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
Ancestry Inference in Complex Admixtures via Variable-length Markov Chain Linkage Models
Bercovici, Sivan; Elmore, Megan; Batzoglou, Serafim
2013-01-01
Abstract 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
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.
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Bibliometric Application of Markov Chains.
ERIC Educational Resources Information Center
Pao, Miranda Lee; McCreery, Laurie
1986-01-01
A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)
McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George
2012-01-01
There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure. PMID:22719759
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…
Gao, Hong; Williamson, Scott; Bustamante, Carlos D.
2007-01-01
Nonrandom mating induces correlations in allelic states within and among loci that can be exploited to understand the genetic structure of natural populations (Wright 1965). For many species, it is of considerable interest to quantify the contribution of two forms of nonrandom mating to patterns of standing genetic variation: inbreeding (mating among relatives) and population substructure (limited dispersal of gametes). Here, we extend the popular Bayesian clustering approach STRUCTURE (Pritchard et al. 2000) for simultaneous inference of inbreeding or selfing rates and population-of-origin classification using multilocus genetic markers. This is accomplished by eliminating the assumption of Hardy–Weinberg equilibrium within clusters and, instead, calculating expected genotype frequencies on the basis of inbreeding or selfing rates. We demonstrate the need for such an extension by showing that selfing leads to spurious signals of population substructure using the standard STRUCTURE algorithm with a bias toward spurious signals of admixture. We gauge the performance of our method using extensive coalescent simulations and demonstrate that our approach can correct for this bias. We also apply our approach to understanding the population structure of the wild relative of domesticated rice, Oryza rufipogon, an important partially selfing grass species. Using a sample of n = 16 individuals sequenced at 111 random loci, we find strong evidence for existence of two subpopulations, which correlates well with geographic location of sampling, and estimate selfing rates for both groups that are consistent with estimates from experimental data (s ≈ 0.48–0.70). PMID:17483417
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…
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.
Document Ranking Based upon Markov Chains.
ERIC Educational Resources Information Center
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
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.
Inferring parental genomic ancestries using pooled semi-Markov processes
Zou, James Y.; Halperin, Eran; Burchard, Esteban; Sankararaman, Sriram
2015-01-01
Motivation: A basic problem of broad public and scientific interest is to use the DNA of an individual to infer the genomic ancestries of the parents. In particular, we are often interested in the fraction of each parent’s genome that comes from specific ancestries (e.g. European, African, Native American, etc). This has many applications ranging from understanding the inheritance of ancestry-related risks and traits to quantifying human assortative mating patterns. Results: We model the problem of parental genomic ancestry inference as a pooled semi-Markov process. We develop a general mathematical framework for pooled semi-Markov processes and construct efficient inference algorithms for these models. Applying our inference algorithm to genotype data from 231 Mexican trios and 258 Puerto Rican trios where we have the true genomic ancestry of each parent, we demonstrate that our method accurately infers parameters of the semi-Markov processes and parents’ genomic ancestries. We additionally validated the method on simulations. Our model of pooled semi-Markov process and inference algorithms may be of independent interest in other settings in genomics and machine learning. Contact: jazo@microsoft.com PMID:26072482
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.
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
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.
Approximating Markov Chains: What and why
Pincus, S.
1996-06-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to {open_quote}{open_quote}solve,{close_quote}{close_quote} or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the {ital attractor}, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. {copyright} {ital 1996 American Institute of Physics.}
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.
Multivariate Markov chain modeling for stock markets
NASA Astrophysics Data System (ADS)
Maskawa, Jun-ichi
2003-06-01
We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.
SATMC: Spectral energy distribution Analysis Through Markov Chains
NASA Astrophysics Data System (ADS)
Johnson, S. P.; Wilson, G. W.; Tang, Y.; Scott, K. S.
2013-12-01
We present the general purpose spectral energy distribution (SED) fitting tool SED Analysis Through Markov Chains (SATMC). Utilizing Monte Carlo Markov Chain (MCMC) algorithms, SATMC fits an observed SED to SED templates or models of the user's choice to infer intrinsic parameters, generate confidence levels and produce the posterior parameter distribution. Here, we describe the key features of SATMC from the underlying MCMC engine to specific features for handling SED fitting. We detail several test cases of SATMC, comparing results obtained from traditional least-squares methods, which highlight its accuracy, robustness and wide range of possible applications. We also present a sample of submillimetre galaxies (SMGs) that have been fitted using the SED synthesis routine GRASIL as input. In general, these SMGs are shown to occupy a large volume of parameter space, particularly in regards to their star formation rates which range from ˜30 to 3000 M⊙ yr-1 and stellar masses which range from ˜1010 to 1012 M⊙. Taking advantage of the Bayesian formalism inherent to SATMC, we also show how the fitting results may change under different parametrizations (i.e. different initial mass functions) and through additional or improved photometry, the latter being crucial to the study of high-redshift galaxies.
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…
Multiple pattern matching: a Markov chain approach.
Lladser, Manuel E; Betterton, M D; Knight, Rob
2008-01-01
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text. PMID:17668213
Manpower planning using Markov Chain model
NASA Astrophysics Data System (ADS)
Saad, Syafawati Ab; Adnan, Farah Adibah; Ibrahim, Haslinda; Rahim, Rahela
2014-07-01
Manpower planning is a planning model which understands the flow of manpower based on the policies changes. For such purpose, numerous attempts have been made by researchers to develop a model to investigate the track of movements of lecturers for various universities. As huge number of lecturers in a university, it is difficult to track the movement of lecturers and also there is no quantitative way used in tracking the movement of lecturers. This research is aimed to determine the appropriate manpower model to understand the flow of lecturers in a university in Malaysia by determine the probability and mean time of lecturers remain in the same status rank. In addition, this research also intended to estimate the number of lecturers in different status rank (lecturer, senior lecturer and associate professor). From the previous studies, there are several methods applied in manpower planning model and appropriate method used in this research is Markov Chain model. Results obtained from this study indicate that the appropriate manpower planning model used is validated by compare to the actual data. The smaller margin of error gives a better result which means that the projection is closer to actual data. These results would give some suggestions for the university to plan the hiring lecturers and budgetary for university in future.
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.
Markov Chains For Testing Redundant Software
NASA Technical Reports Server (NTRS)
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
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.
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.
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…
Building Higher-Order Markov Chain Models with EXCEL
ERIC Educational Resources Information Center
Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K.
2004-01-01
Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…
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…
Analyzing Sequential Categorical Data: Individual Variation in Markov Chains.
ERIC Educational Resources Information Center
Gardner, William
1990-01-01
This paper provides a method for analyzing data consisting of event sequences and covariate observations associated with Markov chains. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. (TJH)
Operations and support cost modeling using Markov chains
NASA Technical Reports Server (NTRS)
Unal, Resit
1989-01-01
Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.
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.
Using Markov Chain Analyses in Counselor Education Research
ERIC Educational Resources Information Center
Duys, David K.; Headrick, Todd C.
2004-01-01
This study examined the efficacy of an infrequently used statistical analysis in counselor education research. A Markov chain analysis was used to examine hypothesized differences between students' use of counseling skills in an introductory course. Thirty graduate students participated in the study. Independent raters identified the microskills…
Regenerative Markov Chain Monte Carlo for any distribution.
Minh, D.
2012-01-01
While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution
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
An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes
ERIC Educational Resources Information Center
Kapland, David
2008-01-01
This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…
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.
Constructing 1/omegaalpha noise from reversible Markov chains.
Erland, Sveinung; Greenwood, Priscilla E
2007-09-01
This paper gives sufficient conditions for the output of 1/omegaalpha 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/omegaalpha condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/omega noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/omegaalpha noise which also has a long memory. PMID:17930206
Statistical significance test for transition matrices of atmospheric Markov chains
NASA Technical Reports Server (NTRS)
Vautard, Robert; Mo, Kingtse C.; Ghil, Michael
1990-01-01
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Space system operations and support cost analysis using Markov chains
NASA Technical Reports Server (NTRS)
Unal, Resit; Dean, Edwin B.; Moore, Arlene A.; Fairbairn, Robert E.
1990-01-01
This paper evaluates the use of Markov chain process in probabilistic life cycle cost analysis and suggests further uses of the process as a design aid tool. A methodology is developed for estimating operations and support cost and expected life for reusable space transportation systems. Application of the methodology is demonstrated for the case of a hypothetical space transportation vehicle. A sensitivity analysis is carried out to explore the effects of uncertainty in key model inputs.
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.
Markov chain evaluation of acute postoperative pain transition states.
Tighe, Patrick J; Bzdega, Matthew; Fillingim, Roger B; Rashidi, Parisa; Aytug, Haldun
2016-03-01
Previous investigations on acute postoperative pain dynamicity have focused on daily pain assessments, and so were unable to examine intraday variations in acute pain intensity. We analyzed 476,108 postoperative acute pain intensity ratings, which were clinically documented on postoperative days 1 to 7 from 8346 surgical patients using Markov chain modeling to describe how patients are likely to transition from one pain state to another in a probabilistic fashion. The Markov chain was found to be irreducible and positive recurrent, with no absorbing states. Transition probabilities ranged from 0.0031, for the transition from state 10 to state 1, to 0.69 for the transition from state 0 to state 0. The greatest density of transitions was noted in the diagonal region of the transition matrix, suggesting that patients were generally most likely to transition to the same pain state as their current state. There were also slightly increased probability densities in transitioning to a state of asleep or 0 from the current state. An examination of the number of steps required to traverse from a particular first pain score to a target state suggested that overall, fewer steps were required to reach a state of 0 (range 6.1-8.8 steps) or asleep (range 9.1-11) than were required to reach a mild pain intensity state. Our results suggest that using Markov chains is a feasible method for describing probabilistic postoperative pain trajectories, pointing toward the possibility of using Markov decision processes to model sequential interactions between pain intensity ratings, and postoperative analgesic interventions. PMID:26588689
Exact Likelihood-free Markov Chain Monte Carlo for Elliptically Contoured Distributions
Marjoram, Paul
2015-01-01
Recent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible. PMID:26167984
Robust Dynamics and Control of a Partially Observed Markov Chain
Elliott, R. J. Malcolm, W. P. Moore, J. P.
2007-12-15
In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.
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.
On Construction of Quantum Markov Chains on Cayley trees
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Mukhamedov, Farrukh; Souissi, Abdessatar
2016-03-01
The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. 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. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting.
Deterioration Prediction Model of Irrigation Facilities by Markov Chain Model
NASA Astrophysics Data System (ADS)
Mori, Takehisa; Nishino, Noriyasu; Fujiwara, Tetsuro
"Stock Management" launched in all over Japan is an activity to use irrigation facilities effectively and to reduce life cycle costs of theirs. Deterioration prediction of the irrigation facility condition is a vital process for the study of maintenance measures and the estimation of maintenance cost. It is important issue to establish the prediction technique with higher accuracy. Thereupon, we established a deterioration prediction model by a statistical method "Markov chain", and analyzed a function diagnosis data of irrigation facilities. As a result, we clarified the deterioration characteristics into each structure type and facilities.
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.
Radiative transfer calculated from a Markov chain formalism
NASA Technical Reports Server (NTRS)
Esposito, L. W.; House, L. L.
1978-01-01
The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.
A Markov chain model for reliability growth and decay
NASA Technical Reports Server (NTRS)
Siegrist, K.
1982-01-01
A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.
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.
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
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.
Kinetics and thermodynamics of first-order Markov chain copolymerization
NASA Astrophysics Data System (ADS)
Gaspard, P.; Andrieux, D.
2014-07-01
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.
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. PMID:25084957
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.
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.
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.
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.
A Quantum Algorithm for Estimating Hitting Times of Markov Chains
NASA Astrophysics Data System (ADS)
Narayan Chowdhury, Anirban; Somma, Rolando
We present a quantum algorithm to estimate the hitting time of a reversible Markov chain faster than classically possible. To this end, we show that the hitting time is given by an expected value of the inverse of a Hermitian matrix. To obtain this expected value, our algorithm combines three important techniques developed in the literature. One such a technique is called spectral gap amplification and we use it to amplify the gap of the Hermitian matrix or reduce its condition number. We then use a new algorithm by Childs, Kothari, and Somma to implement the inverse of a matrix, and finally use methods developed in the context of quantum metrology to reduce the complexity of expected-value estimation for a given precision. The authors acknowledge support from AFOSR Grant Number FA9550-12-1-0057 and the Google Research Award.
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.
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.
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. PMID:27261539
Bayesian restoration of a hidden Markov chain with applications to DNA sequencing.
Churchill, G A; Lazareva, B
1999-01-01
Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution determined by the state of the hidden Markov chain. We present a Bayesian solution to the problem of restoring the sequence of states visited by the hidden Markov chain from a given sequence of observed outputs. Our approach is based on a Monte Carlo Markov chain algorithm that allows us to draw samples from the full posterior distribution of the hidden Markov chain paths. The problem of estimating the probability of individual paths and the associated Monte Carlo error of these estimates is addressed. The method is illustrated by considering a problem of DNA sequence multiple alignment. The special structure for the hidden Markov model used in the sequence alignment problem is considered in detail. In conclusion, we discuss certain interesting aspects of biological sequence alignments that become accessible through the Bayesian approach to HMM restoration. PMID:10421527
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.
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.
Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo.
Craig, B A; Newton, M A; Garrott, R A; Reynolds, J E; Wilcox, J R
1997-06-01
We assess population trends of the Atlantic coast population of Florida manatee, Trichechus manatus latirostris, by reanalyzing aerial survey data collected between 1982 and 1992. To do so, we develop an explicit biological model that accounts for the method by which the manatees are counted, the mammals' movement between surveys, and the behavior of the population total over time. Bayesian inference, enabled by Markov chain Monte Carlo, is used to combine the survey data with the biological model. We compute marginal posterior distributions for all model parameters and predictive distributions for future counts. Several conclusions, such as a decreasing population growth rate and low sighting probabilities, are consistent across different prior specifications. PMID:9192449
A graph theoretic approach to global earthquake sequencing: A Markov chain model
NASA Astrophysics Data System (ADS)
Vasudevan, K.; Cavers, M. S.
2012-12-01
We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. For earthquake zonation, we consider the simplified plate boundary template of Kagan, Bird, and Jackson (KBJ template, 2010). We demonstrate the applicability of the directed graph approach to hazard-related forecasting using some of the properties of graphs that represent the finite Markov chain. We extend the present study to consider Bird's 52-plate zonation (2003) describing the global earthquakes at and within plate boundaries to gain further insight into the usefulness of digraphs corresponding to a Markov chain model.
