 to 2007, which is in the range 4 category set by the India Meteorological Department (IMD). The result reveals that the accuracy in forecasting the amount of rainfall for the next day during the summer monsoon season using ACO technique is 95 % where as the forecast accuracy is 83 % with Markov chain model (MCM). The forecast through ACO and MCM are compared with other existing models and validated with IMD observations from 2008 to 2012.
Fransson, Martin Niclas; Barregard, Lars; Sallsten, Gerd; Akerstrom, Magnus; Johanson, Gunnar
2014-10-01
The health effects of low-level chronic exposure to cadmium are increasingly recognized. To improve the risk assessment, it is essential to know the relation between cadmium intake, body burden, and biomarker levels of cadmium. We combined a physiologically-based toxicokinetic (PBTK) model for cadmium with a data set from healthy kidney donors to re-estimate the model parameters and to test the effects of gender and serum ferritin on systemic uptake. Cadmium levels in whole blood, blood plasma, kidney cortex, and urinary excretion from 82 men and women were used to calculate posterior distributions for model parameters using Markov-chain Monte Carlo analysis. For never- and ever-smokers combined, the daily systemic uptake was estimated at 0.0063 μg cadmium/kg body weight in men, with 35% increased uptake in women and a daily uptake of 1.2 μg for each pack-year per calendar year of smoking. The rate of urinary excretion from cadmium accumulated in the kidney was estimated at 0.000042 day(-1), corresponding to a half-life of 45 years in the kidneys. We have provided an improved model of cadmium kinetics. As the new parameter estimates derive from a single study with measurements in several compartments in each individual, these new estimates are likely to be more accurate than the previous ones where the data used originated from unrelated data sets. The estimated urinary excretion of cadmium accumulated in the kidneys was much lower than previous estimates, neglecting this finding may result in a marked under-prediction of the true kidney burden.
Eells, Samantha J.; Bharadwa, Kiran; McKinnell, James A.; Miller, Loren G.
2014-01-01
Background. Recurrent urinary tract infections (UTIs) are a common problem among women. However, comparative effectiveness strategies for managing recurrent UTIs are lacking. Methods. We performed a systematic literature review of management of women experiencing ≥3 UTIs per year. We then developed a Markov chain Monte Carlo model of recurrent UTI for each management strategy with ≥2 adequate trials published. We simulated a cohort that experienced 3 UTIs/year and a secondary cohort that experienced 8 UTIs/year. Model outcomes were treatment efficacy, patient and payer cost, and health-related quality of life. Results. Five strategies had ≥2 clinical trials published: (1) daily antibiotic (nitrofurantoin) prophylaxis; (2) daily estrogen prophylaxis; (3) daily cranberry prophylaxis; (4) acupuncture prophylaxis; and (5) symptomatic self-treatment. In the 3 UTIs/year model, nitrofurantoin prophylaxis was most effective, reducing the UTI rate to 0.4 UTIs/year, and the most expensive to the payer ($821/year). All other strategies resulted in payer cost savings but were less efficacious. Symptomatic self-treatment was the only strategy that resulted in patient cost savings, and was the most favorable strategy in term of cost per quality-adjusted life-year (QALY) gained. Conclusions. Daily antibiotic use is the most effective strategy for recurrent UTI prevention compared to daily cranberry pills, daily estrogen therapy, and acupuncture. Cost savings to payers and patients were seen for most regimens, and improvement in QALYs were seen with all. Our findings provide clinically meaningful data to guide the physician–patient partnership in determining a preferred method of prevention for this common clinical problem. PMID:24065333
Building Simple Hidden Markov Models. Classroom Notes
ERIC Educational Resources Information Center
Ching, Wai-Ki; Ng, Michael K.
2004-01-01
Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.
Geometric ergodicity of a hybrid sampler for Bayesian inference of phylogenetic branch lengths.
Spade, David A; Herbei, Radu; Kubatko, Laura S
2015-10-01
One of the fundamental goals in phylogenetics is to make inferences about the evolutionary pattern among a group of individuals, such as genes or species, using present-day genetic material. This pattern is represented by a phylogenetic tree, and as computational methods have caught up to the statistical theory, Bayesian methods of making inferences about phylogenetic trees have become increasingly popular. Bayesian inference of phylogenetic trees requires sampling from intractable probability distributions. Common methods of sampling from these distributions include Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods, and one way that both of these methods can proceed is by first simulating a tree topology and then taking a sample from the posterior distribution of the branch lengths given the tree topology and the data set. In many MCMC methods, it is difficult to verify that the underlying Markov chain is geometrically ergodic, and thus, it is necessary to rely on output-based convergence diagnostics in order to assess convergence on an ad hoc basis. These diagnostics suffer from several important limitations, so in an effort to circumvent these limitations, this work establishes geometric convergence for a particular Markov chain that is used to sample branch lengths under a fairly general class of nucleotide substitution models and provides a numerical method for estimating the time this Markov chain takes to converge.
Unmixing hyperspectral images using Markov random fields
Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves
2011-03-14
This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.
Generator estimation of Markov jump processes
NASA Astrophysics Data System (ADS)
Metzner, P.; Dittmer, E.; Jahnke, T.; Schütte, Ch.
2007-11-01
Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782-805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419-441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753-764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421-430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395-410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.
Allen, Bruce C; Hack, C Eric; Clewell, Harvey J
2007-08-01
A Bayesian approach, implemented using Markov Chain Monte Carlo (MCMC) analysis, was applied with a physiologically-based pharmacokinetic (PBPK) model of methylmercury (MeHg) to evaluate the variability of MeHg exposure in women of childbearing age in the U.S. population. The analysis made use of the newly available National Health and Nutrition Survey (NHANES) blood and hair mercury concentration data for women of age 16-49 years (sample size, 1,582). Bayesian analysis was performed to estimate the population variability in MeHg exposure (daily ingestion rate) implied by the variation in blood and hair concentrations of mercury in the NHANES database. The measured variability in the NHANES blood and hair data represents the result of a process that includes interindividual variation in exposure to MeHg and interindividual variation in the pharmacokinetics (distribution, clearance) of MeHg. The PBPK model includes a number of pharmacokinetic parameters (e.g., tissue volumes, partition coefficients, rate constants for metabolism and elimination) that can vary from individual to individual within the subpopulation of interest. Using MCMC analysis, it was possible to combine prior distributions of the PBPK model parameters with the NHANES blood and hair data, as well as with kinetic data from controlled human exposures to MeHg, to derive posterior distributions that refine the estimates of both the population exposure distribution and the pharmacokinetic parameters. In general, based on the populations surveyed by NHANES, the results of the MCMC analysis indicate that a small fraction, less than 1%, of the U.S. population of women of childbearing age may have mercury exposures greater than the EPA RfD for MeHg of 0.1 microg/kg/day, and that there are few, if any, exposures greater than the ATSDR MRL of 0.3 microg/kg/day. The analysis also indicates that typical exposures may be greater than previously estimated from food consumption surveys, but that the variability
NASA Astrophysics Data System (ADS)
Putze, A.; Derome, L.; Maurin, D.; Perotto, L.; Taillet, R.
2009-04-01
Context: Propagation of charged cosmic-rays in the Galaxy depends on the transport parameters, whose number can be large depending on the propagation model under scrutiny. A standard approach for determining these parameters is a manual scan, leading to an inefficient and incomplete coverage of the parameter space. Aims: In analyzing the data from forthcoming experiments, a more sophisticated strategy is required. An automated statistical tool is used, which enables a full coverage of the parameter space and provides a sound determination of the transport and source parameters. The uncertainties in these parameters are also derived. Methods: We implement a Markov Chain Monte Carlo (MCMC), which is well suited to multi-parameter determination. Its specificities (burn-in length, acceptance, and correlation length) are discussed in the context of cosmic-ray physics. Its capabilities and performances are explored in the phenomenologically well-understood Leaky-Box Model. Results: From a technical point of view, a trial function based on binary-space partitioning is found to be extremely efficient, allowing a simultaneous determination of up to nine parameters, including transport and source parameters, such as slope and abundances. Our best-fit model includes both a low energy cut-off and reacceleration, whose values are consistent with those found in diffusion models. A Kolmogorov spectrum for the diffusion slope (δ = 1/3) is excluded. The marginalised probability-density function for δ and α (the slope of the source spectra) are δ ≈ 0.55-0.60 and α ≈ 2.14-2.17, depending on the dataset used and the number of free parameters in the fit. All source-spectrum parameters (slope and abundances) are positively correlated among themselves and with the reacceleration strength, but are negatively correlated with the other propagation parameters. Conclusions: The MCMC is a practical and powerful tool for cosmic-ray physic analyses. It can be used to confirm hypotheses
Kalantari, A S; Cabrera, V E
2012-10-01
The objective of this study was to determine the effect of reproductive performance on dairy cattle herd value. Herd value was defined as the herd's average retention payoff (RPO). Individual cow RPO is the expected profit from keeping the cow compared with immediate replacement. First, a daily dynamic programming model was developed to calculate the RPO of all cow states in a herd. Second, a daily Markov chain model was applied to estimate the herd demographics. Finally, the herd value was calculated by aggregating the RPO of all cows in the herd. Cow states were described by 5 milk yield classes (76, 88, 100, 112, and 124% with respect to the average), 9 lactations, 750 d in milk, and 282 d in pregnancy. Five different reproductive programs were studied (RP1 to RP5). Reproductive program 1 used 100% timed artificial insemination (TAI; 42% conception rate for first TAI and 30% for second and later services) and the other programs combined TAI with estrus detection. The proportion of cows receiving artificial insemination after estrus detection ranged from 30 to 80%, and conception rate ranged from 25 to 35%. These 5 reproductive programs were categorized according to their 21-d pregnancy rate (21-d PR), which is an indication of the rate that eligible cows become pregnant every 21 d. The 21-d PR was 17% for RP1, 14% for RP2, 16% for RP3, 18% for RP4, and 20% for RP5. Results showed a positive relationship between 21-d PR and herd value. The most extreme herd value difference between 2 reproductive programs was $77/cow per yr for average milk yield (RP5 - RP2), $13/cow per yr for lowest milk yield (RP5 - RP1), and $160/cow per yr for highest milk yield (RP5 - RP2). Reproductive programs were ranked based on their calculated herd value. With the exception of the best reproductive program (RP5), all other programs showed some level of ranking change according to milk yield. The most dramatic ranking change was observed in RP1, which moved from being the worst ranked
NASA Astrophysics Data System (ADS)
Strunk, A.; Knudsen, M. F.; Larsen, N. K.; Egholm, D. L.; Jacobsen, B. H.
2015-12-01
Surface exposure dating with cosmogenic nuclides is a dating method under continuous development. It is particularly useful for dating ice-sheet fluctuations in glacial environments, which is essential to increase our understanding of past climate fluctuations and glacial dynamics. Constraining the landscape history in previously glaciated terrains may be difficult, however, due to unknown erosion rates and the presence of inherited nuclides. The potential use of cosmogenic nuclides in landscapes with a complex history of exposure and erosion is therefore often quite limited. In this study, we investigate the landscape history in eastern and western Greenland by applying a novel Markov Chain Monte Carlo (MCMC) inversion approach to the existing 10Be-26Al data from these regions. The new MCMC approach allows us to constrain the most likely landscape history based on comparisons between simulated and measured cosmogenic nuclide concentrations. It is a fundamental assumption of the model approach that the exposure history at the site/location can be divided into two distinct regimes: i) interglacial periods characterized by zero shielding due to overlying ice and a uniform interglacial erosion rate, and ii) glacial periods characterized by 100 % shielding and a uniform glacial erosion rate. We incorporate the exposure/burial history in the model framework by applying a threshold value to the global marine benthic d18O record and include the threshold value as a free model parameter, hereby taking into account global changes in climate. The other free parameters include the glacial and interglacial erosion rates as well as the timing of the Holocene deglaciation. The model essentially simulates numerous different landscape scenarios based on these four parameters and zooms in on the most plausible combination of model parameters. Here, we apply the MCMC-model to the concentrations of 10Be and 26Al measured in three previous studies of glacial fluctuations in Greenland
Destri, C.; Vega, H. J. de; Sanchez, N. G.