Regeneration and Fixed-Width Analysis of Markov Chain Monte Carlo Algorithms
NASA Astrophysics Data System (ADS)
Latuszynski, Krzysztof
2009-07-01
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and sufficient conditions in terms of regeneration for central limit theorems for ergodic Markov chains and a regenerative proof of a CLT version for uniformly ergodic Markov chains with E_{π}f^2< infty. To obtain asymptotic confidence intervals for MCMC estimators, strongly consistent estimators of the asymptotic variance are essential. We relax assumptions required to obtain such estimators. Moreover, under a drift condition, nonasymptotic fixed-width results for MCMC estimators for a general state space setting (not necessarily compact) and not necessarily bounded target function f are obtained. The last chapter is devoted to the idea of adaptive Monte Carlo simulation and provides convergence results and law of large numbers for adaptive procedures under path-stability condition for transition kernels.
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.
2015-01-01
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
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.
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.
Finding and Testing Network Communities by Lumped Markov Chains
Piccardi, Carlo
2011-01-01
Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called “persistence probability” is associated to a cluster, which is then defined as an “-community” if such a probability is not smaller than . Consistently, a partition composed of -communities is an “-partition.” These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired -level allows one to immediately select the -partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure. PMID:22073245
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.
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 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
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...
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...
Cool walking: a new Markov chain Monte Carlo sampling method.
Brown, Scott; Head-Gordon, Teresa
2003-01-15
Effective relaxation processes for difficult systems like proteins or spin glasses require special simulation techniques that permit barrier crossing to ensure ergodic sampling. Numerous adaptations of the venerable Metropolis Monte Carlo (MMC) algorithm have been proposed to improve its sampling efficiency, including various hybrid Monte Carlo (HMC) schemes, and methods designed specifically for overcoming quasi-ergodicity problems such as Jump Walking (J-Walking), Smart Walking (S-Walking), Smart Darting, and Parallel Tempering. We present an alternative to these approaches that we call Cool Walking, or C-Walking. In C-Walking two Markov chains are propagated in tandem, one at a high (ergodic) temperature and the other at a low temperature. Nonlocal trial moves for the low temperature walker are generated by first sampling from the high-temperature distribution, then performing a statistical quenching process on the sampled configuration to generate a C-Walking jump move. C-Walking needs only one high-temperature walker, satisfies detailed balance, and offers the important practical advantage that the high and low-temperature walkers can be run in tandem with minimal degradation of sampling due to the presence of correlations. To make the C-Walking approach more suitable to real problems we decrease the required number of cooling steps by attempting to jump at intermediate temperatures during cooling. We further reduce the number of cooling steps by utilizing "windows" of states when jumping, which improves acceptance ratios and lowers the average number of cooling steps. We present C-Walking results with comparisons to J-Walking, S-Walking, Smart Darting, and Parallel Tempering on a one-dimensional rugged potential energy surface in which the exact normalized probability distribution is known. C-Walking shows superior sampling as judged by two ergodic measures. PMID:12483676
Markov chain analysis of succession in a rocky subtidal community.
Hill, M Forrest; Witman, Jon D; Caswell, Hal
2004-08-01
We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986-1994) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described successional dynamics by species turnover rates, recurrence times, and the entropy of the transition matrix. We used perturbation analysis to quantify the response of diversity to successional rates and species removals. The equilibrium community was dominated by an encrusting sponge (Hymedesmia) and a bryozoan (Crisia eburnea). The equilibrium structure explained 98% of the variance in observed species frequencies. Dominant species have low probabilities of disturbance and high rates of colonization and persistence. On average, species turn over every 3.4 years. Recurrence times varied among species (7-268 years); rare species had the longest recurrence times. The community converged to equilibrium quickly (9.5 years), as measured by Dobrushin's coefficient of ergodicity. The largest changes in evenness would result from removal of the dominant sponge Hymedesmia. Subdominant species appear to increase evenness by slowing the dominance of Hymedesmia. Comparison of the subtidal community with intertidal and coral reef communities revealed that disturbance rates are an order of magnitude higher in coral reef than in rocky intertidal and subtidal communities. Colonization rates and turnover times, however, are lowest and longest in coral reefs, highest and shortest in intertidal communities, and intermediate in subtidal communities. PMID:15278851
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.
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…
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.
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
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.
1994-01-01
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, we 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. PMID:8128968
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.
Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng
2010-01-01
This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632
Borodovsky, M; Peresetsky, A
1994-09-01
Non-homogeneous Markov chain models can represent biologically important regions of DNA sequences. The statistical pattern that is described by these models is usually weak and was found primarily because of strong biological indications. The general method for extracting similar patterns is presented in the current paper. The algorithm incorporates cluster analysis, multiple alignment and entropy minimization. The method was first tested using the set of DNA sequences produced by Markov chain generators. It was shown that artificial gene sequences, which initially have been randomly set up along the multiple alignment panels, are aligned according to the hidden triplet phase. Then the method was applied to real protein-coding sequences and the resulting alignment clearly indicated the triplet phase and produced the parameters of the optimal 3-periodic non-homogeneous Markov chain model. These Markov models were already employed in the GeneMark gene prediction algorithm, which is used in genome sequencing projects. The algorithm can also handle the case in which the sequences to be aligned reveal different statistical patterns, such as Escherichia coli protein-coding sequences belonging to Class II and Class III. The algorithm accepts a random mix of sequences from different classes, and is able to separate them into two groups (clusters), align each cluster separately, and define a non-homogeneous Markov chain model for each sequence cluster. PMID:7952897
A recursive model-reduction method for approximate inference in Gaussian Markov random fields.
Johnson, Jason K; Willsky, Alan S
2008-01-01
This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise, yet faithful, model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable representations of Fisher information on thin chordal graphs. Given the resulting set of thinned cavity models, we also develop a fast preconditioner, which provides a simple iterative method to compute optimal estimates. Thus, our overall approach combines recursive inference, variational learning and iterative estimation. We demonstrate the accuracy and scalability of this approach in several challenging, large-scale remote sensing problems. PMID:18229805
DIM SUM: demography and individual migration simulated using a Markov chain.
Brown, Jeremy M; Savidge, Kevin; McTavish, Emily Jane B
2011-03-01
An increasing number of studies seek to infer demographic history, often jointly with genetic relationships. Despite numerous analytical methods for such data, few simulations have investigated the methods' power and robustness, especially when underlying assumptions have been violated. DIM SUM (Demography and Individual Migration Simulated Using a Markov chain) is a stand-alone Java program for the simulation of population demography and individual migration while recording ancestor-descendant relationships. It does not employ coalescent assumptions or discrete population boundaries. It is extremely flexible, allowing the user to specify border positions, reactions of organisms to borders, local and global carrying capacities, individual dispersal kernels, rates of reproduction and strategies for sampling individuals. Spatial variables may be specified using image files (e.g., as exported from gis software) and may vary through time. In combination with software for genetic marker simulation, DIM SUM will be useful for testing phylogeographic (e.g., nested clade phylogeographic analysis, coalescent-based tests and continuous-landscape frameworks) and landscape-genetic methods, specifically regarding violations of coalescent assumptions. It can also be used to explore the qualitative features of proposed demographic scenarios (e.g. regarding biological invasions) and as a pedagogical tool. DIM SUM (with user's manual) can be downloaded from http://code.google.com/p/bio-dimsum. PMID:21429144
Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood
Wegmann, Daniel; Leuenberger, Christoph; Excoffier, Laurent
2009-01-01
Approximate Bayesian computation (ABC) techniques permit inferences in complex demographic models, but are computationally inefficient. A Markov chain Monte Carlo (MCMC) approach has been proposed (Marjoram et al. 2003), but it suffers from computational problems and poor mixing. We propose several methodological developments to overcome the shortcomings of this MCMC approach and hence realize substantial computational advances over standard ABC. The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment. We also propose to use a partial least-squares (PLS) transformation to choose informative statistics. The accuracy of our approach is examined in the case of the divergence of two populations with and without migration. In that case, our ABC–MCMC approach needs considerably lower computation time to reach the same accuracy than conventional ABC. We then apply our method to a more complex case with the estimation of divergence times and migration rates between three African populations. PMID:19506307
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
Testing the efficiency of Markov chain Monte Carlo with People using facial affect categories.
Martin, Jay B; Griffiths, Thomas L; Sanborn, Adam N
2012-01-01
Exploring how people represent natural categories is a key step toward developing a better understanding of how people learn, form memories, and make decisions. Much research on categorization has focused on artificial categories that are created in the laboratory, since studying natural categories defined on high-dimensional stimuli such as images is methodologically challenging. Recent work has produced methods for identifying these representations from observed behavior, such as reverse correlation (RC). We compare RC against an alternative method for inferring the structure of natural categories called Markov chain Monte Carlo with People (MCMCP). Based on an algorithm used in computer science and statistics, MCMCP provides a way to sample from the set of stimuli associated with a natural category. We apply MCMCP and RC to the problem of recovering natural categories that correspond to two kinds of facial affect (happy and sad) from realistic images of faces. Our results show that MCMCP requires fewer trials to obtain a higher quality estimate of people's mental representations of these two categories. PMID:21972923
Simplification of irreversible Markov chains by removal of states with fast leaving rates.
Jia, Chen
2016-07-01
In the recent work of Ullah et al. (2012a), the authors developed an effective method to simplify reversible Markov chains by removal of states with low equilibrium occupancies. In this paper, we extend this result to irreversible Markov chains. We show that an irreversible chain can be simplified by removal of states with fast leaving rates. Moreover, we reveal that the irreversibility of the chain will always decrease after model simplification. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off. Examples from biology are also given to illustrate the main results of this paper. PMID:27067245
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…
An Evaluation of a Markov Chain Monte Carlo Method for the Rasch Model.
ERIC Educational Resources Information Center
Kim, Seock-Ho
2001-01-01
Examined the accuracy of the Gibbs sampling Markov chain Monte Carlo procedure for estimating item and person (theta) parameters in the one-parameter logistic model. Analyzed four empirical datasets using the Gibbs sampling, conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood methods. Discusses the conditions…
Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model
ERIC Educational Resources Information Center
de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.
2006-01-01
The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…
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...
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…
Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains
NASA Astrophysics Data System (ADS)
Formentin, M.; Külske, C.; Reichenbachs, A.
2012-01-01
We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.
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.
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.
Learning a Markov Logic network for supervised gene regulatory network inference
2013-01-01
Background Gene regulatory network inference remains a challenging problem in systems biology despite the numerous approaches that have been proposed. When substantial knowledge on a gene regulatory network is already available, supervised network inference is appropriate. Such a method builds a binary classifier able to assign a class (Regulation/No regulation) to an ordered pair of genes. Once learnt, the pairwise classifier can be used to predict new regulations. In this work, we explore the framework of Markov Logic Networks (MLN) that combine features of probabilistic graphical models with the expressivity of first-order logic rules. Results We propose to learn a Markov Logic network, e.g. a set of weighted rules that conclude on the predicate “regulates”, starting from a known gene regulatory network involved in the switch proliferation/differentiation of keratinocyte cells, a set of experimental transcriptomic data and various descriptions of genes all encoded into first-order logic. As training data are unbalanced, we use asymmetric bagging to learn a set of MLNs. The prediction of a new regulation can then be obtained by averaging predictions of individual MLNs. As a side contribution, we propose three in silico tests to assess the performance of any pairwise classifier in various network inference tasks on real datasets. A first test consists of measuring the average performance on balanced edge prediction problem; a second one deals with the ability of the classifier, once enhanced by asymmetric bagging, to update a given network. Finally our main result concerns a third test that measures the ability of the method to predict regulations with a new set of genes. As expected, MLN, when provided with only numerical discretized gene expression data, does not perform as well as a pairwise SVM in terms of AUPR. However, when a more complete description of gene properties is provided by heterogeneous sources, MLN achieves the same performance as a black
An informational transition in conditioned Markov chains: Applied to genetics and evolution.
Zhao, Lei; Lascoux, Martin; Waxman, David
2016-08-01
In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states. PMID:27105672
NASA Astrophysics Data System (ADS)
Sadegh, M.; Vrugt, J. A.
2013-12-01
The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at increasingly finer spatial and temporal scales. Reconciling these system models with field and remote sensing data is a difficult task, particularly because average measures of model/data similarity inherently lack the power to provide a meaningful comparative evaluation of the consistency in model form and function. The very construction of the likelihood function - as a summary variable of the (usually averaged) properties of the error residuals - dilutes and mixes the available information into an index having little remaining correspondence to specific behaviors of the system (Gupta et al., 2008). The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh [2013] to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a much stronger and compelling diagnostic power than some aggregated measure of the size of the error residuals. Here, we will introduce an efficient ABC sampling method that is orders of magnitude faster in exploring the posterior parameter distribution than commonly used rejection and Population Monte Carlo (PMC) samplers. Our methodology uses Markov Chain Monte Carlo simulation with DREAM, and takes advantage of a simple computational trick to resolve discontinuity problems with the application of set-theoretic summary statistics. We will also demonstrate a set of summary statistics that are rather insensitive to
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.
Hey, Jody; Nielsen, Rasmus
2007-01-01
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
Hey, Jody; Nielsen, Rasmus
2007-02-20
In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
An 'adding' algorithm for the Markov chain formalism for radiation transfer
NASA Technical Reports Server (NTRS)
Esposito, L. W.
1979-01-01
An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.
A Markov Chain Monte Carlo Based Method for System Identification
Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2002-10-22
This paper describes a novel methodology for the identification of mechanical systems and structures from vibration response measurements. It combines prior information, observational data and predictive finite element models to produce configurations and system parameter values that are most consistent with the available data and model. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. The resulting process enables the estimation of distributions of both individual parameters and system-wide states. Attractive features of this approach include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate; (2) function effectively when exposed to degraded conditions including: noisy data, incomplete data sets and model misspecification; (3) allow alternative estimates to be produced and compared, and (4) incrementally update initial estimates and analysis as more data becomes available. A series of test cases based on a simple fixed-free cantilever beam is presented. These results demonstrate that the algorithm is able to identify the system, based on the stiffness matrix, given applied force and resultant nodal displacements. Moreover, it effectively identifies locations on the beam where damage (represented by a change in elastic modulus) was specified.
A Markov Chain Model for evaluating the effectiveness of randomized surveillance procedures
Edmunds, T.A.
1994-01-01
A Markov Chain Model has been developed to evaluate the effectiveness of randomized surveillance procedures. The model is applicable for surveillance systems that monitor a collection of assets by randomly selecting and inspecting the assets. The model provides an estimate of the detection probability as a function of the amount of time that an adversary would require to steal or sabotage the asset. An interactive computer code has been written to perform the necessary computations.
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
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.
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.
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
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)
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
2014-01-01
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.
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
Williams, Michael S; Ebel, Eric D
2014-11-18
The fitting of statistical distributions to chemical and microbial contamination data is a common application in risk assessment. These distributions are used to make inferences regarding even the most pedestrian of statistics, such as the population mean. The reason for the heavy reliance on a fitted distribution is the presence of left-, right-, and interval-censored observations in the data sets, with censored observations being the result of nondetects in an assay, the use of screening tests, and other practical limitations. Considerable effort has been expended to develop statistical distributions and fitting techniques for a wide variety of applications. Of the various fitting methods, Markov Chain Monte Carlo methods are common. An underlying assumption for many of the proposed Markov Chain Monte Carlo methods is that the data represent independent and identically distributed (iid) observations from an assumed distribution. This condition is satisfied when samples are collected using a simple random sampling design. Unfortunately, samples of food commodities are generally not collected in accordance with a strict probability design. Nevertheless, pseudosystematic sampling efforts (e.g., collection of a sample hourly or weekly) from a single location in the farm-to-table continuum are reasonable approximations of a simple random sample. The assumption that the data represent an iid sample from a single distribution is more difficult to defend if samples are collected at multiple locations in the farm-to-table continuum or risk-based sampling methods are employed to preferentially select samples that are more likely to be contaminated. This paper develops a weighted bootstrap estimation framework that is appropriate for fitting a distribution to microbiological samples that are collected with unequal probabilities of selection. An example based on microbial data, derived by the Most Probable Number technique, demonstrates the method and highlights the
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
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 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.
NASA Astrophysics Data System (ADS)
Shi, X.; Ye, M.; Curtis, G. P.; Lu, D.; Meyer, P. D.; Yabusaki, S.; Wu, J.
2011-12-01
Assessment of parametric uncertainty for groundwater reactive transport models is challenging, because the models are highly nonlinear with respect to their parameters due to nonlinear reaction equations and process coupling. The nonlinearity may yield parameter distributions that are non-Gaussian and have multiple modes. For such parameter distributions, the widely used nonlinear regression methods may not be able to accurately quantify predictive uncertainty. One solution to this problem is to use Markov Chain Monte Carlo (MCMC) techniques. Both the nonlinear regression and MCMC methods are used in this study for quantification of parametric uncertainty of a surface complexation model (SCM), developed to simulate hexavalent uranium [U(VI)] transport in column experiments. Firstly, a brute force Monte Carlo (MC) simulation with hundreds of thousands of model executions is conducted to understand the surface of objective function and predictive uncertainty of uranium concentration. Subsequently, the Gauss-Marquardt-Levenberg method is applied to calibrate the model. It shows that, even with multiple initial guesses, the local optimization method has difficulty of finding the global optimum because of the rough surface of the objective function and local optima/minima due to model nonlinearity. Another problem of the nonlinear regression is the underestimation of predictive uncertainty, as both the linear and nonlinear confidence intervals are narrower than that obtained from the native MC simulation. Since the naïve MC simulation is computationally expensive, the above challenges for parameter estimation and predictive uncertainty analysis are addressed using a computationally efficient MCMC technique, the DiffeRential Evolution Adaptive Metropolis algorithm (DREAM) algorithm. The results obtained from running DREAM compared with those from brute force Monte Carlo simulations shown that MCMC not only successfully infers the multi-modals posterior probability
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 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
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.
Global characterization of geophysical data using lagrangean data and Markov-chain statistics.
NASA Astrophysics Data System (ADS)
Pares-Sierra, Alejandro; Flores-Morales, Ana Laura
2015-04-01
A method for the global analysis of geophysical data is presented. Using short-period Lagrangean transports, calculated off-line from a numerical circulation ocean model (ROMS), a stochastic transition matrix is constructed. Iteration methods for this last, sparse, very-large matrix are used to solve standard Markov chain problem of time of arrival and destination. The method permits the identification of areas of influence, time of residence and connectivity between regions. Application for the Gulf of Mexico and the Eastern Tropical Pacific circulation is presented.
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)
Alavirad, Hamzeh; Malekjani, Mohammad
2014-02-01
We constrain holographic dark energy (HDE) with time varying gravitational coupling constant in the framework of the modified Friedmann equations using cosmological data from type Ia supernovae, baryon acoustic oscillations, cosmic microwave background radiation and X-ray gas mass fraction. Applying a Markov Chain Monte Carlo (MCMC) simulation, we obtain the best fit values of the model and cosmological parameters within 1 σ confidence level (CL) in a flat universe as: , , and the HDE constant . Using the best fit values, the equation of state of the dark component at the present time w d0 at 1 σ CL can cross the phantom boundary w=-1.
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
Markov chain Monte Carlo linkage analysis of a complex qualitative phenotype.
Hinrichs, A; Lin, J H; Reich, T; Bierut, L; Suarez, B K
1999-01-01
We tested a new computer program, LOKI, that implements a reversible jump Markov chain Monte Carlo (MCMC) technique for segregation and linkage analysis. Our objective was to determine whether this software, designed for use with continuously distributed phenotypes, has any efficacy when applied to the discrete disease states of the simulated data from the Mordor data from GAW Problem 1. Although we were able to identify the genomic location for two of the three quantitative trait loci by repeated application of the software, the MCMC sampler experienced significant mixing problems indicating that the method, as currently formulated in LOKI, was not suitable for the discrete phenotypes in this data set. PMID:10597502
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.
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)
Bao, J.; Ren, H.; Hou, Z.; Ray, J.; Swiler, L.; Huang, M.
2015-12-01
We developed a novel scalable multi-chain Markov chain Monte Carlo (MCMC) method for high-dimensional inverse problems. The method is scalable in terms of number of chains and processors, and is useful for Bayesian calibration of computationally expensive simulators typically used for scientific and engineering calculations. In this study, we demonstrate two applications of this method for hydraulic and geological inverse problems. The first one is monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data, where challenges exist in the inversion of GPR tomographic data for handling non-uniqueness and nonlinearity and high-dimensionality of unknowns. We integrated the multi-chain MCMC framework with the pilot point concept, a curved-ray GPR forward model, and a sequential Gaussian simulation (SGSIM) algorithm for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as its spatial correlation range, which are used to construct the whole field of dielectric permittivity using SGSIM. The second application is reservoir porosity and saturation estimation using the multi-chain MCMC approach to jointly invert marine seismic amplitude versus angle (AVA) and controlled-source electro-magnetic (CSEM) data for a layered reservoir model, where the unknowns to be estimated include the porosity and fluid saturation in each reservoir layer and the electrical conductivity of the overburden and bedrock. The computational efficiency, accuracy, and convergence behaviors of the inversion approach are systematically evaluated.
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.
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)
Adu, Nurlia; Indriati Retno, P.; Suharsono
2016-02-01
Monitoring of micro seismic activity in the geothermal field is useful to know the fracture controllers in the geothermal reservoir area. However, in determining the point of micro earthquake, hypocenters still contain inherent uncertainties due to several factors such as mismatches velocity model used by the actual subsurface conditions. For that reason, hypocenter relocation by Markov Chain method is used, to simulate the hypocenter point spatially based opportunities transition containing the principle of conditional probability. The purpose of this relocation is to improve the models of the hypocenter so that the interpretation of the subsurface structure is better. From the result of the relocation of using Markov Chain identified fault structures trending below the surface of the northeast-southwest (NE-SW) with approximately N38°E. This structure is suspected as the continuity of the structure in the surface. The depth of the hypocenter is located 758 m above mean sea level more than 800 m below mean sea level.
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).
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.
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.
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.
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.
Predicting seasonal fate of phenanthrene in aquatic environment with a Markov chain.
Sun, Caiyun; Ma, Qiyun; Zhang, Jiquan; Zhou, Mo; Chen, Yanan
2016-08-01
Phenanthrene (Phe) with carcinogenicity is ubiquitous in the environment, especially in aquatic environment; its toxicity is greater. To help determine toxicity risk and remediation strategies, this study predicted seasonal fate of Phe in aquatic environment. Candidate mechanisms including biodegradation, sorption, desorption, photodegradation, hydrolysis and volatility were studied; the results for experiments under simulated conditions for normal, wet and dry seasons in the Yinma River Basin indicated that biodegradation in sediment, sorption, desorption, and volatility were important pathways for elimination of Phe from aquatic environment and showed seasonal variations. A microcosm which was used to mimic sediment/water system was set up to illustrate seasonal distribution and transport of Phe. A Markov chain was applied to predict seasonal fate of Phe in air/water/sediment environment, the predicted results were perfectly agreed with results of microcosm experiments. Predicted results with a Markov chain suggested that volatility and biodegradation in sediment were main elimination pathways, and contributions of elimination pathways showed seasonal variations; Phe was eliminated from water and sediment to negligible levels over around 250 h in August and over 1000 h in May; in November, Phe was eliminated from water to a negligible level while about 31 % of Phe amount still remained in sediment over 1000 h. PMID:27180837
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.
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.
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
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.
A new method for RGB to CIELAB color space transformation based on Markov chain Monte Carlo
NASA Astrophysics Data System (ADS)
Chen, Yajun; Liu, Ding; Liang, Junli
2013-10-01
During printing quality inspection, the inspection of color error is an important content. However, the RGB color space is device-dependent, usually RGB color captured from CCD camera must be transformed into CIELAB color space, which is perceptually uniform and device-independent. To cope with the problem, a Markov chain Monte Carlo (MCMC) based algorithms for the RGB to the CIELAB color space transformation is proposed in this paper. Firstly, the modeling color targets and testing color targets is established, respectively used in modeling and performance testing process. Secondly, we derive a Bayesian model for estimation the coefficients of a polynomial, which can be used to describe the relation between RGB and CIELAB color space. Thirdly, a Markov chain is set up base on Gibbs sampling algorithm (one of the MCMC algorithm) to estimate the coefficients of polynomial. Finally, the color difference of testing color targets is computed for evaluating the performance of the proposed method. The experimental results showed that the nonlinear polynomial regression based on MCMC algorithm is effective, whose performance is similar to the least square approach and can accurately model the RGB to the CIELAB color space conversion and guarantee the color error evaluation for printing quality inspection system.
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.
Markov chains at the interface of combinatorics, computing, and statistical physics
NASA Astrophysics Data System (ADS)
Streib, Amanda Pascoe
The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is
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
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.
Adaptive relaxation for the steady-state analysis of Markov chains
NASA Technical Reports Server (NTRS)
Horton, Graham
1994-01-01
We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.
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.
NASA Astrophysics Data System (ADS)
Tsai, Christina; Wu, Nai-Kuang
2015-04-01
In this study, transport processes of uniform size sediment particles under steady and uniform flow are described by the multi-state discrete-time Markov chain. The multi-state discrete-time Markov chain is employed to estimate the suspended sediment concentration distribution versus water depth for various steady and uniform flow conditions. Model results are validated against available measurement data and the Rouse profile. Moreover, the multi-state discrete-time Markov chain can be used to quantify the average time spent for the flow to reach the dynamic equilibrium of particle deposition and entrainment processes. In the first part of this study, suspended sediment concentration under three different flow conditions are discussed. As the Rouse number decreases, the difference between the suspended sediment concentration estimated by the Markov chain model and the Rouse profile becomes more significant, and such discrepancy can be observed at a larger relative height from the bed. It can be attributed to the fact that the use of the terminal settling velocity in the transport process can lead to underestimation of the model residence probability and overestimation of the deposition probability. In the second part, laboratory experiments are used to validate the proposed multi-state discrete-time Markov chain model. It is observed that it would take more time for the sediment concentration to reach a dynamic equilibrium as the Rouse number decreases. In addition, the flow depth is found to be a contributing factor that impacts the time spent to reach the concentration dynamic equilibrium. It is recognized that the performance of the proposed multi-state discrete-time Markov chain model relies significantly on the knowledge of the vertical distribution of the turbulence intensity.
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.
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.
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.
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.
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
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.
Markov chain algorithms: a template for building future robust low-power systems
Deka, Biplab; Birklykke, Alex A.; Duwe, Henry; Mansinghka, Vikash K.; Kumar, Rakesh
2014-01-01
Although computational systems are looking towards post CMOS devices in the pursuit of lower power, the expected inherent unreliability of such devices makes it difficult to design robust systems without additional power overheads for guaranteeing robustness. As such, algorithmic structures with inherent ability to tolerate computational errors are of significant interest. We propose to cast applications as stochastic algorithms based on Markov chains (MCs) as such algorithms are both sufficiently general and tolerant to transition errors. We show with four example applications—Boolean satisfiability, sorting, low-density parity-check decoding and clustering—how applications can be cast as MC algorithms. Using algorithmic fault injection techniques, we demonstrate the robustness of these implementations to transition errors with high error rates. Based on these results, we make a case for using MCs as an algorithmic template for future robust low-power systems. PMID:24842030
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.
Markov Chain Monte Carlo Sampling Methods for 1D Seismic and EM Data Inversion
Energy Science and Technology Software Center (ESTSC)
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
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
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.
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.
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
NASA Astrophysics Data System (ADS)
King, J. A.; Mortlock, D. J.; Webb, J. K.; Murphy, M. T.
Recent attempts to constrain cosmological variation in the fine structure constant, alpha , using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for Delta alpha /alpha , the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.
NASA Astrophysics Data System (ADS)
King, Julian; Mortlock, Daniel; Webb, John; Murphy, Michael
2010-11-01
Recent attempts to constrain cosmological variation in the fine structure constant, α, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for Δα/α, the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.
Markov chain Mote Carlo solution of BK equation through Newton-Kantorovich method
NASA Astrophysics Data System (ADS)
BoŻek, Krzysztof; Kutak, Krzysztof; Placzek, Wieslaw
2013-07-01
We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The Newton-Kantorovich method allows to express the non-linear equation as a system of the linear equations which then can be treated by the MCMC (random walk) algorithm. We apply this method to the Balitsky-Kovchegov (BK) equation describing evolution of gluon density at low x. Results of numerical computations show that the MCMC method is both precise and efficient. The presented algorithm may be particularly suited for solving more complicated and higher-dimensional non-linear integral equation, for which traditional methods become unfeasible.
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
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
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
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
Binary 3-D Markov Chain Random Fields: Finite-size Scaling Analysis of Percolation Properties
NASA Astrophysics Data System (ADS)
Harter, T.
2004-12-01
Percolation phenomena in random media have been extensively studied in a wide variety of fields in physics, chemistry, engineering, bio-, earth-, and environmental sciences. Most work has focused on uncorrelated random fields. The critical behavior in media with short-range correlations is thought to be identical to that in uncorrelated systems. However, the percolation threshold, pc, which is 0.3116 in uncorrelated media, has been observed to vary with the correlation scale and also with the random field type. Here, we present percolation properties and finite-size scaling effects in three-dimensional binary cubic lattices represented by correlated Markov-chain random fields and compare them to those in sequential Gaussian and sequential indicator random fields. We find that the computed percolation threshold in correlated random fields is significantly lower than in the uncorrelated lattice and decreases with increasing correlation scale. The rate of decrease rapidly flattens out for correlation lengths larger than 2-3 grid-blocks. At correlation scales of 5-6 grid blocks, pc is found to be 0.126 for the Markov chain random fields and slightly higher for sequential Gaussian and indicator random fields. The universal scaling constants for mean cluster size, backbone fraction, and connectivity are found to be consistent with results on uncorrelated lattices. For numerical studies, it is critical to understand finite-size effects on the percolation and associated phase connectivity properties of lattices. We present detailed statistical results on the percolation properties in finite sized lattice and their dependence on correlation scale. We show that appropriate grid resolution and choice of simulation boundaries is critical to properly simulate correlated natural geologic systems, which may display significant finite-size effects.