2008-02-15
We perform a Monte Carlo Markov chains (MCMC) analysis of the available cosmic microwave background (CMB) and large scale structure (LSS) data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the Ginsburg-Landau spirit with fourth degree trinomial potentials in the inflaton field {phi}. We derive explicit formulae and study in detail the spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations, and the running index dn{sub s}/dlnk. We use these analytic formulas as hard constraints on n{sub s} and r in the MCMC analysis. Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follows: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the {phi}{yields}-{phi} symmetry of the inflaton potentials both for new and for chaotic inflation. (ii) Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data. (iii) Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space. (iv) The chaotic symmetric trinomial potential is almost certainly ruled out (at 95% C.L.). In trinomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which resembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data. (vi) We find a lower bound for r within trinomial new inflation potentials: r>0.016(95%CL) and r>0.049(68%CL). (vii) The preferred new inflation trinomial potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: n{sub s}{approx_equal}0.958, r{approx_equal}0.055. This value
Dynamical inference of hidden biological populations
NASA Astrophysics Data System (ADS)
Luchinsky, D. G.; Smelyanskiy, V. N.; Millonas, M.; McClintock, P. V. E.
2008-10-01
Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.
Exact significance test for Markov order
NASA Astrophysics Data System (ADS)
Pethel, S. D.; Hahs, D. W.
2014-02-01
We describe an exact significance test of the null hypothesis that a Markov chain is nth order. The procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size. Surrogate data are generated using a novel algorithm that guarantees, per shot, a uniform sampling from the set of sequences that exactly match the nth order properties of the observed data. Using the test, the Markov order of Tel Aviv rainfall data is examined.
NASA Astrophysics Data System (ADS)
MacBean, Natasha; Disney, Mathias; Lewis, Philip; Ineson, Phil
2010-05-01
profile as a whole. We present results from an Observing System Simulation Experiment (OSSE) designed to investigate the impact of management and climate change on peatland carbon fluxes, as well as how observations from satellites may be able to constrain modeled carbon fluxes. We use an adapted version of the Carnegie-Ames-Stanford Approach (CASA) model (Potter et al., 1993) that includes a representation of methane dynamics (Potter, 1997). The model formulation is further modified to allow for assimilation of satellite observations of surface soil moisture and land surface temperature. The observations are used to update model estimates using a Metropolis Hastings Markov Chain Monte Carlo (MCMC) approach. We examine the effect of temporal frequency and precision of satellite observations with a view to establishing how, and at what level, such observations would make a significant improvement in model uncertainty. We compare this with the system characteristics of existing and future satellites. We believe this is the first attempt to assimilate surface soil moisture and land surface temperature into an ecosystem model that includes a full representation of CH4 flux. Bubier, J., and T. Moore (1994), An ecological perspective on methane emissions from northern wetlands, TREE, 9, 460-464. Charman, D. (2002), Peatlands and Environmental Change, JohnWiley and Sons, Ltd, England. Gorham, E. (1991), Northern peatlands: Role in the carbon cycle and probable responses to climatic warming, Ecological Applications, 1, 182-195. Lai, D. (2009), Methane dynamics in northern peatlands: A review, Pedosphere, 19, 409-421. Le Mer, J., and P. Roger (2001), Production, oxidation, emission and consumption of methane by soils: A review, European Journal of Soil Biology, 37, 25-50. Limpens, J., F. Berendse, J. Canadell, C. Freeman, J. Holden, N. Roulet, H. Rydin, and Potter, C. (1997), An ecosystem simulation model for methane production and emission from wetlands, Global Biogeochemical
Dorazio, R.M.; Johnson, F.A.
2003-01-01
Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.
On multitarget pairwise-Markov models
NASA Astrophysics Data System (ADS)
Mahler, Ronald
2015-05-01
Single- and multi-target tracking are both typically based on strong independence assumptions regarding both the target states and sensor measurements. In particular, both are theoretically based on the hidden Markov chain (HMC) model. That is, the target process is a Markov chain that is observed by an independent observation process. Since HMC assumptions are invalid in many practical applications, the pairwise Markov chain (PMC) model has been proposed as a way to weaken those assumptions. In this paper it is shown that the PMC model can be directly generalized to multitarget problems. Since the resulting tracking filters are computationally intractable, the paper investigates generalizations of the cardinalized probability hypothesis density (CPHD) filter to applications with PMC models.
Computationally efficient Bayesian inference for inverse problems.
Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.
2007-10-01
Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems - representing indirect estimation of model parameters, inputs, or structural components - can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field. We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.
A new approach to simulating stream isotope dynamics using Markov switching autoregressive models
NASA Astrophysics Data System (ADS)
Birkel, Christian; Paroli, Roberta; Spezia, Luigi; Dunn, Sarah M.; Tetzlaff, Doerthe; Soulsby, Chris
2012-09-01
In this study we applied Markov switching autoregressive models (MSARMs) as a proof-of-concept to analyze the temporal dynamics and statistical characteristics of the time series of two conservative water isotopes, deuterium (δ2H) and oxygen-18 (δ18O), in daily stream water samples over two years in a small catchment in eastern Scotland. MSARMs enabled us to explicitly account for the identified non-linear, non-Normal and non-stationary isotope dynamics of both time series. The hidden states of the Markov chain could also be associated with meteorological and hydrological drivers identifying the short (event) and longer-term (inter-event) transport mechanisms for both isotopes. Inference was based on the Bayesian approach performed through Markov Chain Monte Carlo algorithms, which also allowed us to deal with a high rate of missing values (17%). Although it is usually assumed that both isotopes are conservative and exhibit similar dynamics, δ18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but δ18O demanded autoregressions of the first order, whereas δ2H of the second. Moreover, both the dynamics of observations and the hidden states of the two isotopes were explained by two different sets of covariates. Consequently use of the two tracers for transit time modelling and hydrograph separation may result in different interpretations on the functioning of a catchment system.
Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.
2016-01-01
A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221
Fancher, Chris M; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J; Smith, Ralph C; Wilson, Alyson G; Jones, Jacob L
2016-01-01
A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221
NASA Astrophysics Data System (ADS)
Laloy, Eric; Rogiers, Bart; Vrugt, Jasper A.; Mallants, Dirk; Jacques, Diederik
2013-05-01
This study reports on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model. Our method builds on previous stochastic collocation approaches, e.g., Marzouk and Xiu (2009) and Marzouk and Najm (2009), and uses generalized polynomial chaos (gPC) theory and dimensionality reduction to emulate the output of a large-scale groundwater flow model. The resulting surrogate model is CPU efficient and serves to explore the posterior distribution at a much lower computational cost using two-stage MCMC simulation. The case study reported in this paper demonstrates a two to five times speed-up in sampling efficiency.
Bayesian inference for OPC modeling
NASA Astrophysics Data System (ADS)
Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.
2016-03-01
The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.
Trandimensional Inference in the Geosciences
NASA Astrophysics Data System (ADS)
Bodin, Thomas
2016-04-01
An inverse problem is the task often occurring in many branches of Earth sciences, where the values of some model parameters describing the Earth must be obtained given noisy observations made at the surface. In all applications of inversion, assumptions are made about the nature of the model parametrisation and data noise characteristics, and results can significantly depend on those assumptions. These quantities are often manually `tuned' by means of subjective trial-and-error procedures, and this prevents to accurately quantify uncertainties in the solution. A Bayesian approach allows these assumptions to be relaxed by incorporating relevant parameters as unknowns in the inference problem. Rather than being forced to make decisions on parametrisation, the level of data noise and the weights between data types in advance, as is often the case in an optimization framework, the choice can be informed by the data themselves. Probabilistic sampling techniques such as transdimensional Markov chain Monte Carlo, allow sampling over complex posterior probability density functions, thus providing information on constraint, trade-offs and uncertainty in the unknowns. This presentation will present a review of transdimensional inference, and its application to different problems, ranging from Geochemistry to Solid Earth Geophysics.
Evolutionary inference via the Poisson Indel Process.
Bouchard-Côté, Alexandre; Jordan, Michael I
2013-01-22
We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.
Specification test for Markov models with measurement errors*
Kim, Seonjin; Zhao, Zhibiao
2014-01-01
Most existing works on specification testing assume that we have direct observations from the model of interest. We study specification testing for Markov models based on contaminated observations. The evolving model dynamics of the unobservable Markov chain is implicitly coded into the conditional distribution of the observed process. To test whether the underlying Markov chain follows a parametric model, we propose measuring the deviation between nonparametric and parametric estimates of conditional regression functions of the observed process. Specifically, we construct a nonparametric simultaneous confidence band for conditional regression functions and check whether the parametric estimate is contained within the band. PMID:25346552
Stålhammar, N O
1993-01-01
Escalating medical costs have made it increasingly important to carry out economic evaluations of drug therapy. In the area of acid-related diseases, much of the current interest is focused on comparisons between omeprazole and H2 receptor antagonists. After having discussed the basic methodology used in these analyses, viz. the decision-tree analysis, this paper presents an extension of this methodology, the Markov chain approach, which is more appropriate for analyses of longer time periods. Thereafter, this methodology is used to analyze the cost-effectiveness of omeprazole in intermittent versus maintenance treatment of reflux esophagitis. The cost data are from Sweden and the time period studied is one year. It is found that maintenance treatment provides 63 more healthy days per year at an extra direct cost of SEK 40 per day. From a sensitivity analysis it is concluded that the cost-effectiveness of intermittent versus maintenance treatment is mainly determined by the probability of relapse when off treatment, the severity of the symptoms in the case of a relapse and the value to the patient of a healthy day, i.e. a day free from reflux esophagitis. PMID:8171303
Weijs, Liesbeth; Yang, Raymond S H; Das, Krishna; Covaci, Adrian; Blust, Ronny
2013-05-01
Physiologically based pharmacokinetic (PBPK) modeling in marine mammals is a challenge because of the lack of parameter information and the ban on exposure experiments. To minimize uncertainty and variability, parameter estimation methods are required for the development of reliable PBPK models. The present study is the first to develop PBPK models for the lifetime bioaccumulation of p,p'-DDT, p,p'-DDE, and p,p'-DDD in harbor porpoises. In addition, this study is also the first to apply the Bayesian approach executed with Markov chain Monte Carlo simulations using two data sets of harbor porpoises from the Black and North Seas. Parameters from the literature were used as priors for the first "model update" using the Black Sea data set, the resulting posterior parameters were then used as priors for the second "model update" using the North Sea data set. As such, PBPK models with parameters specific for harbor porpoises could be strengthened with more robust probability distributions. As the science and biomonitoring effort progress in this area, more data sets will become available to further strengthen and update the parameters in the PBPK models for harbor porpoises as a species anywhere in the world. Further, such an approach could very well be extended to other protected marine mammals.
Kuchel, Philip W; Naumann, Christoph; Puckeridge, Max; Chapman, Bogdan E; Szekely, David
2011-09-01
The NMR z-spectra of 7Li+ and 23Na+ in stretched hydrogels contain five minima, or critical values, with a sharp "dagger" on the central dip. The mathematical representation of such z-spectra from spin-3/2 nuclei contains nine distinct (the total is 15 but there is redundancy of the ±order-numbers) relaxation rate constants that are unique for each of the spin states, up to rank 3, order 3. We present an approach to multiple-parameter-value estimation that exploits the high level of separability of the effects of each of the relaxation rate constants on the features of the z-spectrum. The Markov chain Monte Carlo (MCMC) method is computationally demanding but it yielded statistically robust estimates (low coefficients of variation) of the parameter values. We describe the implementation of the MCMC analysis (in the present context) and posit that it can obviate the need for using multiple-quantum filtered RF-pulse sequences to estimate all relaxation rate constants/times under experimentally favorable, but readily achievable, circumstances.