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
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…
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…
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
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.
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.
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
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
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.
Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method
NASA Astrophysics Data System (ADS)
Ferraioli, Luigi; Porter, Edward K.; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Gibert, Ferran; Hewitson, Martin; Hueller, Mauro; Karnesis, Nikolaos; Korsakova, Natalia; Nofrarias, Miquel; Plagnol, Eric; Vitale, Stefano
2014-02-01
We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of the LISA Pathfinder satellite. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data. For this experiment, we return parameter values that are all within ˜1 σ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit of mass noise, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.
Bayesian inference of local trees along chromosomes by the sequential Markov coalescent
Zheng, Chaozhi; Kuhner, Mary K.
2014-01-01
We propose a genealogy sampling algorithm, 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, 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 ten DNA sequences over 50kb. 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., 2000a), a sampler which uses the full model. PMID:24817610
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
NASA Astrophysics Data System (ADS)
Raymond, Vivien
2012-05-01
Gravitational waves are on the verge of opening a brand new window on the Universe. However, gravitational wave astronomy comes with very unique challenges in data analysis and signal processing in order to lead to new discoveries in astrophysics. Among the sources of gravitational waves, inspiraling binary systems of compact objects, neutron stars and/or black holes in the mass range 1Msun--100Msun stand out as likely to be detected and relatively easy to model. The detection of a gravitational wave event is challenging and will be a rewarding achievement by itself. After such a detection, measurement of source properties holds major promise for improving our astrophysical understanding and requires reliable methods for parameter estimation and model selection. This is a complicated problem, because of the large number of parameters (15 for spinning compact objects in a quasi-circular orbit) and the degeneracies between them, the significant amount of structure in the parameter space, and the particularities of the detector noise. This work presents the development of a parameter-estimation and model-selection algorithm, based on Bayesian statistical theory and using Markov chain Monte Carlo methods for ground-based gravitational-wave detectors (LIGO and Virgo). This method started from existing non-spinning and single spin stand-alone analysis codes and was developed into a method able to tackle the complexity of fully spinning systems, and infer all spinning parameters of a compact binary. Not only are spinning parameters believed to be astrophysically significant, but this work has shown that not including them in the analysis can lead to biases in parameter recovery. This work made it possible to answer several scientific questions involving parameter estimation of inspiraling spinning compact objects, which are addressed in the chapters of this dissertation.
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
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.
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.
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.
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.
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.
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. PMID:25759720
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
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
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.
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.
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
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)
Vrugt, Jasper A.; Ter Braak, Cajo J. F.; Clark, Martyn P.; Hyman, James M.; Robinson, Bruce A.
2008-12-01
There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices.
Mapping absorption processes onto a Markov chain, conserving the mean first passage time
NASA Astrophysics Data System (ADS)
Biswas, Katja
2013-04-01
The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k‧ t, t + dt) between a set of states {k} represented by the regions {ζk} in phase or discrete state space. Depending on the dynamics Γi(t) of the original process and the choice of ζk, the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates \\bar{W}(k\\rightarrow k^{\\prime }) can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities \\bar{p}(k^{\\prime }|k) is derived based on either time-discrete measurements {ti} with variable time stepping Δ(i + 1)i = ti + 1 - ti or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory.
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.
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.
Extracting g tensor values from experimental data with Markov Chain Monte Carlo methods
NASA Astrophysics Data System (ADS)
Kulkarni, Anagha; Liu, Weiwen; Zurakowski, Ryan; Doty, Matthew
Quantum Dot Molecules(QDMs) have emerged as a new platform for optoelectronic and spintronic devices.QDMs consist of multiple Quantum Dots (QDs) arranged in close proximity such that interactions between them can tailor their optical and spin properties.These properties can be tuned during growth and in-situ by applying electric fields that vary the coupling between QDs,which controls the formation of delocalized molecular-like states.Engineering the formation of molecular states in QDMS can be used to achieve new functionalities unavailable with individual QDs. Using molecular engineering approaches to tailor QDMs require precise knowledge of parameters such as binding energies of charge complexes,magnitude of many body interactions or components of the g tensor.Precise values of these parameters are difficult to extract from either experimental measurements or theoretical calculations.We develop and demonstrate a Markov Chain Monte Carlo method for extracting elements of the g tensor for a single hole confined in a QDM from photoluminescence data obtained as a function of electric and magnetic fields.This method can be applied to extract precise quantitative values of other physical parameters from sparse experimental data on a variety of systems.
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.
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
Study on the Calculation Models of Bus Delay at Bays Using Queueing Theory and Markov Chain
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
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.
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.
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)
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.
Lin, Yen-Jen; Chen, Yu-Tin; Hsu, Shu-Ni; Peng, Chien-Hua; Tang, Chuan-Yi; Yen, Tzu-Chen; Hsieh, Wen-Ping
2014-01-01
Copy number variation (CNV) has been reported to be associated with disease and various cancers. Hence, identifying the accurate position and the type of CNV is currently a critical issue. There are many tools targeting on detecting CNV regions, constructing haplotype phases on CNV regions, or estimating the numerical copy numbers. However, none of them can do all of the three tasks at the same time. This paper presents a method based on Hidden Markov Model to detect parent specific copy number change on both chromosomes with signals from SNP arrays. A haplotype tree is constructed with dynamic branch merging to model the transition of the copy number status of the two alleles assessed at each SNP locus. The emission models are constructed for the genotypes formed with the two haplotypes. The proposed method can provide the segmentation points of the CNV regions as well as the haplotype phasing for the allelic status on each chromosome. The estimated copy numbers are provided as fractional numbers, which can accommodate the somatic mutation in cancer specimens that usually consist of heterogeneous cell populations. The algorithm is evaluated on simulated data and the previously published regions of CNV of the 270 HapMap individuals. The results were compared with five popular methods: PennCNV, genoCN, COKGEN, QuantiSNP and cnvHap. The application on oral cancer samples demonstrates how the proposed method can facilitate clinical association studies. The proposed algorithm exhibits comparable sensitivity of the CNV regions to the best algorithm in our genome-wide study and demonstrates the highest detection rate in SNP dense regions. In addition, we provide better haplotype phasing accuracy than similar approaches. The clinical association carried out with our fractional estimate of copy numbers in the cancer samples provides better detection power than that with integer copy number states. PMID:24849202
NASA Astrophysics Data System (ADS)
Schofield, Jeremy; Bayat, Hanif
2014-09-01
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
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
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
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
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.
Asteroid orbital inversion using a virtual-observation Markov-chain Monte Carlo method
NASA Astrophysics Data System (ADS)
Muinonen, Karri; Granvik, Mikael; Oszkiewicz, Dagmara; Pieniluoma, Tuomo; Pentikäinen, Hanna
2012-12-01
A novel virtual-observation Markov-chain Monte Carlo method (MCMC) is presented for the asteroid orbital inverse problem posed by small to moderate numbers of astrometric observations. In the method, the orbital-element proposal probability density is chosen to mimic the convolution of the a posteriori density by itself: first, random errors are simulated for each observation, resulting in a set of virtual observations; second, least-squares orbital elements are derived for the virtual observations using the Nelder-Mead downhill simplex method; third, repeating the procedure gives a difference between two sets of what can be called virtual least-squares elements; and, fourth, the difference obtained constitutes a symmetric proposal in a random-walk Metropolis-Hastings algorithm, avoiding the explicit computation of the proposal density. In practice, the proposals are based on a large number of pre-computed sets of orbital elements. Virtual-observation MCMC is thus based on the characterization of the phase-space volume of solutions before the actual MCMC sampling. Virtual-observation MCMC is compared to MCMC orbital ranging, a random-walk Metropolis-Hastings algorithm based on sampling with the help of Cartesian positions at two observation dates, in the case of the near-Earth asteroid (85640) 1998 OX4. In the present preliminary comparison, the methods yield similar results for a 9.1-day observational time interval extracted from the full current astrometry of the asteroid. In the future, both of the methods are to be applied to the astrometric observations of the Gaia mission.
NASA Astrophysics Data System (ADS)
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Nadeeka, P. M.
2014-12-01
This study used high resolution spatially distributed rainfall data produced by NSW/ACT Regional Climate Modelling (NARCliM) project. NARCliM dynamically downscaled four Global Climate Models using three Regional Climate Models within the Weather Research and Forecasting model to generate gridded climate data at 10 km spatial resolution for south eastern Australia. These dataset are being used in this project to evaluate the urban water security of reservoirs on the east coast of Australia. A stochastic model to simulate rainfall series was developed for runoff generation using parameters calibrated to NARCliM. This study has developed a Markov Chain model, which simulates the occurrence of daily rainfall using the transition probability of dry and wet days, while the precipitation for the wet days are generated using a two parameter gamma distribution. We have identified significant seasonal and intra- to inter-decadal variations of the model parameters at our field site. Incorporating the temporal variability (for instance, calibrating the model parameters to each decade independently), we have found that the model satisfactorily preserves the daily, monthly and annual characteristics of the NARCliM rainfall. In addition to the temporal variability, we have observed that the model parameters vary spatially at our site with potential orographic effects that vary both seasonally and decadally. However, the parameters of the model fitted to the NARCliM rainfall are significantly different from the parameters fitted to the ground-based climate station rainfall. Suitability of the model for the generation of long time series (e.g. 1000 years) required for reservoir simulation will be discussed.
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
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
Recovering the inflationary potential: An analysis using flow methods and Markov chain Monte Carlo
NASA Astrophysics Data System (ADS)
Powell, Brian A.
Since its inception in 1980 by Guth [1], inflation has emerged as the dominant paradigm for describing the physics of the early universe. While inflation has matured theoretically over two decades, it has only recently begun to be rigorously tested observationally. Measurements of the cosmic microwave background (CMB) and large-scale structure surveys (LSS) have begun to unravel the mysteries of the inflationary epoch with exquisite and unprecedented accuracy. This thesis is a contribution to the effort of reconstructing the physics of inflation. This information is largely encoded in the potential energy function of the inflaton, the field that drives the inflationary expansion. With little theoretical guidance as to the probable form of this potential, reconstruction is a predominantly data-driven endeavor. This thesis presents an investigation of the constrainability of the inflaton potential given current CMB and LSS data. We develop a methodology based on the inflationary flow formalism that provides an assessment of our current ability to resolve the form of the inflaton potential in the face of experimental and statistical error. We find that there is uncertainty regarding the initial dynamics of the inflaton field, related to the poor constraints that can be drawn on the primordial power spectrum on large scales. We also investigate the future prospects of potential reconstruction, as might be expected when data from ESA's Planck Surveyor becomes available. We develop an approach that utilizes Markov chain Monte Carlo to analyze the statistical properties of the inflaton potential. Besides providing constraints on the parameters of the potential, this method makes it possible to perform model selection on the inflationary model space. While future data will likely determine the general features of the inflaton, there will likely be many different models that remain good fits to the data. Bayesian model selection will then be needed to draw comparisons
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.
NASA Astrophysics Data System (ADS)
Lopes, Artur O.; Neumann, Adriana
2015-05-01
In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.
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
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)
Lopes, Artur; Neumann, Adriana; Thieullen, Philippe
2013-09-01
Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is a discrete time Ruelle operator (transfer operator), and is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability. Given a Lipschitz interaction , we are interested in Gibbs (equilibrium) state for such V. This will be another continuous time stationary Markov chain. In order to analyze this problem we will use a continuous time Ruelle operator (transfer operator) naturally associated to V. Among other things we will show that a continuous time Perron-Frobenius Theorem is true in the case V is a Lipschitz function. We also introduce an entropy, which is negative (see also Lopes et al. in Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature. Arxiv, 2012), and we consider a variational principle of pressure. Finally, we analyze large deviations properties for the empirical measure in the continuous time setting using results by Y. Kifer (Tamsui Oxf. J. Manag. Sci. 321(2):505-524, 1990). In the last appendix of the paper we explain why the techniques we develop here have the capability to be applied to the analysis of convergence of a certain version of the Metropolis algorithm.
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. PMID:21263634
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.
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
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...
Kaushik, Alka; Celler, B G; Ambikairajah, E
2005-01-01
In this paper we are proposing a statistical testing methodology to monitor changing trends in the health status of elderly people. The occupancy pattern of elderly people can be modeled using a Markov chain, estimating transition probabilities of the chain and test hypotheses about them. The profile of the person for a given period can be stored as a transition matrix of a discrete, regular, ergodic Markov chain. The observation of the occupancy pattern for a given test period can be established as a test Markov chain using information from sensors such as infrared sensors, magnetic switches etc. In the absence of real time data, we have used uniformly distributed transition probabilities to define the profile of the Markov chain and then generated test Markov chain based on this model. The transition probabilities are extracted for the test and profile Markov chain using Maximum Likelihood Estimates (MLE). The statistical testing of occupancy monitoring establishes a basis for statistical inference about the system performance without generating any real time statistics for the occupancy pattern. Chi square test and likelihood ratio tests ensure that the sequences generated from the two Markov chains are statistically same. Any difference in profile Markov chain and test Markov chain could indicate a changed health status of the elderly person. PMID:17282661
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
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.
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.
Feldman, Olga; Korotkov, Vladimir N; Logofet, Dmitrii O
2005-10-01
The monoculture strategy of forest management, where the same tree species (e.g., Picea abies) is cultivated in a number of successive planting-growing-felling cycles, is generally considered to be economically efficient, yet not sustainable as it reduces biodiversity in the forest. The sound alternative suggests a long-term strategy of forest management in which different forest types rotate either with planting after clear cutting, or by natural forest succession, yet the commercial output remains dubious. We suggest an approach to formalization and modelling forest dynamics in the long-term by means of Markov chains, the monoculture strategy resulting in an absorbing chain and the rotation one in a regular chain. The approach is illustrated with a case study of Russkii Les, a managed forest located in the Moscow Region, Russia, and the nearby forest reserve having been used as a data source for undisturbed forest dynamics. Starting with conceptual schemes of transitions among certain forest types (states of the chain) in the monoculture and rotation cases, we estimated the transition probabilities by an original method based on average duration of the corresponding states and on the likelihood of alternative transitions from a state into the next one. Formal analysis of the regular chain reveals an opportunity to achieve particular management objectives within the rotation strategy, in particular, to get the distribution of forest types in accordance with an adopted hierarchy of their commercial values, i.e. more valuable types have greater shares. PMID:16111801
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.
NASA Astrophysics Data System (ADS)
Shaw, M. Sam; Coe, Joshua D.; Sewell, Thomas D.
2009-06-01
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 6-31G* 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.
NASA Astrophysics Data System (ADS)
Shaw, M. Sam; Coe, Joshua D.; Sewell, Thomas D.
2009-12-01
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 6-31G* 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
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.