Bayesian Markov Random Field analysis for protein function prediction based on network data.
Kourmpetis, Yiannis A I; van Dijk, Aalt D J; Bink, Marco C A M; van Ham, Roeland C H J; ter Braak, Cajo J F
2010-02-24
Inference of protein functions is one of the most important aims of modern biology. To fully exploit the large volumes of genomic data typically produced in modern-day genomic experiments, automated computational methods for protein function prediction are urgently needed. Established methods use sequence or structure similarity to infer functions but those types of data do not suffice to determine the biological context in which proteins act. Current high-throughput biological experiments produce large amounts of data on the interactions between proteins. Such data can be used to infer interaction networks and to predict the biological process that the protein is involved in. Here, we develop a probabilistic approach for protein function prediction using network data, such as protein-protein interaction measurements. We take a Bayesian approach to an existing Markov Random Field method by performing simultaneous estimation of the model parameters and prediction of protein functions. We use an adaptive Markov Chain Monte Carlo algorithm that leads to more accurate parameter estimates and consequently to improved prediction performance compared to the standard Markov Random Fields method. We tested our method using a high quality S. cereviciae validation network with 1622 proteins against 90 Gene Ontology terms of different levels of abstraction. Compared to three other protein function prediction methods, our approach shows very good prediction performance. Our method can be directly applied to protein-protein interaction or coexpression networks, but also can be extended to use multiple data sources. We apply our method to physical protein interaction data from S. cerevisiae and provide novel predictions, using 340 Gene Ontology terms, for 1170 unannotated proteins and we evaluate the predictions using the available literature.
Phase transitions in Hidden Markov Models
NASA Astrophysics Data System (ADS)
Bechhoefer, John; Lathouwers, Emma
In Hidden Markov Models (HMMs), a Markov process is not directly accessible. In the simplest case, a two-state Markov model ``emits'' one of two ``symbols'' at each time step. We can think of these symbols as noisy measurements of the underlying state. With some probability, the symbol implies that the system is in one state when it is actually in the other. The ability to judge which state the system is in sets the efficiency of a Maxwell demon that observes state fluctuations in order to extract heat from a coupled reservoir. The state-inference problem is to infer the underlying state from such noisy measurements at each time step. We show that there can be a phase transition in such measurements: for measurement error rates below a certain threshold, the inferred state always matches the observation. For higher error rates, there can be continuous or discontinuous transitions to situations where keeping a memory of past observations improves the state estimate. We can partly understand this behavior by mapping the HMM onto a 1d random-field Ising model at zero temperature. We also present more recent work that explores a larger parameter space and more states. Research funded by NSERC, Canada.
ERIC Educational Resources Information Center
Kayser, Brian D.
The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…
Variational Inference for Watson Mixture Model.
Taghia, Jalil; Leijon, Arne
2016-09-01
This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets. PMID:26571512
Time series segmentation with shifting means hidden markov models
NASA Astrophysics Data System (ADS)
Kehagias, Ath.; Fortin, V.
2006-08-01
We present a new family of hidden Markov models and apply these to the segmentation of hydrological and environmental time series. The proposed hidden Markov models have a discrete state space and their structure is inspired from the shifting means models introduced by Chernoff and Zacks and by Salas and Boes. An estimation method inspired from the EM algorithm is proposed, and we show that it can accurately identify multiple change-points in a time series. We also show that the solution obtained using this algorithm can serve as a starting point for a Monte-Carlo Markov chain Bayesian estimation method, thus reducing the computing time needed for the Markov chain to converge to a stationary distribution.
Genome-wide inference of ancestral recombination graphs.
Rasmussen, Matthew D; Hubisz, Melissa J; Gronau, Ilan; Siepel, Adam
2014-01-01
The complex correlation structure of a collection of orthologous DNA sequences is uniquely captured by the "ancestral recombination graph" (ARG), a complete record of coalescence and recombination events in the history of the sample. However, existing methods for ARG inference are computationally intensive, highly approximate, or limited to small numbers of sequences, and, as a consequence, explicit ARG inference is rarely used in applied population genomics. Here, we introduce a new algorithm for ARG inference that is efficient enough to apply to dozens of complete mammalian genomes. The key idea of our approach is to sample an ARG of [Formula: see text] chromosomes conditional on an ARG of [Formula: see text] chromosomes, an operation we call "threading." Using techniques based on hidden Markov models, we can perform this threading operation exactly, up to the assumptions of the sequentially Markov coalescent and a discretization of time. An extension allows for threading of subtrees instead of individual sequences. Repeated application of these threading operations results in highly efficient Markov chain Monte Carlo samplers for ARGs. We have implemented these methods in a computer program called ARGweaver. Experiments with simulated data indicate that ARGweaver converges rapidly to the posterior distribution over ARGs and is effective in recovering various features of the ARG for dozens of sequences generated under realistic parameters for human populations. In applications of ARGweaver to 54 human genome sequences from Complete Genomics, we find clear signatures of natural selection, including regions of unusually ancient ancestry associated with balancing selection and reductions in allele age in sites under directional selection. The patterns we observe near protein-coding genes are consistent with a primary influence from background selection rather than hitchhiking, although we cannot rule out a contribution from recurrent selective sweeps. PMID:24831947
Genome-Wide Inference of Ancestral Recombination Graphs
Rasmussen, Matthew D.; Hubisz, Melissa J.; Gronau, Ilan; Siepel, Adam
2014-01-01
The complex correlation structure of a collection of orthologous DNA sequences is uniquely captured by the “ancestral recombination graph” (ARG), a complete record of coalescence and recombination events in the history of the sample. However, existing methods for ARG inference are computationally intensive, highly approximate, or limited to small numbers of sequences, and, as a consequence, explicit ARG inference is rarely used in applied population genomics. Here, we introduce a new algorithm for ARG inference that is efficient enough to apply to dozens of complete mammalian genomes. The key idea of our approach is to sample an ARG of chromosomes conditional on an ARG of chromosomes, an operation we call “threading.” Using techniques based on hidden Markov models, we can perform this threading operation exactly, up to the assumptions of the sequentially Markov coalescent and a discretization of time. An extension allows for threading of subtrees instead of individual sequences. Repeated application of these threading operations results in highly efficient Markov chain Monte Carlo samplers for ARGs. We have implemented these methods in a computer program called ARGweaver. Experiments with simulated data indicate that ARGweaver converges rapidly to the posterior distribution over ARGs and is effective in recovering various features of the ARG for dozens of sequences generated under realistic parameters for human populations. In applications of ARGweaver to 54 human genome sequences from Complete Genomics, we find clear signatures of natural selection, including regions of unusually ancient ancestry associated with balancing selection and reductions in allele age in sites under directional selection. The patterns we observe near protein-coding genes are consistent with a primary influence from background selection rather than hitchhiking, although we cannot rule out a contribution from recurrent selective sweeps. PMID:24831947
Methods for Bayesian power spectrum inference with galaxy surveys
Jasche, Jens; Wandelt, Benjamin D.
2013-12-10
We derive and implement a full Bayesian large scale structure inference method aiming at precision recovery of the cosmological power spectrum from galaxy redshift surveys. Our approach improves upon previous Bayesian methods by performing a joint inference of the three-dimensional density field, the cosmological power spectrum, luminosity dependent galaxy biases, and corresponding normalizations. We account for all joint and correlated uncertainties between all inferred quantities. Classes of galaxies with different biases are treated as separate subsamples. This method therefore also allows the combined analysis of more than one galaxy survey. In particular, it solves the problem of inferring the power spectrum from galaxy surveys with non-trivial survey geometries by exploring the joint posterior distribution with efficient implementations of multiple block Markov chain and Hybrid Monte Carlo methods. Our Markov sampler achieves high statistical efficiency in low signal-to-noise regimes by using a deterministic reversible jump algorithm. This approach reduces the correlation length of the sampler by several orders of magnitude, turning the otherwise numerically unfeasible problem of joint parameter exploration into a numerically manageable task. We test our method on an artificial mock galaxy survey, emulating characteristic features of the Sloan Digital Sky Survey data release 7, such as its survey geometry and luminosity-dependent biases. These tests demonstrate the numerical feasibility of our large scale Bayesian inference frame work when the parameter space has millions of dimensions. This method reveals and correctly treats the anti-correlation between bias amplitudes and power spectrum, which are not taken into account in current approaches to power spectrum estimation, a 20% effect across large ranges in k space. In addition, this method results in constrained realizations of density fields obtained without assuming the power spectrum or bias parameters
Samah, S; Valadez-Moctezuma, E; Peláez-Luna, K S; Morales-Manzano, S; Meza-Carrera, P; Cid-Contreras, R C
2016-01-01
Molecular methods are powerful tools in characterizing and determining relationships between plants. The aim of this study was to study genetic divergence between 103 accessions of Mexican Opuntia. To accomplish this, polymerase chain reaction (PCR)-restriction fragment length polymorphism analysis of three chloroplast intergenic spacers (atpB-rbcL, trnL-trnF, and psbA-trnH), one chloroplast gene (ycf1), two nuclear genes (ppc and PhyC), and one mitochondrial gene (cox3) was conducted. The amplified products from all the samples had very similar molecular sizes, and there were only very small differences between the undigested PCR amplicons for all regions, with the exception of ppc. We obtained 5850 bp from the seven regions, and 136 fragments were detected with eight enzymes, 37 of which (27.2%) were polymorphic. We found that 40% of the fragments from the chloroplast regions were polymorphic, 9.8% of the bands detected in the nuclear genes were polymorphic, and 20% of the bands in the mitochondrial locus were polymorphic. trnL-trnF and psbA-trnH were the most variable regions. The Nei and Li/Dice distance was very short, and ranged from 0 to 0.12; indeed, 77 of the 103 genotypes had the same genetic profile. All the xoconostle accessions (acidic fruits) were grouped together without being separated from three genotypes of prickly pear (sweet fruits). We assume that the genetic divergence between prickly pears and xoconostles is very low, and question the number of Opuntia species currently considered in Mexico. PMID:27323120
Samah, S; Valadez-Moctezuma, E; Peláez-Luna, K S; Morales-Manzano, S; Meza-Carrera, P; Cid-Contreras, R C
2016-06-03
Molecular methods are powerful tools in characterizing and determining relationships between plants. The aim of this study was to study genetic divergence between 103 accessions of Mexican Opuntia. To accomplish this, polymerase chain reaction (PCR)-restriction fragment length polymorphism analysis of three chloroplast intergenic spacers (atpB-rbcL, trnL-trnF, and psbA-trnH), one chloroplast gene (ycf1), two nuclear genes (ppc and PhyC), and one mitochondrial gene (cox3) was conducted. The amplified products from all the samples had very similar molecular sizes, and there were only very small differences between the undigested PCR amplicons for all regions, with the exception of ppc. We obtained 5850 bp from the seven regions, and 136 fragments were detected with eight enzymes, 37 of which (27.2%) were polymorphic. We found that 40% of the fragments from the chloroplast regions were polymorphic, 9.8% of the bands detected in the nuclear genes were polymorphic, and 20% of the bands in the mitochondrial locus were polymorphic. trnL-trnF and psbA-trnH were the most variable regions. The Nei and Li/Dice distance was very short, and ranged from 0 to 0.12; indeed, 77 of the 103 genotypes had the same genetic profile. All the xoconostle accessions (acidic fruits) were grouped together without being separated from three genotypes of prickly pear (sweet fruits). We assume that the genetic divergence between prickly pears and xoconostles is very low, and question the number of Opuntia species currently considered in Mexico.
Computational statistics using the Bayesian Inference Engine
NASA Astrophysics Data System (ADS)
Weinberg, Martin D.
2013-09-01
This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.
Universal recovery map for approximate Markov chains
Sutter, David; Fawzi, Omar; Renner, Renato
2016-01-01
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I(A:C|B) of a tripartite quantum state ρABC can be bounded from below by its distance to the closest recovered state RB→BC(ρAB), where the C-part is reconstructed from the B-part only and the recovery map RB→BC merely depends on ρBC. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems. PMID:27118889
sick: The Spectroscopic Inference Crank
NASA Astrophysics Data System (ADS)
Casey, Andrew R.