KENNETH M. HANSON; JANE M. BOOKER
2000-09-08
The authors an uncertainty analysis of data taken using the Rossi technique, in which the horizontal oscilloscope sweep is driven sinusoidally in time ,while the vertical axis follows the signal amplitude. The analysis is done within a Bayesian framework. Complete inferences are obtained by tilting the Markov chain Monte Carlo technique, which produces random samples from the posterior probability distribution expressed in terms of the parameters.
NASA Astrophysics Data System (ADS)
Naylor, Mark; Mudd, Simon; Yoo, Kyungsoo
2010-05-01
Hillslope topography and soil thickness respond to changes in river incision or deposition. For example, accelerated river incision leads to a wave of steepening and soil thinning that begins at the channel and moves upslope [1]. Because of the coupled response of topography, soil thickness and channel incision or deposition rates, it may be possible to use hillslope properties to reconstruct the erosional or depositional history of channels. A prerequisite for such inversion of hillslope properties to reconstruct historical landscape dynamics is a method that allows one to quantify both the most likely channel history as well as the uncertainties in changing channel erosion or deposition rates through time. Here we present robust methods ideally suited for this purpose: Monte Carlo Markov Chain (MCMC) methods. Specifically, MCMC methods [2] involve (i) taking some assumed base level history, (ii) perturbing that history (iii) running a forward model to estimate new hillslope profiles (iv) choosing whether to accept the new history by a Metropolis-Hastings Algorithm [3] (v) storing the favoured history and repeating. In this way we iterate towards the most likely channel history whilst exploring parameter space in such a way that confidence intervals can quantified. Here we demonstrate how this approach returns not only a best estimate history, but also credibility intervals which reflect the progressive loss of information with time. These techniques are generic and should be employed more generally within geomorphology. [1] Mudd, S.M., and D.J. Furbish (2007), Responses of soil mantled hillslopes to transient channel incision rates, Journal of Geophysical Research-Earth Surface, 112, F03S18, doi:10.1029/2006JF000516 [2] K. Gallagher, K. Charvin, S. Nielsen, M. Sambridge and J. Stephenson (2009) Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems Marine and Petroleum Geology 26
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…
ERIC Educational Resources Information Center
Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun
2002-01-01
Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)
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%.
Approximate Bayesian Computation using Markov Chain Monte Carlo simulation: DREAM(ABC)
NASA Astrophysics Data System (ADS)
Sadegh, Mojtaba; Vrugt, Jasper A.
2014-08-01
The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh (2013) to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for a residual-based likelihood function in favor of one or multiple different summary statistics that exhibit superior diagnostic power. Here we propose several methodological improvements over commonly used ABC sampling methods to permit inference of complex system models. Our methodology entitled DREAM(ABC) uses the DiffeRential Evolution Adaptive Metropolis algorithm as its main building block and takes advantage of a continuous fitness function to efficiently explore the behavioral model space. Three case studies demonstrate that DREAM(ABC) is at least an order of magnitude more efficient than commonly used ABC sampling methods for more complex models. DREAM(ABC) is also more amenable to distributed, multi-processor, implementation, a prerequisite to diagnostic inference of CPU-intensive system models.
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.
2014-01-01
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
The condition of a finite Markov chain and perturbation bounds for the limiting probabilities
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.
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
Stochastic Inversion of Electrical Resistivity Changes Using a Markov Chain, Monte Carlo Approach
Ramirez, A; Nitao, J; Hanley, W; Aines, R; Glaser, R; Sengupta, S; Dyer, K; Hickling, T; Daily, W
2004-09-21
We describe a stochastic inversion method for mapping subsurface regions where the electrical resistivity is changing. The technique combines prior information, electrical resistance data and forward models to produce subsurface resistivity models that are most consistent with all available data. Bayesian inference and a Metropolis simulation algorithm form the basis for this approach. Attractive features include its ability to: (1) provide quantitative measures of the uncertainty of a generated estimate and, (2) allow alternative model estimates to be identified, compared and ranked. Methods that monitor convergence and summarize important trends of the posterior distribution are introduced. Results from a physical model test and a field experiment were used to assess performance. The stochastic inversions presented provide useful estimates of the most probable location, shape, and volume of the changing region, and the most likely resistivity change. The proposed method is computationally expensive, requiring the use of extensive computational resources to make its application practical.
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 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.
NASA Astrophysics Data System (ADS)
Moradkhani, Hamid; Yan, Hongxiang
2016-04-01
Soil moisture simulation and prediction are increasingly used to characterize agricultural droughts but the process suffers from data scarcity and quality. The satellite soil moisture observations could be used to improve model predictions with data assimilation. Remote sensing products, however, are typically discontinuous in spatial-temporal coverages; while simulated soil moisture products are potentially biased due to the errors in forcing data, parameters, and deficiencies of model physics. This study attempts to provide a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a fully distributed hydrologic model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. A geostatistical model is introduced to overcome the satellite soil moisture discontinuity issue where satellite data does not cover the whole study region or is significantly biased, and the dominant land cover is dense vegetation. The results indicate that joint assimilation of soil moisture and streamflow has minimal effect in improving the streamflow prediction, however, the surface soil moisture field is significantly improved. The combination of DA and geostatistical approach can further improve the surface soil moisture prediction.
Weijs, Liesbeth; Roach, Anthony C; Yang, Raymond S H; McDougall, Robin; Lyons, Michael; Housand, Conrad; Tibax, Detlef; Manning, Therese; Chapman, John; Edge, Katelyn; Covaci, Adrian; Blust, Ronny
2014-01-01
Physiologically based pharmacokinetic (PBPK) models for wild animal populations such as marine mammals typically have a high degree of model uncertainty and variability due to the scarcity of information and the embryonic nature of this field. Parameters values used in marine mammals models are usually taken from other mammalian species (e.g. rats or mice) and might not be entirely suitable to properly explain the kinetics of pollutants in marine mammals. Therefore, several parameters for a PBPK model for the bioaccumulation and pharmacokinetics of PCB 153 in long-finned pilot whales were estimated in the present study using the Bayesian approach executed with Markov chain Monte Carlo (MCMC) simulations. This method uses 'prior' information of the parameters, either from the literature or from previous model runs. The advantage is that this method uses such 'prior' parameters to calculate probability distributions to determine 'posterior' values that best explain the field observations. Those field observations or datasets were PCB 153 concentrations in blubber of long-finned pilot whales from Sandy Cape and Stanley, Tasmania, Australia. The model predictions showed an overall decrease in PCB 153 levels in blubber over the lifetime of the pilot whales. All parameters from the Sandy Cape model were updated using the Stanley dataset, except for the concentration of PCB 153 in the milk. The model presented here is a promising and preliminary start to PBPK modeling in long-finned pilot whales that would provide a basis for non-invasive studies in these protected marine mammals. PMID:24080004
Geng, Bo; Zhou, Xiaobo; Zhu, Jinmin; Hung, Y S; Wong, Stephen T C
2008-04-01
Computational identification of missing enzymes plays a significant role in accurate and complete reconstruction of metabolic network for both newly sequenced and well-studied organisms. For a metabolic reaction, given a set of candidate enzymes identified according to certain biological evidences, a powerful mathematical model is required to predict the actual enzyme(s) catalyzing the reactions. In this study, several plausible predictive methods are considered for the classification problem in missing enzyme identification, and comparisons are performed with an aim to identify a method with better performance than the Bayesian model used in previous work. In particular, a regression model consisting of a linear term and a nonlinear term is proposed to apply to the problem, in which the reversible jump Markov-chain-Monte-Carlo (MCMC) learning technique (developed in [Andrieu C, Freitas Nando de, Doucet A. Robust full Bayesian learning for radial basis networks 2001;13:2359-407.]) is adopted to estimate the model order and the parameters. We evaluated the models using known reactions in Escherichia coli, Mycobacterium tuberculosis, Vibrio cholerae and Caulobacter cresentus bacteria, as well as one eukaryotic organism, Saccharomyces Cerevisiae. Although support vector regression also exhibits comparable performance in this application, it was demonstrated that the proposed model achieves favorable prediction performance, particularly sensitivity, compared with the Bayesian method. PMID:17950040
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)
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.
NASA Astrophysics Data System (ADS)
Xu, F.; Diner, D. J.; Davis, A. B.; Latyshev, S.; Garay, M. J.; Kalashnikova, O.; Ge, C.; Wang, J.
2013-12-01
A vector Markov chain (MarCh) radiative transfer (RT) code developed at JPL that includes forward modeling of radiance and polarization fields and linearization (analytical estimation of Jacobians) was incorporated into an aerosol and surface retrieval package for a plane-parallel atmosphere/surface system. The RT computation by MarCh is based on matrix operations. To improve the code's computational efficiency, the forward model is currently undergoing acceleration through the exploration of different strategies for matrix operation and inversion, including numerical optimization, multi-threading/multi-processing techniques on a CPU. Implementation on a graphics processing unit (GPU) is also planned. Following a benchmarking study of the forward model, the performance of MarCh in aerosol and surface retrieval is being tested. With an optimized algorithm, we started from aerosol optical depth and surface retrieval using imagery acquired by Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) over Fresno, CA. Aerosol properties including concentration and size distribution of different species provided by the Weather Research and Forecasting (WRF)-Chem model were used to constrain the retrieval and reduce the parameter space. The assumptions of spectral invariance in the angular shape of surface bidirectional reflectance factors (BRFs) and the magnitude of polarized surface BRFs were tested. The aerosol and surface properties are then relaxed in a stepwise way to refine the aerosol retrieval results and enable comparison with independent retrievals obtained from a collocated AErosol RObotic NETwork (AERONET) station.
Pirzkal, N.; Rothberg, B.; Koekemoer, Anton; Nilsson, Kim K.; Finkelstein, S.; Malhotra, Sangeeta; Rhoads, James
2012-04-01
We have developed a new method for fitting spectral energy distributions (SEDs) to identify and constrain the physical properties of high-redshift (4 < z < 8) galaxies. Our approach uses an implementation of Bayesian based Markov Chain Monte Carlo that we have dubbed '{pi}MC{sup 2}'. It allows us to compare observations to arbitrarily complex models and to compute 95% credible intervals that provide robust constraints for the model parameters. The work is presented in two sections. In the first, we test {pi}MC{sup 2} using simulated SEDs to not only confirm the recovery of the known inputs but to assess the limitations of the method and identify potential hazards of SED fitting when applied specifically to high-redshift (z > 4) galaxies. In the second part of the paper we apply {pi}MC{sup 2} to thirty-three 4 < z < 8 objects, including the spectroscopically confirmed Grism ACS Program for Extragalactic Science Ly{alpha} sample (4 < z < 6), supplemented by newly obtained Hubble Space Telescope/WFC3 near-IR observations, and several recently reported broadband selected z > 6 galaxies. Using {pi}MC{sup 2}, we are able to constrain the stellar mass of these objects and in some cases their stellar age and find no evidence that any of these sources formed at a redshift larger than z = 8, a time when the universe was Almost-Equal-To 0.6 Gyr old.
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.
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
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
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. PMID:26976482
Saloranta, Tuomo M; Armitage, James M; Haario, Heikki; Naes, Kristoffer; Cousins, Ian T; Barton, David N
2008-01-01
Multimedia environmental fate models are useful tools to investigate the long-term impacts of remediation measures designed to alleviate potential ecological and human health concerns in contaminated areas. Estimating and communicating the uncertainties associated with the model simulations is a critical task for demonstrating the transparency and reliability of the results. The Extended Fourier Amplitude Sensitivity Test(Extended FAST) method for sensitivity analysis and Bayesian Markov chain Monte Carlo (MCMC) method for uncertainty analysis and model calibration have several advantages over methods typically applied for multimedia environmental fate models. Most importantly, the simulation results and their uncertainties can be anchored to the available observations and their uncertainties. We apply these techniques for simulating the historical fate of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in the Grenland fjords, Norway, and for predicting the effects of different contaminated sediment remediation (capping) scenarios on the future levels of PCDD/Fs in cod and crab therein. The remediation scenario simulations show that a significant remediation effect can first be seen when significant portions of the contaminated sediment areas are cleaned up, and that increase in capping area leads to both earlier achievement of good fjord status and narrower uncertainty in the predicted timing for this. PMID:18350897
Fathizad, Hassan; Rostami, Noredin; Faramarzi, Marzban
2015-10-01
The study of changes and destruction rate in the previous years as well as the possibility of prediction of these changes in the following years has a key role in optimal planning, controlling, and restricting non-normative changes in the future. This research was approached to detecting land use/cover changes (1985-2007) and to forecast the changes in the future (2021) use of multitemporal satellite imagery in semi-arid area in western Iran. A supervised classification of multilayer perceptron (MLP) was applied for detecting land use changes. The study area was classified into five classes, those of forest, rangeland, agriculture, residential, and barren lands. The change detection analysis indicated a decreasing trend in forest cover by 30.42%, while other land uses were increased during 1985 to 2007. The land use changes were predicted using Markov chain model for 2021. The model was calibrated by comparing the simulated map with the real detected classes of land cover in 2007. Then, for further model processing, an acceptable accuracy at 83% was achieved between them. Finally, land use changes were predicted by using transition matrix derived from calibrated approach. The findings of this study demonstrate a rapid change in land use/cover for the coming years. Transforming the forest into other land uses especially rangeland and cropland is the main land cover changes in the future. Therefore, the planning of protection and restoration of forest cover should be an essential program for decision-makers in the study area. PMID:26373304
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.
Waldmann, Patrik; Hallander, Jon; Hoti, Fabian; Sillanpää, Mikko J.
2008-01-01
Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler. PMID:18558655
Waldmann, Patrik; Hallander, Jon; Hoti, Fabian; Sillanpää, Mikko J
2008-06-01
Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler. PMID:18558655
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
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
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
Li, Jun; Calo, Victor M.
2013-09-15
We present a single-particle Lennard–Jones (L-J) model for CO{sub 2} and N{sub 2}. 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 CO{sub 2} and N{sub 2} 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 CH{sub 4}, CO{sub 2} and N{sub 2} 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)
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
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
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.
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)
WöHling, Thomas; Vrugt, Jasper A.