2016-03-01
There exists an inordinate amount of spectral data in both public and private astronomical archives that remain severely under-utilized. The lack of reliable open-source tools for analyzing large volumes of spectra contributes to this situation, which is poised to worsen as large surveys successively release orders of magnitude more spectra. In this article I introduce sick, the spectroscopic inference crank, a flexible and fast Bayesian tool for inferring astrophysical parameters from spectra. sick is agnostic to the wavelength coverage, resolving power, or general data format, allowing any user to easily construct a generative model for their data, regardless of its source. sick can be used to provide a nearest-neighbor estimate of model parameters, a numerically optimized point estimate, or full Markov Chain Monte Carlo sampling of the posterior probability distributions. This generality empowers any astronomer to capitalize on the plethora of published synthetic and observed spectra, and make precise inferences for a host of astrophysical (and nuisance) quantities. Model intensities can be reliably approximated from existing grids of synthetic or observed spectra using linear multi-dimensional interpolation, or a Cannon-based model. Additional phenomena that transform the data (e.g., redshift, rotational broadening, continuum, spectral resolution) are incorporated as free parameters and can be marginalized away. Outlier pixels (e.g., cosmic rays or poorly modeled regimes) can be treated with a Gaussian mixture model, and a noise model is included to account for systematically underestimated variance. Combining these phenomena into a scalar-justified, quantitative model permits precise inferences with credible uncertainties on noisy data. I describe the common model features, the implementation details, and the default behavior, which is balanced to be suitable for most astronomical applications. Using a forward model on low-resolution, high signal
Neuwald, Andrew F; Liu, Jun S
2004-01-01
Background Certain protein families are highly conserved across distantly related organisms and belong to large and functionally diverse superfamilies. The patterns of conservation present in these protein sequences presumably are due to selective constraints maintaining important but unknown structural mechanisms with some constraints specific to each family and others shared by a larger subset or by the entire superfamily. To exploit these patterns as a source of functional information, we recently devised a statistically based approach called contrast hierarchical alignment and interaction network (CHAIN) analysis, which infers the strengths of various categories of selective constraints from co-conserved patterns in a multiple alignment. The power of this approach strongly depends on the quality of the multiple alignments, which thus motivated development of theoretical concepts and strategies to improve alignment of conserved motifs within large sets of distantly related sequences. Results Here we describe a hidden Markov model (HMM), an algebraic system, and Markov chain Monte Carlo (MCMC) sampling strategies for alignment of multiple sequence motifs. The MCMC sampling strategies are useful both for alignment optimization and for adjusting position specific background amino acid frequencies for alignment uncertainties. Associated statistical formulations provide an objective measure of alignment quality as well as automatic gap penalty optimization. Improved alignments obtained in this way are compared with PSI-BLAST based alignments within the context of CHAIN analysis of three protein families: Giα subunits, prolyl oligopeptidases, and transitional endoplasmic reticulum (p97) AAA+ ATPases. Conclusion While not entirely replacing PSI-BLAST based alignments, which likewise may be optimized for CHAIN analysis using this approach, these motif-based methods often more accurately align very distantly related sequences and thus can provide a better measure of
MODELING PAVEMENT DETERIORATION PROCESSES BY POISSON HIDDEN MARKOV MODELS
NASA Astrophysics Data System (ADS)
Nam, Le Thanh; Kaito, Kiyoyuki; Kobayashi, Kiyoshi; Okizuka, Ryosuke
In pavement management, it is important to estimate lifecycle cost, which is composed of the expenses for repairing local damages, including potholes, and repairing and rehabilitating the surface and base layers of pavements, including overlays. In this study, a model is produced under the assumption that the deterioration process of pavement is a complex one that includes local damages, which occur frequently, and the deterioration of the surface and base layers of pavement, which progresses slowly. The variation in pavement soundness is expressed by the Markov deterioration model and the Poisson hidden Markov deterioration model, in which the frequency of local damage depends on the distribution of pavement soundness, is formulated. In addition, the authors suggest a model estimation method using the Markov Chain Monte Carlo (MCMC) method, and attempt to demonstrate the applicability of the proposed Poisson hidden Markov deterioration model by studying concrete application cases.
Estimation and uncertainty of reversible Markov models.
Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank
2015-11-01
Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software--http://pyemma.org--as of version 2.0. PMID:26547152
Estimation and uncertainty of reversible Markov models
NASA Astrophysics Data System (ADS)
Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank
2015-11-01
Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software — http://pyemma.org — as of version 2.0.
Uncertainty and inference in deterministic and noisy chaos
NASA Astrophysics Data System (ADS)
Strelioff, Christopher Charles
We study dynamical systems which exhibit chaotic dynamics with a focus on sources of real and apparent randomness including sensitivity to perturbation, dynamical noise, measurement uncertainty and finite data samples for inference. This choice of topics is motivated by a desire to adapt established theoretical tools such as the Perron-Frobenius operator and symbolic dynamics to experimental data. First, we study prediction of chaotic time series when a perfect model is available but the initial condition is measured with uncertainty. A common approach for predicting future data given these circumstances is to apply the model despite the uncertainty. In systems with fold dynamics, we find prediction is improved over this strategy by recognizing this behavior. A systematic study of the logistic map demonstrates prediction can be extended three time steps using an approximation of the relevant Perron-Frobenius operator dynamics. Next, we show how to infer kth order Markov chains from finite data by applying Bayesian methods to both parameter estimation and model-order selection. In this pursuit, we connect inference to statistical mechanics through information-theoretic (type theory) techniques and establish a direct relationship between Bayesian evidence and the partition function. This allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Also, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes. Finally, we study a binary partition of time series data from the logistic map with additive noise, inferring optimal, effectively generating partitions and kth order Markov chain models. Here we adapt Bayesian inference, developed above, for applied symbolic dynamics. We show that reconciling Kolmogorov's maximum-entropy partition with the methods of Bayesian model selection requires the use of two separate
Assessment of optimized Markov models in protein fold classification.
Lampros, Christos; Simos, Thomas; Exarchos, Themis P; Exarchos, Konstantinos P; Papaloukas, Costas; Fotiadis, Dimitrios I
2014-08-01
Protein fold classification is a challenging task strongly associated with the determination of proteins' structure. In this work, we tested an optimization strategy on a Markov chain and a recently introduced Hidden Markov Model (HMM) with reduced state-space topology. The proteins with unknown structure were scored against both these models. Then the derived scores were optimized following a local optimization method. The Protein Data Bank (PDB) and the annotation of the Structural Classification of Proteins (SCOP) database were used for the evaluation of the proposed methodology. The results demonstrated that the fold classification accuracy of the optimized HMM was substantially higher compared to that of the Markov chain or the reduced state-space HMM approaches. The proposed methodology achieved an accuracy of 41.4% on fold classification, while Sequence Alignment and Modeling (SAM), which was used for comparison, reached an accuracy of 38%. PMID:25152041
Sun, Shuying; Yu, Xiaoqing
2016-03-01
DNA methylation is an epigenetic event that plays an important role in regulating gene expression. It is important to study DNA methylation, especially differential methylation patterns between two groups of samples (e.g. patients vs. normal individuals). With next generation sequencing technologies, it is now possible to identify differential methylation patterns by considering methylation at the single CG site level in an entire genome. However, it is challenging to analyze large and complex NGS data. In order to address this difficult question, we have developed a new statistical method using a hidden Markov model and Fisher's exact test (HMM-Fisher) to identify differentially methylated cytosines and regions. We first use a hidden Markov chain to model the methylation signals to infer the methylation state as Not methylated (N), Partly methylated (P), and Fully methylated (F) for each individual sample. We then use Fisher's exact test to identify differentially methylated CG sites. We show the HMM-Fisher method and compare it with commonly cited methods using both simulated data and real sequencing data. The results show that HMM-Fisher outperforms the current available methods to which we have compared. HMM-Fisher is efficient and robust in identifying heterogeneous DM regions. PMID:26854292
Degradation monitoring using probabilistic inference
NASA Astrophysics Data System (ADS)
Alpay, Bulent
In order to increase safety and improve economy and performance in a nuclear power plant (NPP), the source and extent of component degradations should be identified before failures and breakdowns occur. It is also crucial for the next generation of NPPs, which are designed to have a long core life and high fuel burnup to have a degradation monitoring system in order to keep the reactor in a safe state, to meet the designed reactor core lifetime and to optimize the scheduled maintenance. Model-based methods are based on determining the inconsistencies between the actual and expected behavior of the plant, and use these inconsistencies for detection and diagnostics of degradations. By defining degradation as a random abrupt change from the nominal to a constant degraded state of a component, we employed nonlinear filtering techniques based on state/parameter estimation. We utilized a Bayesian recursive estimation formulation in the sequential probabilistic inference framework and constructed a hidden Markov model to represent a general physical system. By addressing the problem of a filter's inability to estimate an abrupt change, which is called the oblivious filter problem in nonlinear extensions of Kalman filtering, and the sample impoverishment problem in particle filtering, we developed techniques to modify filtering algorithms by utilizing additional data sources to improve the filter's response to this problem. We utilized a reliability degradation database that can be constructed from plant specific operational experience and test and maintenance reports to generate proposal densities for probable degradation modes. These are used in a multiple hypothesis testing algorithm. We then test samples drawn from these proposal densities with the particle filtering estimates based on the Bayesian recursive estimation formulation with the Metropolis Hastings algorithm, which is a well-known Markov chain Monte Carlo method (MCMC). This multiple hypothesis testing
Hidden Markov Models: The Best Models for Forager Movements?
Joo, Rocio; Bertrand, Sophie; Tam, Jorge; Fablet, Ronan
2013-01-01
One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs). We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs). They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour), while their behavioural modes (fishing, searching and cruising) were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines) for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%), significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance. PMID:24058400
An application of Bayesian inference for solar-like pulsators
NASA Astrophysics Data System (ADS)
Benomar, O.
2008-12-01
As the amount of data collected by space-borne asteroseismic instruments (such as CoRoT and Kepler) increases drastically, it will be useful to have automated processes to extract a maximum of information from these data. The use of a Bayesian approach could be very help- ful for this goal. Only a few attempts have been made in this way (e.g. Brewer et al. 2007). We propose to use Markov Chain Monte Carlo simulations (MCMC) with Metropolis-Hasting (MH) based algorithms to infer the main stellar oscillation parameters from the power spec- trum, in the case of solar-like pulsators. Given a number of modes to be fitted, the algorithm is able to give the best set of parameters (frequency, linewidth, amplitude, rotational split- ting) corresponding to a chosen input model. We illustrate this algorithm with one of the first CoRoT targets: HD 49933.
Nonparametric inference of network structure and dynamics
NASA Astrophysics Data System (ADS)
Peixoto, Tiago P.
The network structure of complex systems determine their function and serve as evidence for the evolutionary mechanisms that lie behind them. Despite considerable effort in recent years, it remains an open challenge to formulate general descriptions of the large-scale structure of network systems, and how to reliably extract such information from data. Although many approaches have been proposed, few methods attempt to gauge the statistical significance of the uncovered structures, and hence the majority cannot reliably separate actual structure from stochastic fluctuations. Due to the sheer size and high-dimensionality of many networks, this represents a major limitation that prevents meaningful interpretations of the results obtained with such nonstatistical methods. In this talk, I will show how these issues can be tackled in a principled and efficient fashion by formulating appropriate generative models of network structure that can have their parameters inferred from data. By employing a Bayesian description of such models, the inference can be performed in a nonparametric fashion, that does not require any a priori knowledge or ad hoc assumptions about the data. I will show how this approach can be used to perform model comparison, and how hierarchical models yield the most appropriate trade-off between model complexity and quality of fit based on the statistical evidence present in the data. I will also show how this general approach can be elegantly extended to networks with edge attributes, that are embedded in latent spaces, and that change in time. The latter is obtained via a fully dynamic generative network model, based on arbitrary-order Markov chains, that can also be inferred in a nonparametric fashion. Throughout the talk I will illustrate the application of the methods with many empirical networks such as the internet at the autonomous systems level, the global airport network, the network of actors and films, social networks, citations among
Bayesian Selection of Markov Models for Symbol Sequences: Application to Microsaccadic Eye Movements
Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias
2012-01-01
Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems. PMID:22970124
Luo, Sheng; Ma, Junsheng; Kieburtz, Karl D.