2011-04-01
In the past two decades significant progress has been made toward the application of inverse modeling to estimate the water retention and hydraulic conductivity functions of the vadose zone at different spatial scales. Many of these contributions have focused on estimating only a few soil hydraulic parameters, without recourse to appropriately capturing and addressing spatial variability. The assumption of a homogeneous medium significantly simplifies the complexity of the resulting inverse problem, allowing the use of classical parameter estimation algorithms. Here we present an inverse modeling study with a high degree of vertical complexity that involves calibration of a 25 parameter Richards'-based HYDRUS-1D model using in situ measurements of volumetric water content and pressure head from multiple depths in a heterogeneous vadose zone in New Zealand. We first determine the trade-off in the fitting of both data types using the AMALGAM multiple objective evolutionary search algorithm. Then we adopt a Bayesian framework and derive posterior probability density functions of parameter and model predictive uncertainty using the recently developed differential evolution adaptive metropolis, DREAMZS adaptive Markov chain Monte Carlo scheme. We use four different formulations of the likelihood function each differing in their underlying assumption about the statistical properties of the error residual and data used for calibration. We show that AMALGAM and DREAMZS can solve for the 25 hydraulic parameters describing the water retention and hydraulic conductivity functions of the multilayer heterogeneous vadose zone. Our study clearly highlights that multiple data types are simultaneously required in the likelihood function to result in an accurate soil hydraulic characterization of the vadose zone of interest. Remaining error residuals are most likely caused by model deficiencies that are not encapsulated by the multilayer model and can not be accessed by the
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
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
Li, Yun-He; Wang, Shuang; Zhang, Xin; Li, Xiao-Dong E-mail: swang@mail.ustc.edu.cn E-mail: zhangxin@mail.neu.edu.cn
2013-02-01
In this paper, we report the results of constraining the holographic dark energy model with spatial curvature and massive neutrinos, based on a Markov Chain Monte Carlo global fit technique. The cosmic observational data include the full WMAP 7-yr temperature and polarization data, the type Ia supernova data from Union2.1 sample, the baryon acoustic oscillation data from SDSS DR7 and WiggleZ Dark Energy Survey, and the latest measurements of H{sub 0} from HST. To deal with the perturbations of dark energy, we adopt the parameterized post-Friedmann method. We find that, for the simplest holographic dark energy model without spatial curvature and massive neutrinos, the phenomenological parameter c < 1 at more than 4σ confidence level. The inclusion of spatial curvature enlarges the error bars and leads to c < 1 only in about 2.5σ range; in contrast, the inclusion of massive neutrinos does not have significant influence on c. We also find that, for the holographic dark energy model with spatial curvature but without massive neutrinos, the 3σ error bars of the current fractional curvature density Ω{sub k0} are still in order of 10{sup −2}; for the model with massive neutrinos but without spatial curvature, the 2σ upper bound of the total mass of neutrinos is Σm{sub ν} < 0.48 eV. Moreover, there exists clear degeneracy between spatial curvature and massive neutrinos in the holographic dark energy model, which enlarges the upper bound of Σm{sub ν} by more than 2 times. In addition, we demonstrate that, making use of the full WMAP data can give better constraints on the holographic dark energy model, compared with the case using the WMAP ''distance priors''.
Arora, Bhavna; Mohanty, Binayak P; McGuire, Jennifer T
2015-04-15
Predicting and controlling the concentrations of redox-sensitive elements are primary concerns for environmental remediation of contaminated sites. These predictions are complicated by dynamic flow processes as hydrologic variability is a governing control on conservative and reactive chemical concentrations. Subsurface heterogeneity in the form of layers and lenses further complicates the flow dynamics of the system impacting chemical concentrations including redox-sensitive elements. In response to these complexities, this study investigates the role of heterogeneity and hydrologic processes in an effective parameter upscaling scheme from the column to the landfill scale. We used a Markov chain Monte Carlo (MCMC) algorithm to derive upscaling coefficients for hydrological and geochemical parameters, which were tested for variations across heterogeneous systems (layers and lenses) and interaction of flow processes based on the output uncertainty of dominant biogeochemical concentrations at the Norman Landfill site, a closed municipal landfill with prevalent organic and trace metal contamination. The results from MCMC analysis indicated that geochemical upscaling coefficients based on effective concentration ratios incorporating local heterogeneity across layered and lensed systems produced better estimates of redox-sensitive biogeochemistry at the field scale. MCMC analysis also suggested that inclusion of hydrological parameters in the upscaling scheme reduced the output uncertainty of effective mean geochemical concentrations by orders of magnitude at the Norman Landfill site. This was further confirmed by posterior density plots of the scaling coefficients that revealed unimodal characteristics when only geochemical processes were involved, but produced multimodal distributions when hydrological parameters were included. The multimodality again suggests the effect of heterogeneity and lithologic variability on the distribution of redox-sensitive elements at the
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Hernandez, F.; Liang, X.
2014-12-01
Given the inherent uncertainty in almost all of the variables involved, recent research is re-addressing the problem of calibrating hydrologic models from a stochastic perspective: the focus is shifting from finding a single parameter configuration that minimizes the model error, to approximating the maximum likelihood multivariate probability distribution of the parameters. To this end, Markov chain Monte Carlo (MCMC) formulations are widely used, where the distribution is defined as a smoothed ensemble of particles or members, each of which represents a feasible parameterization. However, the updating of these ensembles needs to strike a careful balance so that the particles adequately resemble the real distribution without either clustering or drifting excessively. In this study, we explore the implementation of two techniques that attempt to improve the quality of the resulting ensembles, both for the approximation of the model parameters and of the unknown states, in a dual calibration-data assimilation framework. The first feature of our proposed algorithm, in an effort to keep members from clustering on areas of high likelihood in light of the observations, is the introduction of diversity-inducing operators after each resampling. This approach has been successfully used before, and here we aim at testing additional operators which are also borrowed from the Evolutionary Computation literature. The second feature is a novel arrangement of the particles into two alternative data structures. The first one is a non-sorted Pareto population which favors 1) particles with high likelihood, and 2) particles that introduce a certain level of heterogeneity. The second structure is a partitioned array, in which each partition requires its members to have increasing levels of divergence from the particles in the areas of larger likelihood. Our newly proposed algorithm will be evaluated and compared to traditional MCMC methods in terms of convergence speed, and the
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.
NASA Technical Reports Server (NTRS)
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
Fridman, Arthur
2003-01-01
Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford [Mumford, D. (1996) in ICIAM 95, eds. Kirchgassner, K., Marenholtz, O. & Mennicken, R. (Akademie Verlag, Berlin), pp. 233–256] proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. PMID:12829802
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)
NASA Astrophysics Data System (ADS)
Raymond, V.; van der Sluys, M. V.; Mandel, I.; Kalogera, V.; Röver, C.; Christensen, N.
2010-06-01
Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo and GEO-600). We present parameter estimation results from our Markov-chain Monte Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals either into synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ('glitch'). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.
NASA Astrophysics Data System (ADS)
Cavers, M. S.; Vasudevan, K.
2015-02-01
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, the orthogonal basis set 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 behavior. 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 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.
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
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
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.
Shishmarev, Dmitry; Chapman, Bogdan E; Naumann, Christoph; Mamone, Salvatore; Kuchel, Philip W
2015-01-01
The (1)H NMR signal of the methyl group of sodium acetate is shown to be a triplet in the anisotropic environment of stretched gelatin gel. The multiplet structure of the signal is due to the intra-methyl residual dipolar couplings. The relaxation properties of the spin system were probed by recording steady-state irradiation envelopes ('z-spectra'). A quantum-mechanical model based on irreducible spherical tensors formed by the three magnetically equivalent spins of the methyl group was used to simulate and fit experimental z-spectra. The multiple parameter values of the relaxation model were estimated by using a Bayesian-based Markov chain Monte Carlo algorithm. PMID:25486634
NASA Astrophysics Data System (ADS)
Pasyanos, Michael E.; Franz, Gregory A.; Ramirez, Abelardo L.
2006-03-01
In an effort to build seismic models that are the 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 deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude-longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data-rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.
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.
Transitive reasoning distorts induction in causal chains.
von Sydow, Momme; Hagmayer, York; Meder, Björn
2016-04-01
A probabilistic causal chain A→B→C may intuitively appear to be transitive: If A probabilistically causes B, and B probabilistically causes C, A probabilistically causes C. However, probabilistic causal relations can only guaranteed to be transitive if the so-called Markov condition holds. In two experiments, we examined how people make probabilistic judgments about indirect relationships A→C in causal chains A→B→C that violate the Markov condition. We hypothesized that participants would make transitive inferences in accordance with the Markov condition although they were presented with counterevidence showing intransitive data. For instance, participants were successively presented with data entailing positive dependencies A→B and B→C. At the same time, the data entailed that A and C were statistically independent. The results of two experiments show that transitive reasoning via a mediating event B influenced and distorted the induction of the indirect relation between A and C. Participants' judgments were affected by an interaction of transitive, causal-model-based inferences and the observed data. Our findings support the idea that people tend to chain individual causal relations into mental causal chains that obey the Markov condition and thus allow for transitive reasoning, even if the observed data entail that such inferences are not warranted. PMID:26620811
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
NASA Astrophysics Data System (ADS)
Zhu, Qi; Burzykowski, Tomasz
2011-03-01
To reduce the influence of the between-spectra variability on the results of peptide quantification, one can consider the 18O-labeling approach. Ideally, with such labeling technique, a mass shift of 4 Da of the isotopic distributions of peptides from the labeled sample is induced, which allows one to distinguish the two samples and to quantify the relative abundance of the peptides. It is worth noting, however, that the presence of small quantities of 16O and 17O atoms during the labeling step can cause incomplete labeling. In practice, ignoring incomplete labeling may result in the biased estimation of the relative abundance of the peptide in the compared samples. A Markov model was developed to address this issue (Zhu, Valkenborg, Burzykowski. J. Proteome Res. 9, 2669-2677, 2010). The model assumed that the peak intensities were normally distributed with heteroscedasticity using a power-of-the-mean variance funtion. Such a dependence has been observed in practice. Alternatively, we formulate the model within the Bayesian framework. This opens the possibility to further extend the model by the inclusion of random effects that can be used to capture the biological/technical variability of the peptide abundance. The operational characteristics of the model were investigated by applications to real-life mass-spectrometry data sets and a simulation study.
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)
von Toussaint, Udo
2011-07-01
Bayesian inference provides a consistent method for the extraction of information from physics experiments even in ill-conditioned circumstances. The approach provides a unified rationale for data analysis, which both justifies many of the commonly used analysis procedures and reveals some of the implicit underlying assumptions. This review summarizes the general ideas of the Bayesian probability theory with emphasis on the application to the evaluation of experimental data. As case studies for Bayesian parameter estimation techniques examples ranging from extra-solar planet detection to the deconvolution of the apparatus functions for improving the energy resolution and change point estimation in time series are discussed. Special attention is paid to the numerical techniques suited for Bayesian analysis, with a focus on recent developments of Markov chain Monte Carlo algorithms for high-dimensional integration problems. Bayesian model comparison, the quantitative ranking of models for the explanation of a given data set, is illustrated with examples collected from cosmology, mass spectroscopy, and surface physics, covering problems such as background subtraction and automated outlier detection. Additionally the Bayesian inference techniques for the design and optimization of future experiments are introduced. Experiments, instead of being merely passive recording devices, can now be designed to adapt to measured data and to change the measurement strategy on the fly to maximize the information of an experiment. The applied key concepts and necessary numerical tools which provide the means of designing such inference chains and the crucial aspects of data fusion are summarized and some of the expected implications are highlighted.
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
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Karalidi, Theodora; Apai, Dániel; Schneider, Glenn; Hanson, Jake R.; Pasachoff, Jay M.
2015-11-01
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.
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.
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.
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
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.
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. PMID:18632387
Kidd, Marie J.; Chen, Zhiliang; Wang, Yan; Jackson, Katherine J.; Zhang, Lyndon; Boyd, Scott D.; Fire, Andrew Z.; Tanaka, Mark M.; Gaëta, Bruno A.; Collins, Andrew M.
2014-01-01
The existence of many highly similar genes in the lymphocyte receptor gene loci makes them difficult to investigate, and the determination of phased “haplotypes” has been particularly problematic. However, V(D)J gene rearrangements provide an opportunity to infer the association of Ig genes along the chromosomes. The chromosomal distribution of H chain genes in an Ig genotype can be inferred through analysis of VDJ rearrangements in individuals who are heterozygous at points within the IGH locus. We analyzed VDJ rearrangements from 44 individuals for whom sufficient unique rearrangements were available to allow comprehensive genotyping. Nine individuals were identified who were heterozygous at the IGHJ6 locus and for whom sufficient suitable VDJ rearrangements were available to allow comprehensive haplotyping. Each of the 18 resulting IGHV|IGHD|IGHJ haplotypes was unique. Apparent deletion polymorphisms were seen that involved as many as four contiguous, functional IGHV genes. Two deletion polymorphisms involving multiple contiguous IGHD genes were also inferred. Three previously unidentified gene duplications were detected, where two sequences recognized as allelic variants of a single gene were both inferred to be on a single chromosome. Phased genomic data brings clarity to the study of the contribution of each gene to the available repertoire of rearranged VDJ genes. Analysis of rearrangement frequencies suggests that particular genes may have substantially different yet predictable propensities for rearrangement within different haplotypes. Together with data highlighting the extent of haplotypic variation within the population, this suggests that there may be substantial variability in the available Ab repertoires of different individuals. PMID:22205028
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
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.
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
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. PMID:11318215
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
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.
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 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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Stanaway, D. J.; Flores, A. N.; Haggerty, R.; Benner, S. G.; Feris, K. P.
2011-12-01
Concurrent assessment of biogeochemical and solute transport data (i.e. advection, dispersion, transient storage) within lotic systems remains a challenge in eco-hydrological research. Recently, the Resazurin-Resorufin Smart Tracer System (RRST) was proposed as a mechanism to measure microbial activity at the sediment-water interface [Haggerty et al., 2008, 2009] associating metabolic and hydrologic processes and allowing for the reach scale extrapolation of biotic function in the context of a dynamic physical environment. This study presents a Markov Chain Monte Carlo (MCMC) data assimilation technique to solve the inverse model of the Raz Rru Advection Dispersion Equation (RRADE). The RRADE is a suite of dependent 1-D reactive ADEs, associated through the microbially mediated reduction of Raz to Rru (k12). This reduction is proportional to DO consumption (R^2=0.928). MCMC is a suite of algorithms that solve Bayes theorem to condition uncertain model states and parameters on imperfect observations. Here, the RRST is employed to quantify the effect of chronic metal exposure on hyporheic microbial metabolism along a 100+ year old metal contamination gradient in the Clark Fork River (CF). We hypothesized that 1) the energetic cost of metal tolerance limits heterotrophic microbial respiration in communities evolved in chronic metal contaminated environments, with respiration inhibition directly correlated to degree of contamination (observational experiment) and 2) when experiencing acute metal stress, respiration rate inhibition of metal tolerant communities is less than that of naïve communities (manipulative experiment). To test these hypotheses, 4 replicate columns containing sediment collected from differently contaminated CF reaches and reference sites were fed a solution of RRST, NaCl, and cadmium (manipulative experiment only) within 24 hrs post collection. Column effluent was collected and measured for Raz, Rru, and EC to determine the Raz Rru breakthrough
NASA Astrophysics Data System (ADS)
O'Shaughnessy, Richard; Farr, Ben; Ochsner, Evan; Cho, Hee-Suk; Kim, Chunglee; Lee, Chang-Hwan
2014-03-01
Most calculations of the gravitational wave signal from merging compact binaries limit attention to the leading-order quadrupole when constructing models for detection or parameter estimation. Some studies have claimed that if additional "higher harmonics" are included consistently in the gravitational wave signal and search model, binary parameters can be measured much more precisely. Using the lalinference Markov-chain Monte Carlo parameter estimation code, we construct posterior parameter constraints associated with two distinct nonprecessing black hole-neutron star (BH-NS) binaries, each with and without higher-order harmonics. All simulations place a plausible signal into a three-detector network with Gaussian noise. Our simulations suggest that higher harmonics provide little information, principally allowing us to measure a previously unconstrained angle associated with the source geometry well but otherwise improving knowledge of all other parameters by a few percent for our loud fiducial signal (ρ =20). Even at this optimistic signal amplitude, different noise realizations have a more significant impact on parameter accuracy than higher harmonics. We compare our results with the "effective Fisher matrix" introduced previously as a method to obtain robust analytic predictions for complicated signals with multiple significant harmonics. We find generally good agreement with these predictions, confirm that intrinsic parameter measurement accuracy is nearly independent of detector network geometry, and show that uncertainties in extrinsic and intrinsic parameters can, to a good approximation, be separated. For our fiducial example, the individual masses can be determined to lie between 7.11-11.48M⊙ and 1.77-1.276M⊙ at greater than 99% confidence level, accounting for unknown BH spin. Assuming comparable control over waveform systematics, measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions. Using analytic arguments to
NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-06-01
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling
Choi, Boseung; Rempala, Grzegorz A.