2013-01-01
Many randomized clinical trials collect multivariate longitudinal measurements in different scales, for example, binary, ordinal, and continuous. Multilevel item response models are used to evaluate the global treatment effects across multiple outcomes while accounting for all sources of correlation. Continuous measurements are often assumed to be normally distributed. But the model inference is not robust when the normality assumption is violated because of heavy tails and outliers. In this article, we develop a Bayesian method for multilevel item response models replacing the normal distributions with symmetric heavy-tailed normal/independent distributions. The inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in BUGS language. Our proposed method is evaluated by simulation studies and is applied to Earlier versus Later Levodopa Therapy in Parkinson’s Disease study, a motivating clinical trial assessing the effect of Levodopa therapy on the Parkinson’s disease progression rate. PMID:23494809
Luo, Sheng; Ma, Junsheng; Kieburtz, Karl D
2013-09-30
Many randomized clinical trials collect multivariate longitudinal measurements in different scales, for example, binary, ordinal, and continuous. Multilevel item response models are used to evaluate the global treatment effects across multiple outcomes while accounting for all sources of correlation. Continuous measurements are often assumed to be normally distributed. But the model inference is not robust when the normality assumption is violated because of heavy tails and outliers. In this article, we develop a Bayesian method for multilevel item response models replacing the normal distributions with symmetric heavy-tailed normal/independent distributions. The inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in BUGS language. Our proposed method is evaluated by simulation studies and is applied to Earlier versus Later Levodopa Therapy in Parkinson's Disease study, a motivating clinical trial assessing the effect of Levodopa therapy on the Parkinson's disease progression rate. PMID:23494809
Signal inference with unknown response: Calibration-uncertainty renormalized estimator
NASA Astrophysics Data System (ADS)
Dorn, Sebastian; Enßlin, Torsten A.; Greiner, Maksim; Selig, Marco; Boehm, Vanessa
2015-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.
Signal inference with unknown response: calibration-uncertainty renormalized estimator.
Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa
2015-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.
Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent
Wen, Dingqiao; Yu, Yun; Nakhleh, Luay
2016-01-01
The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation. PMID:27144273
Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent.
Wen, Dingqiao; Yu, Yun; Nakhleh, Luay
2016-05-01
The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation. PMID:27144273
Vertically Integrated Seismological Analysis II : Inference
NASA Astrophysics Data System (ADS)
Arora, N. S.; Russell, S.; Sudderth, E.
2009-12-01
Methods for automatically associating detected waveform features with hypothesized seismic events, and localizing those events, are a critical component of efforts to verify the Comprehensive Test Ban Treaty (CTBT). As outlined in our companion abstract, we have developed a hierarchical model which views detection, association, and localization as an integrated probabilistic inference problem. In this abstract, we provide more details on the Markov chain Monte Carlo (MCMC) methods used to solve this inference task. MCMC generates samples from a posterior distribution π(x) over possible worlds x by defining a Markov chain whose states are the worlds x, and whose stationary distribution is π(x). In the Metropolis-Hastings (M-H) method, transitions in the Markov chain are constructed in two steps. First, given the current state x, a candidate next state x‧ is generated from a proposal distribution q(x‧ | x), which may be (more or less) arbitrary. Second, the transition to x‧ is not automatic, but occurs with an acceptance probability—α(x‧ | x) = min(1, π(x‧)q(x | x‧)/π(x)q(x‧ | x)). The seismic event model outlined in our companion abstract is quite similar to those used in multitarget tracking, for which MCMC has proved very effective. In this model, each world x is defined by a collection of events, a list of properties characterizing those events (times, locations, magnitudes, and types), and the association of each event to a set of observed detections. The target distribution π(x) = P(x | y), the posterior distribution over worlds x given the observed waveform data y at all stations. Proposal distributions then implement several types of moves between worlds. For example, birth moves create new events; death moves delete existing events; split moves partition the detections for an event into two new events; merge moves combine event pairs; swap moves modify the properties and assocations for pairs of events. Importantly, the rules for
Markov sequential pattern recognition : dependency and the unknown class.
Malone, Kevin Thomas; Haschke, Greg Benjamin; Koch, Mark William
2004-10-01
The sequential probability ratio test (SPRT) minimizes the expected number of observations to a decision and can solve problems in sequential pattern recognition. Some problems have dependencies between the observations, and Markov chains can model dependencies where the state occupancy probability is geometric. For a non-geometric process we show how to use the effective amount of independent information to modify the decision process, so that we can account for the remaining dependencies. Along with dependencies between observations, a successful system needs to handle the unknown class in unconstrained environments. For example, in an acoustic pattern recognition problem any sound source not belonging to the target set is in the unknown class. We show how to incorporate goodness of fit (GOF) classifiers into the Markov SPRT, and determine the worse case nontarget model. We also develop a multiclass Markov SPRT using the GOF concept.
Bayesian inference tools for inverse problems
NASA Astrophysics Data System (ADS)
Mohammad-Djafari, Ali
2013-08-01
In this paper, first the basics of Bayesian inference with a parametric model of the data is presented. Then, the needed extensions are given when dealing with inverse problems and in particular the linear models such as Deconvolution or image reconstruction in Computed Tomography (CT). The main point to discuss then is the prior modeling of signals and images. A classification of these priors is presented, first in separable and Markovien models and then in simple or hierarchical with hidden variables. For practical applications, we need also to consider the estimation of the hyper parameters. Finally, we see that we have to infer simultaneously on the unknowns, the hidden variables and the hyper parameters. Very often, the expression of this joint posterior law is too complex to be handled directly. Indeed, rarely we can obtain analytical solutions to any point estimators such the Maximum A posteriori (MAP) or Posterior Mean (PM). Three main tools are then can be used: Laplace approximation (LAP), Markov Chain Monte Carlo (MCMC) and Bayesian Variational Approximations (BVA). To illustrate all these aspects, we will consider a deconvolution problem where we know that the input signal is sparse and propose to use a Student-t prior for that. Then, to handle the Bayesian computations with this model, we use the property of Student-t which is modelling it via an infinite mixture of Gaussians, introducing thus hidden variables which are the variances. Then, the expression of the joint posterior of the input signal samples, the hidden variables (which are here the inverse variances of those samples) and the hyper-parameters of the problem (for example the variance of the noise) is given. From this point, we will present the joint maximization by alternate optimization and the three possible approximation methods. Finally, the proposed methodology is applied in different applications such as mass spectrometry, spectrum estimation of quasi periodic biological signals and
Phylodynamic inference for structured epidemiological models.
Rasmussen, David A; Volz, Erik M; Koelle, Katia
2014-04-01
Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates. PMID:24743590
Indexed semi-Markov process for wind speed modeling.
NASA Astrophysics Data System (ADS)
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first
Bayesian inference of a lake water quality model by emulating its posterior density
NASA Astrophysics Data System (ADS)
Dietzel, A.; Reichert, P.
2014-10-01
We use a Gaussian stochastic process emulator to interpolate the posterior probability density of a computationally demanding application of the biogeochemical-ecological lake model BELAMO to accelerate statistical inference of deterministic model and error model parameters. The deterministic model consists of a mechanistic description of key processes influencing the mass balance of nutrients, dissolved oxygen, organic particles, and phytoplankton and zooplankton in the lake. This model is complemented by a Gaussian stochastic process to describe the remaining model bias and by Normal, independent observation errors. A small subsample of the Markov chain representing the posterior of the model parameters is propagated through the full model to get model predictions and uncertainty estimates. We expect this approximation to be more accurate at only slightly higher computational costs compared to using a Normal approximation to the posterior probability density and linear error propagation to the results as we did in an earlier paper. The performance of the two techniques is compared for a didactical example as well as for the lake model. As expected, for the didactical example, the use of the emulator led to posterior marginals of the model parameters that are closer to those calculated by Markov chain simulation using the full model than those based on the Normal approximation. For the lake model, the new technique proved applicable without an excessive increase in computational requirements, but we faced challenges in the choice of the design data set for emulator calibration. As the posterior is a scalar function of the parameters, the suggested technique is an alternative to the emulation of a potentially more complex, structured output of the simulation model that allows for the use of a less case-specific emulator. This is at the cost that still the full model has to be used for prediction (which can be done with a smaller, approximately independent subsample
A Markov model of the Indus script.
Rao, Rajesh P N; Yadav, Nisha; Vahia, Mayank N; Joglekar, Hrishikesh; Adhikari, R; Mahadevan, Iravatham
2009-08-18
Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571
On Markov parameters in system identification
NASA Technical Reports Server (NTRS)
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
A clustering approach for estimating parameters of a profile hidden Markov model.
Aghdam, Rosa; Pezeshk, Hamid; Malekpour, Seyed Amir; Shemehsavar, Soudabeh; Eslahchi, Changiz
2013-01-01
A Profile Hidden Markov Model (PHMM) is a standard form of a Hidden Markov Models used for modeling protein and DNA sequence families based on multiple alignment. In this paper, we implement Baum-Welch algorithm and the Bayesian Monte Carlo Markov Chain (BMCMC) method for estimating parameters of small artificial PHMM. In order to improve the prediction accuracy of the estimation of the parameters of the PHMM, we classify the training data using the weighted values of sequences in the PHMM then apply an algorithm for estimating parameters of the PHMM. The results show that the BMCMC method performs better than the Maximum Likelihood estimation. PMID:23865165
Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.
Epstein, Michael; Calderhead, Ben; Girolami, Mark A; Sivilotti, Lucia G
2016-07-26
The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel
Crossing over...Markov meets Mendel.
Mneimneh, Saad
2012-01-01
Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the
Crossing over...Markov meets Mendel.
Mneimneh, Saad
2012-01-01
Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the
Markov Analysis of Sleep Dynamics
NASA Astrophysics Data System (ADS)
Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.
2009-05-01
A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.
Likelihood-Free Inference in High-Dimensional Models.
Kousathanas, Athanasios; Leuenberger, Christoph; Helfer, Jonas; Quinodoz, Mathieu; Foll, Matthieu; Wegmann, Daniel
2016-06-01
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza. PMID:27052569
Generalized Fiducial Inference for Binary Logistic Item Response Models.
Liu, Yang; Hannig, Jan
2016-06-01
Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data. PMID:26769340
Likelihood-Free Inference in High-Dimensional Models.
Kousathanas, Athanasios; Leuenberger, Christoph; Helfer, Jonas; Quinodoz, Mathieu; Foll, Matthieu; Wegmann, Daniel
2016-06-01
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza.
Bayesian population genomic inference of crossing over and gene conversion.
Padhukasahasram, Badri; Rannala, Bruce
2011-10-01
Meiotic recombination is a fundamental cellular mechanism in sexually reproducing organisms and its different forms, crossing over and gene conversion both play an important role in shaping genetic variation in populations. Here, we describe a coalescent-based full-likelihood Markov chain Monte Carlo (MCMC) method for jointly estimating the crossing-over, gene-conversion, and mean tract length parameters from population genomic data under a Bayesian framework. Although computationally more expensive than methods that use approximate likelihoods, the relative efficiency of our method is expected to be optimal in theory. Furthermore, it is also possible to obtain a posterior sample of genealogies for the data using this method. We first check the performance of the new method on simulated data and verify its correctness. We also extend the method for inference under models with variable gene-conversion and crossing-over rates and demonstrate its ability to identify recombination hotspots. Then, we apply the method to two empirical data sets that were sequenced in the telomeric regions of the X chromosome of Drosophila melanogaster. Our results indicate that gene conversion occurs more frequently than crossing over in the su-w and su-s gene sequences while the local rates of crossing over as inferred by our program are not low. The mean tract lengths for gene-conversion events are estimated to be ∼70 bp and 430 bp, respectively, for these data sets. Finally, we discuss ideas and optimizations for reducing the execution time of our algorithm.
Bayesian Inference for Time Trends in Parameter Values using Weighted Evidence Sets
D. L. Kelly; A. Malkhasyan
2010-09-01
There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performed for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “in-dustry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an applica-tion of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates an approach to incorporating multiple sources of data via applicability weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.
An empirical Bayesian approach for model-based inference of cellular signaling networks
2009-01-01
Background A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways. Results As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF) signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies. Conclusion In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements. PMID:19900289
Relative survival multistate Markov model.
Huszti, Ella; Abrahamowicz, Michal; Alioum, Ahmadou; Binquet, Christine; Quantin, Catherine
2012-02-10
Prognostic studies often have to deal with two important challenges: (i) separating effects of predictions on different 'competing' events and (ii) uncertainty about cause of death. Multistate Markov models permit multivariable analyses of competing risks of, for example, mortality versus disease recurrence. On the other hand, relative survival methods help estimate disease-specific mortality risks even in the absence of data on causes of death. In this paper, we propose a new Markov relative survival (MRS) model that attempts to combine these two methodologies. Our MRS model extends the existing multistate Markov piecewise constant intensities model to relative survival modeling. The intensity of transitions leading to death in the MRS model is modeled as the sum of an estimable excess hazard of mortality from the disease of interest and an 'offset' defined as the expected hazard of all-cause 'natural' mortality obtained from relevant life-tables. We evaluate the new MRS model through simulations, with a design based on registry-based prognostic studies of colon cancer. Simulation results show almost unbiased estimates of prognostic factor effects for the MRS model. We also applied the new MRS model to reassess the role of prognostic factors for mortality in a study of colorectal cancer. The MRS model considerably reduces the bias observed with the conventional Markov model that does not permit accounting for unknown causes of death, especially if the 'true' effects of a prognostic factor on the two types of mortality differ substantially.
Inference on cancer screening exam accuracy using population-level administrative data.
Jiang, H; Brown, P E; Walter, S D
2016-01-15
This paper develops a model for cancer screening and cancer incidence data, accommodating the partially unobserved disease status, clustered data structures, general covariate effects, and dependence between exams. The true unobserved cancer and detection status of screening participants are treated as latent variables, and a Markov Chain Monte Carlo algorithm is used to estimate the Bayesian posterior distributions of the diagnostic error rates and disease prevalence. We show how the Bayesian approach can be used to draw inferences about screening exam properties and disease prevalence while allowing for the possibility of conditional dependence between two exams. The techniques are applied to the estimation of the diagnostic accuracy of mammography and clinical breast examination using data from the Ontario Breast Screening Program in Canada. PMID:26278587
Chakraborty, Shubhankar; Roy Chaudhuri, Partha; Das, Prasanta Kr
2016-07-01
In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors. PMID:27475597
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2013-10-01
Many segmentation algorithms in medical image analysis use Bayesian modeling to augment local image appearance with prior anatomical knowledge. Such methods often contain a large number of free parameters that are first estimated and then kept fixed during the actual segmentation process. However, a faithful Bayesian analysis would marginalize over such parameters, accounting for their uncertainty by considering all possible values they may take. Here we propose to incorporate this uncertainty into Bayesian segmentation methods in order to improve the inference process. In particular, we approximate the required marginalization over model parameters using computationally efficient Markov chain Monte Carlo techniques. We illustrate the proposed approach using a recently developed Bayesian method for the segmentation of hippocampal subfields in brain MRI scans, showing a significant improvement in an Alzheimer's disease classification task. As an additional benefit, the technique also allows one to compute informative "error bars" on the volume estimates of individual structures.
Chakraborty, Shubhankar; Roy Chaudhuri, Partha; Das, Prasanta Kr
2016-07-01
In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors.
NASA Astrophysics Data System (ADS)
Chakraborty, Shubhankar; Roy Chaudhuri, Partha; Das, Prasanta Kr.
2016-07-01
In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors.
Inference on cancer screening exam accuracy using population-level administrative data.
Jiang, H; Brown, P E; Walter, S D
2016-01-15
This paper develops a model for cancer screening and cancer incidence data, accommodating the partially unobserved disease status, clustered data structures, general covariate effects, and dependence between exams. The true unobserved cancer and detection status of screening participants are treated as latent variables, and a Markov Chain Monte Carlo algorithm is used to estimate the Bayesian posterior distributions of the diagnostic error rates and disease prevalence. We show how the Bayesian approach can be used to draw inferences about screening exam properties and disease prevalence while allowing for the possibility of conditional dependence between two exams. The techniques are applied to the estimation of the diagnostic accuracy of mammography and clinical breast examination using data from the Ontario Breast Screening Program in Canada.
Bayesian inference of sampled ancestor trees for epidemiology and fossil calibration.
Gavryushkina, Alexandra; Welch, David; Stadler, Tanja; Drummond, Alexei J
2014-12-01
Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume that all samples are tips, they do not allow for this possibility. We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC) algorithm to infer what we call sampled ancestor trees, that is, trees in which sampled individuals can be direct ancestors of other sampled individuals. We use a family of birth-death models where individuals may remain in the tree process after sampling, in particular we extend the birth-death skyline model [Stadler et al., 2013] to sampled ancestor trees. This method allows the detection of sampled ancestors as well as estimation of the probability that an individual will be removed from the process when it is sampled. We show that even if sampled ancestors are not of specific interest in an analysis, failing to account for them leads to significant bias in parameter estimates. We also show that sampled ancestor birth-death models where every sample comes from a different time point are non-identifiable and thus require one parameter to be known in order to infer other parameters. We apply our phylogenetic inference accounting for sampled ancestors to epidemiological data, where the possibility of sampled ancestors enables us to identify individuals that infected other individuals after being sampled and to infer fundamental epidemiological parameters. We also apply the method to infer divergence times and diversification rates when fossils are included along with extant species samples, so that fossilisation events are modelled as a part of the tree branching process. Such modelling has many advantages as argued in the literature. The sampler is available as an open-source BEAST2 package (https://github.com/CompEvol/sampled-ancestors). PMID:25474353
Bayesian Inference of Sampled Ancestor Trees for Epidemiology and Fossil Calibration
Gavryushkina, Alexandra; Welch, David; Stadler, Tanja; Drummond, Alexei J.
2014-01-01
Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume that all samples are tips, they do not allow for this possibility. We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC) algorithm to infer what we call sampled ancestor trees, that is, trees in which sampled individuals can be direct ancestors of other sampled individuals. We use a family of birth-death models where individuals may remain in the tree process after sampling, in particular we extend the birth-death skyline model [Stadler et al., 2013] to sampled ancestor trees. This method allows the detection of sampled ancestors as well as estimation of the probability that an individual will be removed from the process when it is sampled. We show that even if sampled ancestors are not of specific interest in an analysis, failing to account for them leads to significant bias in parameter estimates. We also show that sampled ancestor birth-death models where every sample comes from a different time point are non-identifiable and thus require one parameter to be known in order to infer other parameters. We apply our phylogenetic inference accounting for sampled ancestors to epidemiological data, where the possibility of sampled ancestors enables us to identify individuals that infected other individuals after being sampled and to infer fundamental epidemiological parameters. We also apply the method to infer divergence times and diversification rates when fossils are included along with extant species samples, so that fossilisation events are modelled as a part of the tree branching process. Such modelling has many advantages as argued in the literature. The sampler is available as an open-source BEAST2 package (https://github.com/CompEvol/sampled-ancestors). PMID:25474353
Multiple testing for neuroimaging via hidden Markov random field.
Shu, Hai; Nan, Bin; Koeppe, Robert
2015-09-01
Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative.
Multivariate longitudinal data analysis with mixed effects hidden Markov models.
Raffa, Jesse D; Dubin, Joel A
2015-09-01
Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. PMID:25761965
On Factor Maps that Send Markov Measures to Gibbs Measures
NASA Astrophysics Data System (ADS)
Yoo, Jisang
2010-12-01
Let X and Y be mixing shifts of finite type. Let π be a factor map from X to Y that is fiber-mixing, i.e., given x,bar{x}in X with π(x)=π(bar{x})=yin Y, there is z∈ π -1( y) that is left asymptotic to x and right asymptotic to bar{x}. We show that any Markov measure on X projects to a Gibbs measure on Y under π (for a Hölder continuous potential). In other words, all hidden Markov chains (i.e. sofic measures) realized by π are Gibbs measures. In 2003, Chazottes and Ugalde gave a sufficient condition for a sofic measure to be a Gibbs measure. Our sufficient condition generalizes their condition and is invariant under conjugacy and time reversal. We provide examples demonstrating our result.
Multiple testing for neuroimaging via hidden Markov random field.
Shu, Hai; Nan, Bin; Koeppe, Robert
2015-09-01
Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative. PMID:26012881
Markov reliability models for digital flight control systems
NASA Technical Reports Server (NTRS)
Mcgough, John; Reibman, Andrew; Trivedi, Kishor
1989-01-01
The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.
Markov random field surface reconstruction.
Paulsen, Rasmus R; Baerentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaptation of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse Cholesky factorization, and a multiscale iterative optimization scheme. The method is demonstrated on a set of scanned human heads and, both in terms of accuracy and the ability to close holes, the proposed method is shown to have similar or superior performance when compared to current state-of-the-art algorithms.
Markov Tracking for Agent Coordination
NASA Technical Reports Server (NTRS)
Washington, Richard; Lau, Sonie (Technical Monitor)
1998-01-01
Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.
Receiver function deconvolution using transdimensional hierarchical Bayesian inference
NASA Astrophysics Data System (ADS)
Kolb, J. M.; Lekić, V.
2014-06-01
Teleseismic waves can convert from shear to compressional (Sp) or compressional to shear (Ps) across impedance contrasts in the subsurface. Deconvolving the parent waveforms (P for Ps or S for Sp) from the daughter waveforms (S for Ps or P for Sp) generates receiver functions which can be used to analyse velocity structure beneath the receiver. Though a variety of deconvolution techniques have been developed, they are all adversely affected by background and signal-generated noise. In order to take into account the unknown noise characteristics, we propose a method based on transdimensional hierarchical Bayesian inference in which both the noise magnitude and noise spectral character are parameters in calculating the likelihood probability distribution. We use a reversible-jump implementation of a Markov chain Monte Carlo algorithm to find an ensemble of receiver functions whose relative fits to the data have been calculated while simultaneously inferring the values of the noise parameters. Our noise parametrization is determined from pre-event noise so that it approximates observed noise characteristics. We test the algorithm on synthetic waveforms contaminated with noise generated from a covariance matrix obtained from observed noise. We show that the method retrieves easily interpretable receiver functions even in the presence of high noise levels. We also show that we can obtain useful estimates of noise amplitude and frequency content. Analysis of the ensemble solutions produced by our method can be used to quantify the uncertainties associated with individual receiver functions as well as with individual features within them, providing an objective way for deciding which features warrant geological interpretation. This method should make possible more robust inferences on subsurface structure using receiver function analysis, especially in areas of poor data coverage or under noisy station conditions.
Fusion moves for Markov random field optimization.
Lempitsky, Victor; Rother, Carsten; Roth, Stefan; Blake, Andrew
2010-08-01
The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph-cut-based algorithms (so-called QPBO-graph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph-cut approaches, which allows them to be used as building blocks within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads, 2) for fast MRF optimization by combining cheap-to-compute solutions, and 3) for the optimization of highly nonconvex continuous-labeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation).