2012-01-01
We present a new method for Bayesian Markov Chain Monte Carlo–based inference in certain types of stochastic models, suitable for modeling noisy epidemic data. We apply the so-called uniformization representation of a Markov process, in order to efficiently generate appropriate conditional distributions in the Gibbs sampler algorithm. The approach is shown to work well in various data-poor settings, that is, when only partial information about the epidemic process is available, as illustrated on the synthetic data from SIR-type epidemics and the Center for Disease Control and Prevention data from the onset of the H1N1 pandemic in the United States. PMID:21835814
A compositional framework for Markov processes
NASA Astrophysics Data System (ADS)
Baez, John C.; Fong, Brendan; Pollard, Blake S.
2016-03-01
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.
Spectral likelihood expansions for Bayesian inference
NASA Astrophysics Data System (ADS)
Nagel, Joseph B.; Sudret, Bruno
2016-03-01
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.
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.
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
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Anirban; Mondal, Arun; Mukherjee, Sandip; Khatua, Dipam; Ghosh, Subhajit; Mitra, Debasish; Ghosh, Tuhin
2014-08-01
In the Himalayan states of India, with increasing population and activities, large areas of forested land are being converted into other land-use features. There is a definite cause and effect relationship between changing practice for development and changes in land use. So, an estimation of land use dynamics and a futuristic trend pattern is essential. A combination of geospatial and statistical techniques were applied to assess the present and future land use/land cover scenario of Gangtok, the subHimalayan capital of Sikkim. Multi-temporal satellite imageries of the Landsat series were used to map the changes in land use of Gangtok from 1990 to 2010. Only three major land use classes (built-up area and bare land, step cultivated area, and forest) were considered as the most dynamic land use practices of Gangtok. The conventional supervised classification, and spectral indices-based thresholding using NDVI (Normalized Difference Vegetation Index) and SAVI (Soil Adjusted Vegetation Index) were applied along with the accuracy assessments. Markov modelling was applied for prediction of land use/land cover change and was validated. SAVI provides the most accurate estimate, i.e., the difference between predicted and actual data is minimal. Finally, a combination of Markov modelling and SAVI was used to predict the probable land-use scenario in Gangtok in 2020 AD, which indicted that more forest areas will be converted for step cultivation by the year 2020.
Bayesian comparison of Markov models of molecular dynamics with detailed balance constraint
NASA Astrophysics Data System (ADS)
Bacallado, Sergio; Chodera, John D.; Pande, Vijay
2009-07-01
Discrete-space Markov models are a convenient way of describing the kinetics of biomolecules. The most common strategies used to validate these models employ statistics from simulation data, such as the eigenvalue spectrum of the inferred rate matrix, which are often associated with large uncertainties. Here, we propose a Bayesian approach, which makes it possible to differentiate between models at a fixed lag time making use of short trajectories. The hierarchical definition of the models allows one to compare instances with any number of states. We apply a conjugate prior for reversible Markov chains, which was recently introduced in the statistics literature. The method is tested in two different systems, a Monte Carlo dynamics simulation of a two-dimensional model system and molecular dynamics simulations of the terminally blocked alanine dipeptide.
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.
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.
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
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.
Bayesian Inference of CMB Gravitational Lensing
NASA Astrophysics Data System (ADS)
Anderes, Ethan; Wandelt, Benjamin D.; Lavaux, Guilhem
2015-08-01
The Planck satellite, along with several ground-based telescopes, has mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational influence of the intervening matter distribution. A natural modeling approach is to write a Bayesian hierarchical model for the lensed CMB in terms of the unlensed CMB and the lensing potential. So far there has been no feasible algorithm for inferring the posterior distribution of the lensing potential from the lensed CMB map. We propose a solution that allows efficient Markov Chain Monte Carlo sampling from the joint posterior of the lensing potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique. The main conceptual step in the solution is a re-parameterization of CMB lensing in terms of the lensed CMB and the “inverse lensing” potential. We demonstrate a fast implementation on simulated data, including noise and a sky cut, that uses a further acceleration based on a very mild approximation of the inverse lensing potential. We find that the resulting Markov Chain has short correlation lengths and excellent convergence properties, making it promising for applications to high-resolution CMB data sets in the future.
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.
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. PMID:23275296
BAYESIAN HIERARCHICAL MODELING FOR SIGNALING PATHWAY INFERENCE FROM SINGLE CELL INTERVENTIONAL DATA1
Luo, Ruiyan; Zhao, Hongyu
2011-01-01
Recent technological advances have made it possible to simultaneously measure multiple protein activities at the single cell level. With such data collected under different stimulatory or inhibitory conditions, it is possible to infer the causal relationships among proteins from single cell interventional data. In this article we propose a Bayesian hierarchical modeling framework to infer the signaling pathway based on the posterior distributions of parameters in the model. Under this framework, we consider network sparsity and model the existence of an association between two proteins both at the overall level across all experiments and at each individual experimental level. This allows us to infer the pairs of proteins that are associated with each other and their causal relationships. We also explicitly consider both intrinsic noise and measurement error. Markov chain Monte Carlo is implemented for statistical inference. We demonstrate that this hierarchical modeling can effectively pool information from different interventional experiments through simulation studies and real data analysis. PMID:22162986
NASA Astrophysics Data System (ADS)
Yoshioka, N.; Sakaguchi, H.
2005-12-01
A laboratory experiment was performed to detect nucleation processes by transmission elastic waves across a fault with a gouge layer. The apparatus consists of an upper block, a lower block and a gouge layer between the two blocks. The gouge layer is formed with quartz sand with a given particle size distribution and a given thickness. Normal force is the constant self-weight of the upper block and shear force is applied to the upper block by a linear motor through a leaf spring. Elastic waves are continuously transmitted across the fault throughout the shear stress application up to a final stick-slip event. It is observed that a precursory slip and a dilatancy always precede a stick-slip event. The waveform of the transmitted waves significantly changes as the shear stress is increased even when the horizontal displacement is negligibly small. In particular, the amplitude becomes dramatically small with the onset of precursory slip. These facts suggest that the stress chain inside the gouge layer is changed with the application of shear stress. In order to elucidate the mechanism of the observation, a numerical simulation was performed for the gouge layer using the discrete element method (DEM). The loading procedure in the numerical simulation exactly follows the way of the laboratory experiment. The results show that the precursory slip and vertical movements of the upper block are well reproduced by the simulation. The initial stress chains which are homogeneously distributed in the gouge later are drastically changed by shear stress application. With the increment of shear force, some selected force chains become thicker forming columnar structures in the major principal stress direction (direction of the superimposed force of the shear force and the self-weight of the upper block). Dilation due to rotation of the thick column induces volume expansion and it reduces the number of passes to transmit wave from the lower block to the upper block as a result. The
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.
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
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
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
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
Methods for Bayesian Power Spectrum Inference with Galaxy Surveys
NASA Astrophysics Data System (ADS)
Jasche, Jens; Wandelt, Benjamin D.
2013-12-01
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
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
Benchmarking of a Markov multizone model of contaminant transport.
Jones, Rachael M; Nicas, Mark
2014-10-01
A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). PMID:25143517
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.
Performability analysis using semi-Markov reward processes
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Marie, Raymond A.; Sericola, Bruno; Trivedi, Kishor S.
1990-01-01
Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.
Bayesian large-scale structure inference: initial conditions and the cosmic web
NASA Astrophysics Data System (ADS)
Leclercq, Florent; Wandelt, Benjamin
2014-05-01
We describe an innovative statistical approach for the ab initio simultaneous analysis of the formation history and morphology of the large-scale structure of the inhomogeneous Universe. Our algorithm explores the joint posterior distribution of the many millions of parameters involved via efficient Hamiltonian Markov Chain Monte Carlo sampling. We describe its application to the Sloan Digital Sky Survey data release 7 and an additional non-linear filtering step. We illustrate the use of our findings for cosmic web analysis: identification of structures via tidal shear analysis and inference of dark matter voids.
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
Crime Specialization, Seriousness Progression, and Markov Chains.
ERIC Educational Resources Information Center
Holland, Terrill R.; McGarvey, Bill
1984-01-01
Subjected sequences of violent and nonviolent offenses to log-linear analyses of the stabilities and magnitudes of their transition probabilities. Results were seen to support previous research in which nonviolent criminality emerged as more fundamental than violence in potential for pattern development. (LLL)
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
Receptive Field Inference with Localized Priors
Park, Mijung; Pillow, Jonathan W.
2011-01-01
The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. PMID:22046110
Bayesian quantitative trait locus mapping using inferred haplotypes.
Durrant, Caroline; Mott, Richard
2010-03-01
We describe a fast hierarchical Bayesian method for mapping quantitative trait loci by haplotype-based association, applicable when haplotypes are not observed directly but are inferred from multiple marker genotypes. The method avoids the use of a Monte Carlo Markov chain by employing priors for which the likelihood factorizes completely. It is parameterized by a single hyperparameter, the fraction of variance explained by the quantitative trait locus, compared to the frequentist fixed-effects model, which requires a parameter for the phenotypic effect of each combination of haplotypes; nevertheless it still provides estimates of haplotype effects. We use simulation to show that the method matches the power of the frequentist regression model and, when the haplotypes are inferred, exceeds it for small QTL effect sizes. The Bayesian estimates of the haplotype effects are more accurate than the frequentist estimates, for both known and inferred haplotypes, which indicates that this advantage is independent of the effect of uncertainty in haplotype inference and will hold in comparison with frequentist methods in general. We apply the method to data from a panel of recombinant inbred lines of Arabidopsis thaliana, descended from 19 inbred founders. PMID:20048050
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
A Markov model for NASA's Ground Communications Facility
NASA Technical Reports Server (NTRS)
Adeyemi, O.
1974-01-01
A 'natural' way of constructing finite-state Markov chains (FSMC) is presented for those noise burst channels that can be modeled by them. In particular, a five-state Markov chain is given as a model of errors occurring at the Ground Communications Facility (GCF). A maximum likelihood procedure applicable to any FSMC is developed for estimating all the model parameters starting from the data of error runs. A few of the statistics important for estimating the performance of error control strategies on the channel are provided.
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.
A semi-Markov model for price returns
NASA Astrophysics Data System (ADS)
D'Amico, Guglielmo; Petroni, Filippo
2012-10-01
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.
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
NASA Astrophysics Data System (ADS)
Sraj, Ihab; Mandli, Kyle T.; Knio, Omar M.; Dawson, Clint N.; Hoteit, Ibrahim
2014-11-01
Tsunami computational models are employed to explore multiple flooding scenarios and to predict water elevations. However, accurate estimation of water elevations requires accurate estimation of many model parameters including the Manning's n friction parameterization. Our objective is to develop an efficient approach for the uncertainty quantification and inference of the Manning's n coefficient which we characterize here by three different parameters set to be constant in the on-shore, near-shore and deep-water regions as defined using iso-baths. We use Polynomial Chaos (PC) to build an inexpensive surrogate for the GEOCLAW model and employ Bayesian inference to estimate and quantify uncertainties related to relevant parameters using the DART buoy data collected during the Tōhoku tsunami. The surrogate model significantly reduces the computational burden of the Markov Chain Monte-Carlo (MCMC) sampling of the Bayesian inference. The PC surrogate is also used to perform a sensitivity analysis.
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.
Probabilistic Resilience in Hidden Markov Models
NASA Astrophysics Data System (ADS)
Panerati, Jacopo; Beltrame, Giovanni; Schwind, Nicolas; Zeltner, Stefan; Inoue, Katsumi
2016-05-01
Originally defined in the context of ecological systems and environmental sciences, resilience has grown to be a property of major interest for the design and analysis of many other complex systems: resilient networks and robotics systems other the desirable capability of absorbing disruption and transforming in response to external shocks, while still providing the services they were designed for. Starting from an existing formalization of resilience for constraint-based systems, we develop a probabilistic framework based on hidden Markov models. In doing so, we introduce two new important features: stochastic evolution and partial observability. Using our framework, we formalize a methodology for the evaluation of probabilities associated with generic properties, we describe an efficient algorithm for the computation of its essential inference step, and show that its complexity is comparable to other state-of-the-art inference algorithms.
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
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
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
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. PMID:25679743
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
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.
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
Inference algorithms and learning theory for Bayesian sparse factor analysis
NASA Astrophysics Data System (ADS)
Rattray, Magnus; Stegle, Oliver; Sharp, Kevin; Winn, John
2009-12-01
Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.
Bayesian Inference of Natural Selection from Allele Frequency Time Series.
Schraiber, Joshua G; Evans, Steven N; Slatkin, Montgomery
2016-05-01
The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We developed a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in nonequilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package. PMID:27010022
NASA Astrophysics Data System (ADS)
King, Gary; Rosen, Ori; Tanner, Martin A.
2004-09-01
This collection of essays brings together a diverse group of scholars to survey the latest strategies for solving ecological inference problems in various fields. The last half-decade has witnessed an explosion of research in ecological inference--the process of trying to infer individual behavior from aggregate data. Although uncertainties and information lost in aggregation make ecological inference one of the most problematic types of research to rely on, these inferences are required in many academic fields, as well as by legislatures and the Courts in redistricting, by business in marketing research, and by governments in policy analysis.