Cheng, Jade Yu; Mailund, Thomas
2015-08-01
With full genome data from several closely related species now readily available, we have the ultimate data for demographic inference. Exploiting these full genomes, however, requires models that can explicitly model recombination along alignments of full chromosomal length. Over the last decade a class of models, based on the sequential Markov coalescence model combined with hidden Markov models, has been developed and used to make inference in simple demographic scenarios. To move forward to more complex demographic modelling we need better and more automated ways of specifying these models and efficient optimisation algorithms for inferring the parameters in complex and often high-dimensional models. In this paper we present a framework for building such coalescence hidden Markov models for pairwise alignments and present results for using heuristic optimisation algorithms for parameter estimation. We show that we can build more complex demographic models than our previous frameworks and that we obtain more accurate parameter estimates using heuristic optimisation algorithms than when using our previous gradient based approaches. Our new framework provides a flexible way of constructing coalescence hidden Markov models almost automatically. While estimating parameters in more complex models is still challenging we show that using heuristic optimisation algorithms we still get a fairly good accuracy.
Incorporating dose-rate effects in Markov radiation cell survival models.
Sachs, R K; Hlatky, L; Hahnfeldt, P; Chen, P L
1990-11-01
Markov models for the survival of cells subjected to ionizing radiation take stochastic fluctuations into account more systematically than do non-Markov counterparts. Albright's Markov RMR (repair-misrepair) model (Radiat. Res. 118, 1-20, 1989) and Curtis's Markov LPL (lethal-potentially lethal) model [in Quantitative Mathematical Models in Radiation Biology (J. Kiefer, Ed.), pp. 127-146. Springer, New York, 1989], which assume acute irradiation, are here generalized to finite dose rates. Instead of treating irradiation as an instantaneous event we introduce an irradiation period T and analyze processes during the interval T as well as afterward. Albright's RMR transition matrix is used throughout for computing the time development of repair and misrepair. During irradiation an additional matrix is added to describe the evolving radiation damage. Albright's and Curtis's Markov models are recovered as limiting cases by taking T----0 with total dose fixed; the opposite limit, of low dose rates, is also analyzed. Deviations from Poisson behavior in the statistical distributions of lesions are calculated. Other continuous-time Markov chain models ("compartmental models") are discussed briefly, for example, models which incorporate cell proliferation and saturable repair models. It is found that for low dose rates the Markov RMR and LPL models give lower survivals compared to the original non-Markov versions. For acute irradiation and high doses, the Markov models predict higher survivals. In general, theoretical extrapolations which neglect some random fluctuations have a systematic bias toward overoptimism when damage to irradiated tumors is compared with damage to surrounding tissues. PMID:2247602
Inferring transient particle transport dynamics in live cells.
Monnier, Nilah; Barry, Zachary; Park, Hye Yoon; Su, Kuan-Chung; Katz, Zachary; English, Brian P; Dey, Arkajit; Pan, Keyao; Cheeseman, Iain M; Singer, Robert H; Bathe, Mark
2015-09-01
Live-cell imaging and particle tracking provide rich information on mechanisms of intracellular transport. However, trajectory analysis procedures to infer complex transport dynamics involving stochastic switching between active transport and diffusive motion are lacking. We applied Bayesian model selection to hidden Markov modeling to infer transient transport states from trajectories of mRNA-protein complexes in live mouse hippocampal neurons and metaphase kinetochores in dividing human cells. The software is available at http://hmm-bayes.org/.
MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics
NASA Astrophysics Data System (ADS)
Feroz, F.; Hobson, M. P.; Bridges, M.
2009-10-01
We present further development and the first public release of our multimodal nested sampling algorithm, called MULTINEST. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MULTINEST algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MULTINEST software, which is fully parallelized using MPI and includes an interface to COSMOMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SUPERBAYES package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org.
Bayesian Inference for Latent Biologic Structure with Determinantal Point Processes (DPP)
Xu, Yanxun; Müller, Peter; Telesca, Donatello
2016-01-01
Summary We discuss the use of the determinantal point process (DPP) as a prior for latent structure in biomedical applications, where inference often centers on the interpretation of latent features as biologically or clinically meaningful structure. Typical examples include mixture models, when the terms of the mixture are meant to represent clinically meaningful subpopulations (of patients, genes, etc.). Another class of examples are feature allocation models. We propose the DPP prior as a repulsive prior on latent mixture components in the first example, and as prior on feature-specific parameters in the second case. We argue that the DPP is in general an attractive prior model for latent structure when biologically relevant interpretation of such structure is desired. We illustrate the advantages of DPP prior in three case studies, including inference in mixture models for magnetic resonance images (MRI) and for protein expression, and a feature allocation model for gene expression using data from The Cancer Genome Atlas. An important part of our argument are efficient and straightforward posterior simulation methods. We implement a variation of reversible jump Markov chain Monte Carlo simulation for inference under the DPP prior, using a density with respect to the unit rate Poisson process. PMID:26873271
Markov and semi-Markov processes as a failure rate
NASA Astrophysics Data System (ADS)
Grabski, Franciszek
2016-06-01
In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.
Joint Inference of Identity by Descent Along Multiple Chromosomes from Population Samples
Zheng, Chaozhi; Kuhner, Mary K.
2014-01-01
Abstract There has been much interest in detecting genomic identity by descent (IBD) segments from modern dense genetic marker data and in using them to identify human disease susceptibility loci. Here we present a novel Bayesian framework using Markov chain Monte Carlo (MCMC) realizations to jointly infer IBD states among multiple individuals not known to be related, together with the allelic typing error rate and the IBD process parameters. The data are phased single nucleotide polymorphism (SNP) haplotypes. We model changes in latent IBD state along homologous chromosomes by a continuous time Markov model having the Ewens sampling formula as its stationary distribution. We show by simulation that this model for the IBD process fits quite well with the coalescent predictions. Using simulation data sets of 40 haplotypes over regions of 1 and 10 million base pairs (Mbp), we show that the jointly estimated IBD states are very close to the true values, although the presence of linkage disequilibrium decreases the accuracy. We also present comparisons with the ibd_haplo program, which estimates IBD among sets of four haplotypes. Our new IBD detection method focuses on the scale between genome-wide methods using simple IBD models and complex coalescent-based methods that are limited to short genome segments. At the scale of a few Mbp, our approach offers potentially more power for fine-scale IBD association mapping. PMID:24606562
Dana L. Kelly; Albert Malkhasyan
2010-06-01
There is a nearly ubiquitous assumption in PSA that parameter values are at least piecewise-constant in time. As a result, Bayesian inference tends to incorporate many years of plant operation, over which there have been significant changes in plant operational and maintenance practices, plant management, etc. These changes can cause significant changes in parameter values over time; however, failure to perform Bayesian inference in the proper time-dependent framework can mask these changes. Failure to question the assumption of constant parameter values, and failure to perform Bayesian inference in the proper time-dependent framework were noted as important issues in NUREG/CR-6813, performed for the U. S. Nuclear Regulatory Commission’s Advisory Committee on Reactor Safeguards in 2003. That report noted that “industry lacks tools to perform time-trend analysis with Bayesian updating.” This paper describes an application of time-dependent Bayesian inference methods developed for the European Commission Ageing PSA Network. These methods utilize open-source software, implementing Markov chain Monte Carlo sampling. The paper also illustrates the development of a generic prior distribution, which incorporates multiple sources of generic data via weighting factors that address differences in key influences, such as vendor, component boundaries, conditions of the operating environment, etc.
A Markov switching model for annual hydrologic time series
NASA Astrophysics Data System (ADS)
Akıntuǧ, B.; Rasmussen, P. F.
2005-09-01
This paper investigates the properties of Markov switching (MS) models (also known as hidden Markov models) for generating annual time series. This type of model has been used in a number of recent studies in the water resources literature. The model considered here assumes that climate is switching between M states and that the state sequence can be described by a Markov chain. Observations are assumed to be drawn from a normal distribution whose parameters depend on the state variable. We present the stochastic properties of this class of models along with procedures for model identification and parameter estimation. Although, at a first glance, MS models appear to be quite different from ARMA models, we show that it is possible to find an ARMA model that has the same autocorrelation function and the same marginal distribution as any given MS model. Hence, despite the difference in model structure, there are strong similarities between MS and ARMA models. MS and ARMA models are applied to the time series of mean annual discharge of the Niagara River. Although it is difficult to draw any general conclusion from a single case study, it appears that MS models (and ARMA models derived from MS models) generally have stronger autocorrelation at higher lags than ARMA models estimated by conventional maximum likelihood. This may be an important property if the purpose of the study is the analysis of multiyear droughts.
Decoding coalescent hidden Markov models in linear time
Harris, Kelley; Sheehan, Sara; Kamm, John A.; Song, Yun S.
2014-01-01
In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population. PMID:25340178
A Test of the Need Hierarchy Concept by a Markov Model of Change in Need Strength.
ERIC Educational Resources Information Center
Rauschenberger, John; And Others
1980-01-01
In this study of 547 high school graduates, Alderfer's and Maslow's need hierarchy theories were expressed in Markov chain form and were subjected to empirical test. Both models were disconfirmed. Corroborative multiwave correlational analysis also failed to support the need hierarchy concept. (Author/IRT)
A Hidden Markov Approach to Modeling Interevent Earthquake Times
NASA Astrophysics Data System (ADS)
Chambers, D.; Ebel, J. E.; Kafka, A. L.; Baglivo, J.
2003-12-01
A hidden Markov process, in which the interevent time distribution is a mixture of exponential distributions with different rates, is explored as a model for seismicity that does not follow a Poisson process. In a general hidden Markov model, one assumes that a system can be in any of a finite number k of states and there is a random variable of interest whose distribution depends on the state in which the system resides. The system moves probabilistically among the states according to a Markov chain; that is, given the history of visited states up to the present, the conditional probability that the next state is a specified one depends only on the present state. Thus the transition probabilities are specified by a k by k stochastic matrix. Furthermore, it is assumed that the actual states are unobserved (hidden) and that only the values of the random variable are seen. From these values, one wishes to estimate the sequence of states, the transition probability matrix, and any parameters used in the state-specific distributions. The hidden Markov process was applied to a data set of 110 interevent times for earthquakes in New England from 1975 to 2000. Using the Baum-Welch method (Baum et al., Ann. Math. Statist. 41, 164-171), we estimate the transition probabilities, find the most likely sequence of states, and estimate the k means of the exponential distributions. Using k=2 states, we found the data were fit well by a mixture of two exponential distributions, with means of approximately 5 days and 95 days. The steady state model indicates that after approximately one fourth of the earthquakes, the waiting time until the next event had the first exponential distribution and three fourths of the time it had the second. Three and four state models were also fit to the data; the data were inconsistent with a three state model but were well fit by a four state model.
Bayesian inference of protein ensembles from SAXS data.
Antonov, L D; Olsson, S; Boomsma, W; Hamelryck, T
2016-02-17
The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble. PMID:26548662
FUBAR: a fast, unconstrained bayesian approximation for inferring selection.
Murrell, Ben; Moola, Sasha; Mabona, Amandla; Weighill, Thomas; Sheward, Daniel; Kosakovsky Pond, Sergei L; Scheffler, Konrad
2013-05-01
Model-based analyses of natural selection often categorize sites into a relatively small number of site classes. Forcing each site to belong to one of these classes places unrealistic constraints on the distribution of selection parameters, which can result in misleading inference due to model misspecification. We present an approximate hierarchical Bayesian method using a Markov chain Monte Carlo (MCMC) routine that ensures robustness against model misspecification by averaging over a large number of predefined site classes. This leaves the distribution of selection parameters essentially unconstrained, and also allows sites experiencing positive and purifying selection to be identified orders of magnitude faster than by existing methods. We demonstrate that popular random effects likelihood methods can produce misleading results when sites assigned to the same site class experience different levels of positive or purifying selection--an unavoidable scenario when using a small number of site classes. Our Fast Unconstrained Bayesian AppRoximation (FUBAR) is unaffected by this problem, while achieving higher power than existing unconstrained (fixed effects likelihood) methods. The speed advantage of FUBAR allows us to analyze larger data sets than other methods: We illustrate this on a large influenza hemagglutinin data set (3,142 sequences). FUBAR is available as a batch file within the latest HyPhy distribution (http://www.hyphy.org), as well as on the Datamonkey web server (http://www.datamonkey.org/).
Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S
2016-06-01
Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability. PMID:26934154
A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs
NASA Technical Reports Server (NTRS)
Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k+1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts.
On the Markov Property for Nonlinear Discrete-Time Systems with Markovian Inputs
NASA Technical Reports Server (NTRS)
Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The behavior of a general hybrid system in discrete-time can be represented by a non-linear difference equation x(k + 1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite-state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only fundamental measure-theoretical concepts.
Probabilistic Inference of Transcription Factor Binding from Multiple Data Sources
Lähdesmäki, Harri; Rust, Alistair G.; Shmulevich, Ilya
2008-01-01
An important problem in molecular biology is to build a complete understanding of transcriptional regulatory processes in the cell. We have developed a flexible, probabilistic framework to predict TF binding from multiple data sources that differs from the standard hypothesis testing (scanning) methods in several ways. Our probabilistic modeling framework estimates the probability of binding and, thus, naturally reflects our degree of belief in binding. Probabilistic modeling also allows for easy and systematic integration of our binding predictions into other probabilistic modeling methods, such as expression-based gene network inference. The method answers the question of whether the whole analyzed promoter has a binding site, but can also be extended to estimate the binding probability at each nucleotide position. Further, we introduce an extension to model combinatorial regulation by several TFs. Most importantly, the proposed methods can make principled probabilistic inference from multiple evidence sources, such as, multiple statistical models (motifs) of the TFs, evolutionary conservation, regulatory potential, CpG islands, nucleosome positioning, DNase hypersensitive sites, ChIP-chip binding segments and other (prior) sequence-based biological knowledge. We developed both a likelihood and a Bayesian method, where the latter is implemented with a Markov chain Monte Carlo algorithm. Results on a carefully constructed test set from the mouse genome demonstrate that principled data fusion can significantly improve the performance of TF binding prediction methods. We also applied the probabilistic modeling framework to all promoters in the mouse genome and the results indicate a sparse connectivity between transcriptional regulators and their target promoters. To facilitate analysis of other sequences and additional data, we have developed an on-line web tool, ProbTF, which implements our probabilistic TF binding prediction method using multiple data sources
Uncovering Mental Representations with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Sanborn, Adam N.; Griffiths, Thomas L.; Shiffrin, Richard M.
2010-01-01
A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these…
Maximal Parrondo's Paradox for Classical and Quantum Markov Chains
NASA Astrophysics Data System (ADS)
Grünbaum, F. Alberto; Pejic, Michael
2016-02-01
Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. In this paper, we will analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox. The game we have utilized is simpler than games for which this behavior has been previously noted in the classical and quantum cases. We will show that in certain situations the paradox can occur to a greater degree in the quantum version than is possible in the classical versions.
Markov chain analysis of random walks in disordered media
NASA Astrophysics Data System (ADS)
Mukherjee, Sonali; Nakanishi, Hisao; Fuchs, Norman H.
1994-06-01
We study the dynamical exponents dw and ds for a particle diffusing in a disordered medium (modeled by a percolation cluster), from the regime of extreme disorder (i.e., when the percolation cluster is a fractal at p=pc) to the Lorentz gas regime when the cluster has weak disorder at p>pc and the leading behavior is standard diffusion. The velocity autocorrelation function and the return to the starting point probability are related to the asymptotic spectral properties of the hopping transition probability matrix of the diffusing particle; the latter is numerically analyzed by the Arnoldi-Saad algorithm We propose and present evidence for a scaling relation for the second largest eigenvalue in terms of the size of the cluster, ||lnλ2||~S-dw/df. This relation provides a very efficient and accurate method of extracting the spectral dimension ds where ds=2df/dw.
A Markov Chain Approach to Probabilistic Swarm Guidance
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Bayard, David S.
2012-01-01
This paper introduces a probabilistic guidance approach for the coordination of swarms of autonomous agents. The main idea is to drive the swarm to a prescribed density distribution in a prescribed region of the configuration space. In its simplest form, the probabilistic approach is completely decentralized and does not require communication or collabo- ration between agents. Agents make statistically independent probabilistic decisions based solely on their own state, that ultimately guides the swarm to the desired density distribution in the configuration space. In addition to being completely decentralized, the probabilistic guidance approach has a novel autonomous self-repair property: Once the desired swarm density distribution is attained, the agents automatically repair any damage to the distribution without collaborating and without any knowledge about the damage.
Predicting Precipitation in Darwin: An Experiment with Markov Chains
ERIC Educational Resources Information Center
Boncek, John; Harden, Sig
2009-01-01
As teachers of first-year college mathematics and science students, the authors are constantly on the lookout for simple classroom exercises that improve their students' analytical and computational skills. In this article, the authors outline a project entitled "Predicting Precipitation in Darwin." In this project, students: (1) analyze and…
de Finetti Priors using Markov chain Monte Carlo computations
Bacallado, Sergio; Diaconis, Persi; Holmes, Susan
2015-01-01
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases. PMID:26412947
Super-Resolution Using Hidden Markov Model and Bayesian Detection Estimation Framework
NASA Astrophysics Data System (ADS)
Humblot, Fabrice; Mohammad-Djafari, Ali
2006-12-01
This paper presents a new method for super-resolution (SR) reconstruction of a high-resolution (HR) image from several low-resolution (LR) images. The HR image is assumed to be composed of homogeneous regions. Thus, the a priori distribution of the pixels is modeled by a finite mixture model (FMM) and a Potts Markov model (PMM) for the labels. The whole a priori model is then a hierarchical Markov model. The LR images are assumed to be obtained from the HR image by lowpass filtering, arbitrarily translation, decimation, and finally corruption by a random noise. The problem is then put in a Bayesian detection and estimation framework, and appropriate algorithms are developed based on Markov chain Monte Carlo (MCMC) Gibbs sampling. At the end, we have not only an estimate of the HR image but also an estimate of the classification labels which leads to a segmentation result.
A coupled hidden Markov model for disease interactions.
Sherlock, Chris; Xifara, Tatiana; Telfer, Sandra; Begon, Mike
2013-08-01
To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis-Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites. PMID:24223436
A coupled hidden Markov model for disease interactions.
Sherlock, Chris; Xifara, Tatiana; Telfer, Sandra; Begon, Mike
2013-08-01
To investigate interactions between parasite species in a host, a population of field voles was studied longitudinally, with presence or absence of six different parasites measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session, leading to incomplete profiles for all subjects. We use a discrete time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, which cycles through each of the diseases, first using an adaptive Metropolis-Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters. We find evidence for interactions between several pairs of parasites and of an acquired immune response for two of the parasites.
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
Thayakaran, R; Ramesh, N I
2013-01-01
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.
Bayesian functional integral method for inferring continuous data from discrete measurements.
Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul
2012-02-01
Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. PMID:22325261
Fast and accurate approximate inference of transcript expression from RNA-seq data
Hensman, James; Papastamoulis, Panagiotis; Glaus, Peter; Honkela, Antti; Rattray, Magnus
2015-01-01
Motivation: Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared with competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo and Variational Bayes (VB) are typically used. While providing a high degree of accuracy and modelling flexibility, standard implementations can be prohibitively slow for large datasets and complex transcriptome annotations. Results: We propose a novel approximate inference scheme based on VB and apply it to an existing model of transcript expression inference from RNA-seq data. Recent advances in VB algorithmics are used to improve the convergence of the algorithm beyond the standard Variational Bayes Expectation Maximization algorithm. We apply our algorithm to simulated and biological datasets, demonstrating a significant increase in speed with only very small loss in accuracy of expression level estimation. We carry out a comparative study against seven popular alternative methods and demonstrate that our new algorithm provides excellent accuracy and inter-replicate consistency while remaining competitive in computation time. Availability and implementation: The methods were implemented in R and C++, and are available as part of the BitSeq project at github.com/BitSeq. The method is also available through the BitSeq Bioconductor package. The source code to reproduce all simulation results can be accessed via github.com/BitSeq/BitSeqVB_benchmarking. Contact: james.hensman@sheffield.ac.uk or panagiotis.papastamoulis@manchester.ac.uk or Magnus.Rattray@manchester.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online
Quantification of heart rate variability by discrete nonstationary non-Markov stochastic processes
NASA Astrophysics Data System (ADS)
Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail
2002-04-01
We develop the statistical theory of discrete nonstationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of nonstationary effects. The developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized TCF. Using the projection operators technique we find the chain of finite-difference non-Markov kinetic equations for discrete nonstationary TCF and for the set of nonstationary discrete memory functions (MF's). The last one contains supplementary information about nonstationary properties of the complex system on the whole. Another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity, which contains some information of the nonstationarity effects. The full set of dynamic, spectral and kinetic parameters, and kinetic functions (TCF, short MF's statistical spectra of non-Markovity parameter, and statistical spectra of nonstationarity parameter) has made it possible to acquire the in-depth information about discreteness, non-Markov effects, long-range memory, and nonstationarity of the underlying processes. The developed theory is applied to analyze the long-time (Holter) series of RR intervals of human ECG's. We had two groups of patients: the healthy ones and the patients after myocardial infarction. In both groups we observed effects of fractality, standard and restricted self-organized criticality, and also a certain specific arrangement of spectral lines. The received results demonstrate that the power spectra of all orders (n=1,2,...) MF mn(t) exhibit the neatly expressed fractal features. We have found out that the full sets of non-Markov, discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can
Bayesian inference for a wave-front model of the neolithization of Europe.
Baggaley, Andrew W; Sarson, Graeme R; Shukurov, Anvar; Boys, Richard J; Golightly, Andrew
2012-07-01
We consider a wave-front model for the spread of neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from southern and western Europe. Our wave-front model allows for both an isotropic background spread (incorporating the effects of local geography) and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wave front, and use Gaussian process emulators to further increase the efficiency of our model, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and discuss the inferred distribution of the parameter specifying this uncertainty, along with the distributions of the parameters of our wave-front model. We subsequently use predictive distributions, taking account of parameter uncertainty, to identify radiocarbon sites which do not agree well with our model. These sites may warrant further archaeological study or motivate refinements to the model.
A framework for inferring fitness landscapes of patient-derived viruses using quasispecies theory.
Seifert, David; Di Giallonardo, Francesca; Metzner, Karin J; Günthard, Huldrych F; Beerenwinkel, Niko
2015-01-01
Fitness is a central quantity in evolutionary models of viruses. However, it remains difficult to determine viral fitness experimentally, and existing in vitro assays can be poor predictors of in vivo fitness of viral populations within their hosts. Next-generation sequencing can nowadays provide snapshots of evolving virus populations, and these data offer new opportunities for inferring viral fitness. Using the equilibrium distribution of the quasispecies model, an established model of intrahost viral evolution, we linked fitness parameters to the composition of the virus population, which can be estimated by next-generation sequencing. For inference, we developed a Bayesian Markov chain Monte Carlo method to sample from the posterior distribution of fitness values. The sampler can overcome situations where no maximum-likelihood estimator exists, and it can adaptively learn the posterior distribution of highly correlated fitness landscapes without prior knowledge of their shape. We tested our approach on simulated data and applied it to clinical human immunodeficiency virus 1 samples to estimate their fitness landscapes in vivo. The posterior fitness distributions allowed for differentiating viral haplotypes from each other, for determining neutral haplotype networks, in which no haplotype is more or less credibly fit than any other, and for detecting epistasis in fitness landscapes. Our implemented approach, called QuasiFit, is available at http://www.cbg.ethz.ch/software/quasifit.
Algorithms for Discovery of Multiple Markov Boundaries
Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.
2013-01-01
Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052
Bayesian Inference and Online Learning in Poisson Neuronal Networks.
Huang, Yanping; Rao, Rajesh P N
2016-08-01
Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carl