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
Sunspots and ENSO relationship using Markov method
NASA Astrophysics Data System (ADS)
Hassan, Danish; Iqbal, Asif; Ahmad Hassan, Syed; Abbas, Shaheen; Ansari, Muhammad Rashid Kamal
2016-01-01
The various techniques have been used to confer the existence of significant relations between the number of Sunspots and different terrestrial climate parameters such as rainfall, temperature, dewdrops, aerosol and ENSO etc. Improved understanding and modelling of Sunspots variations can explore the information about the related variables. This study uses a Markov chain method to find the relations between monthly Sunspots and ENSO data of two epochs (1996-2009 and 1950-2014). Corresponding transition matrices of both data sets appear similar and it is qualitatively evaluated by high values of 2-dimensional correlation found between transition matrices of ENSO and Sunspots. The associated transition diagrams show that each state communicates with the others. Presence of stronger self-communication (between same states) confirms periodic behaviour among the states. Moreover, closeness found in the expected number of visits from one state to the other show the existence of a possible relation between Sunspots and ENSO data. Moreover, perfect validation of dependency and stationary tests endorses the applicability of the Markov chain analyses on Sunspots and ENSO data. This shows that a significant relation between Sunspots and ENSO data exists. Improved understanding and modelling of Sunspots variations can help to explore the information about the related variables. This study can be useful to explore the influence of ENSO related local climatic variability.
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
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.
Nonparametric identification and maximum likelihood estimation for hidden Markov models
Alexandrovich, G.; Holzmann, H.; Leister, A.
2016-01-01
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop a nonparametric maximum likelihood estimation theory. First, we show that the asymptotic contrast, the Kullback–Leibler divergence of the hidden Markov model, also identifies the true parameter vector nonparametrically. Second, for classes of state-dependent densities which are arbitrary mixtures of a parametric family, we establish the consistency of the nonparametric maximum likelihood estimator. Here, identification of the mixing distributions need not be assumed. Numerical properties of the estimates and of nonparametric goodness of fit tests are investigated in a simulation study.
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
NASA Astrophysics Data System (ADS)
Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.
2012-01-01
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak-Sneppen model of evolution, in which the system represents an evolutionary `fitness landscape' and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large- N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ N on {1,2,…, N} K . Our main results are that, under appropriate conditions on κ N , the system exhibits threshold behavior at s ∗∈[0,1], where s ∗ is a function of κ N , and the marginal distribution of a randomly selected element converges to U[ s ∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the `mean-field' or `random neighbor' Bak-Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster-Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.
NASA Astrophysics Data System (ADS)
Caticha, Ariel
2011-03-01
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.
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
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
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
NASA Astrophysics Data System (ADS)
Ticchi, Alessandro; Faisal, Aldo A.; Brain; Behaviour Lab Team
2015-03-01
Experimental evidence at the behavioural-level shows that the brains are able to make Bayes-optimal inference and decisions (Kording and Wolpert 2004, Nature; Ernst and Banks, 2002, Nature), yet at the circuit level little is known about how neural circuits may implement Bayesian learning and inference (but see (Ma et al. 2006, Nat Neurosci)). Molecular sources of noise are clearly established to be powerful enough to pose limits to neural function and structure in the brain (Faisal et al. 2008, Nat Rev Neurosci; Faisal et al. 2005, Curr Biol). We propose a spking neuron model where we exploit molecular noise as a useful resource to implement close-to-optimal inference by sampling. Specifically, we derive a synaptic plasticity rule which, coupled with integrate-and-fire neural dynamics and recurrent inhibitory connections, enables a neural population to learn the statistical properties of the received sensory input (prior). Moreover, the proposed model allows to combine prior knowledge with additional sources of information (likelihood) from another neural population, and to implement in spiking neurons a Markov Chain Monte Carlo algorithm which generates samples from the inferred posterior distribution.
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.
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
A Markov model of the Indus script
Rao, Rajesh P. N.; Yadav, Nisha; Vahia, Mayank N.; Joglekar, Hrishikesh; Adhikari, R.; Mahadevan, Iravatham
2009-01-01
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
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
Aggelopoulos, Nikolaos C
2015-08-01
Perceptual inference refers to the ability to infer sensory stimuli from predictions that result from internal neural representations built through prior experience. Methods of Bayesian statistical inference and decision theory model cognition adequately by using error sensing either in guiding action or in "generative" models that predict the sensory information. In this framework, perception can be seen as a process qualitatively distinct from sensation, a process of information evaluation using previously acquired and stored representations (memories) that is guided by sensory feedback. The stored representations can be utilised as internal models of sensory stimuli enabling long term associations, for example in operant conditioning. Evidence for perceptual inference is contributed by such phenomena as the cortical co-localisation of object perception with object memory, the response invariance in the responses of some neurons to variations in the stimulus, as well as from situations in which perception can be dissociated from sensation. In the context of perceptual inference, sensory areas of the cerebral cortex that have been facilitated by a priming signal may be regarded as comparators in a closed feedback loop, similar to the better known motor reflexes in the sensorimotor system. The adult cerebral cortex can be regarded as similar to a servomechanism, in using sensory feedback to correct internal models, producing predictions of the outside world on the basis of past experience. PMID:25976632
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.
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. PMID:23773521
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Leemput, Koen Van
2013-01-01
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. PMID:23773521
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.
Zhao, Quanhua; Li, Yu; Liu, Zhenggang
2013-01-01
This paper presents a new segmentation-based algorithm for oil spill feature extraction from Synthetic Aperture Radar (SAR) intensity images. The proposed algorithm combines a Voronoi tessellation, Bayesian inference and Markov Chain Monte Carlo (MCMC) scheme. The shape and distribution features of dark spots can be obtained by segmenting a scene covering an oil spill and/or look-alikes into two homogenous regions: dark spots and their marine surroundings. The proposed algorithm is applied simultaneously to several real SAR intensity images and simulated SAR intensity images which are used for accurate evaluation. The results show that the proposed algorithm can extract the shape and distribution parameters of dark spot areas, which are useful for recognizing oil spills in a further classification stage. PMID:24233074
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.
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.
Weighted-indexed semi-Markov models for modeling financial returns
NASA Astrophysics Data System (ADS)
D'Amico, Guglielmo; Petroni, Filippo
2012-07-01
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains for studying the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted-indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series such as the first-passage-time distributions and the persistence of volatility. The model is applied to data from the Italian and German stock markets from 1 January 2007 until the end of December 2010.
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.
NASA Astrophysics Data System (ADS)
Ma, Xiang; Zabaras, Nicholas
2009-03-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media.
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.
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.
Monte Carlo Integration Using Spatial Structure of Markov Random Field
NASA Astrophysics Data System (ADS)
Yasuda, Muneki
2015-03-01
Monte Carlo integration (MCI) techniques are important in various fields. In this study, a new MCI technique for Markov random fields (MRFs) is proposed. MCI consists of two successive parts: the first involves sampling using a technique such as the Markov chain Monte Carlo method, and the second involves an averaging operation using the obtained sample points. In the averaging operation, a simple sample averaging technique is often employed. The method proposed in this paper improves the averaging operation by addressing the spatial structure of the MRF and is mathematically guaranteed to statistically outperform standard MCI using the simple sample averaging operation. Moreover, the proposed method can be improved in a systematic manner and is numerically verified by numerical simulations using planar Ising models. In the latter part of this paper, the proposed method is applied to the inverse Ising problem and we observe that it outperforms the maximum pseudo-likelihood estimation.
Markov Boundary Discovery with Ridge Regularized Linear Models
Visweswaran, Shyam
2016-01-01
Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate association to a response. However, many investigators are reluctant to draw causal interpretations of the selected variables due to the incomplete knowledge of the capabilities of RRLMs in causal inference. Under reasonable assumptions, we show that a modified form of RRLMs can get “very close” to identifying a subset of the Markov boundary by providing a worst-case bound on the space of possible solutions. The results hold for any convex loss, even when the underlying functional relationship is nonlinear, and the solution is not unique. Our approach combines ideas in Markov boundary and sufficient dimension reduction theory. Experimental results show that the modified RRLMs are competitive against state-of-the-art algorithms in discovering part of the Markov boundary from gene expression data. PMID:27170915
Choice of Units and the Causal Markov Condition
NASA Astrophysics Data System (ADS)
Zhang, Jiji; Spirtes, Peter
2014-03-01
Elliott Sober's well-known challenge to the principle of the common cause -- and to its generalization, the causal Markov condition -- appeals to the apparent positive correlation between two causally unconnected quantities: Venetian sea levels and British bread prices. In this paper we examine Kevin Hoover's and Daniel Steel's opposite evaluations of Sober's case. We argue that the difference in their assessments results from a difference in their choice of units and populations for statistical modeling. Our analysis suggests yet another diagnosis of Sober's counterexample: the failure of the causal Markov condition in the population chosen by Sober and Steel is due to the presence of causal relations that hold between the relevant properties across units. Such inter-unit causation is left unrepresented in causal models congenial to statistical analysis, because statistics does not deal with inter-unit relationships once the units are fixed. Accordingly, the causal Markov condition is formulated in terms of causal structures that depict intra-unit causal relations only. It is therefore worth highlighting a methodological principle for causal inference: the units should be so chosen that they do not interfere with each other, a principle that, fortunately, is often observed in practice.
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.
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
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
Rodrigo, Allen G; Tsai, Peter; Shearman, Helen
2009-01-01
Coalescent-based Bayesian Markov chain Monte Carlo (MCMC) inference generates estimates of evolutionary parameters and their posterior probability distributions. As the number of sequences increases, the length of time taken to complete an MCMC analysis increases as well. Here, we investigate an approach to distribute the MCMC analysis across a cluster of computers. To do this, we use bootstrapped topologies as fixed genealogies, perform a single MCMC analysis on each genealogy without topological rearrangements, and pool the results across all MCMC analyses. We show, through simulations, that although the standard MCMC performs better than the bootstrap-MCMC at estimating the effective population size (scaled by mutation rate), the bootstrap-MCMC returns better estimates of growth rates. Additionally, we find that our bootstrap-MCMC analyses are, on average, 37 times faster for equivalent effective sample sizes. PMID:19812730
COCIS: Markov processes in single molecule fluorescence
Talaga, David S.
2009-01-01
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system. PMID:19543444
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)
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 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.
Markov constant and quantum instabilities
NASA Astrophysics Data System (ADS)
Pelantová, Edita; Starosta, Štěpán; Znojil, Miloslav
2016-04-01
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.
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.
Estimation with Right-Censored Observations Under A Semi-Markov Model
Hu, X. Joan
2013-01-01
The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition probability of the semi-Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi-Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. PMID:23874060
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.
Discovering Student Web Usage Profiles Using Markov Chains
ERIC Educational Resources Information Center
Marques, Alice; Belo, Orlando
2011-01-01
Nowadays, Web based platforms are quite common in any university, supporting a very diversified set of applications and services. Ranging from personal management to student evaluation processes, Web based platforms are doing a great job providing a very flexible way of working, promote student enrolment, and making access to academic information…
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…
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.
Recognizing Chromospheric Objects via Markov Chain Monte Carlo
NASA Technical Reports Server (NTRS)
Mukhtar, Saleem; Turmon, Michael J.
1997-01-01
The solar chromosphere consists of three classes which contribute differentially to ultraviolet radiation reaching the earth. We describe a data set of solar images, means of segmenting the images into the constituent classes, and a novel high-level representation for compact objects based on a triangulated spatial membership function.
Markov Chain Estimation of Avian Seasonal Fecundity, Presentation
Avian seasonal fecundity is of interest from evolutionary, ecological, and conservation perspectives. However, direct estimation of seasonal fecundity is difficult, especially with multibrooded birds, and models representing the renesting and quitting processes are usually requi...
Generators of quantum Markov semigroups
NASA Astrophysics Data System (ADS)
Androulakis, George; Ziemke, Matthew
2015-08-01
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48, 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6, 211-216 (1955)], and Kraus [Ann. Phys. 64, 311-335 (1970)] imply that the generator of the semigroup has the form L ( A ) = ∑ n = 1 ∞ Vn ∗ A V n + G A + A G ∗ , where Vn and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus' result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains.
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
Testing the Markov hypothesis in fluid flows
NASA Astrophysics Data System (ADS)
Meyer, Daniel W.; Saggini, Frédéric
2016-05-01
Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered.
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.
Uncertainty Analysis in Fatigue Life Prediction of Gas Turbine Blades Using Bayesian Inference
NASA Astrophysics Data System (ADS)
Li, Yan-Feng; Zhu, Shun-Peng; Li, Jing; Peng, Weiwen; Huang, Hong-Zhong
2015-12-01
This paper investigates Bayesian model selection for fatigue life estimation of gas turbine blades considering model uncertainty and parameter uncertainty. Fatigue life estimation of gas turbine blades is a critical issue for the operation and health management of modern aircraft engines. Since lots of life prediction models have been presented to predict the fatigue life of gas turbine blades, model uncertainty and model selection among these models have consequently become an important issue in the lifecycle management of turbine blades. In this paper, fatigue life estimation is carried out by considering model uncertainty and parameter uncertainty simultaneously. It is formulated as the joint posterior distribution of a fatigue life prediction model and its model parameters using Bayesian inference method. Bayes factor is incorporated to implement the model selection with the quantified model uncertainty. Markov Chain Monte Carlo method is used to facilitate the calculation. A pictorial framework and a step-by-step procedure of the Bayesian inference method for fatigue life estimation considering model uncertainty are presented. Fatigue life estimation of a gas turbine blade is implemented to demonstrate the proposed method.
Inference of Homologous Recombination in Bacteria Using Whole-Genome Sequences
Didelot, Xavier; Lawson, Daniel; Darling, Aaron; Falush, Daniel
2010-01-01
Bacteria and archaea reproduce clonally, but sporadically import DNA into their chromosomes from other organisms. In many of these events, the imported DNA replaces an homologous segment in the recipient genome. Here we present a new method to reconstruct the history of recombination events that affected a given sample of bacterial genomes. We introduce a mathematical model that represents both the donor and the recipient of each DNA import as an ancestor of the genomes in the sample. The model represents a simplification of the previously described coalescent with gene conversion. We implement a Monte Carlo Markov chain algorithm to perform inference under this model from sequence data alignments and show that inference is feasible for whole-genome alignments through parallelization. Using simulated data, we demonstrate accurate and reliable identification of individual recombination events and global recombination rate parameters. We applied our approach to an alignment of 13 whole genomes from the Bacillus cereus group. We find, as expected from laboratory experiments, that the recombination rate is higher between closely related organisms and also that the genome contains several broad regions of elevated levels of recombination. Application of the method to the genomic data sets that are becoming available should reveal the evolutionary history and private lives of populations of bacteria and archaea. The methods described in this article have been implemented in a computer software package, ClonalOrigin, which is freely available from http://code.google.com/p/clonalorigin/. PMID:20923983
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. PMID:25406469
Scene Construction, Visual Foraging, and Active Inference
Mirza, M. Berk; Adams, Rick A.; Mathys, Christoph D.; Friston, Karl J.
2016-01-01
This paper describes an active inference scheme for visual searches and the perceptual synthesis entailed by scene construction. Active inference assumes that perception and action minimize variational free energy, where actions are selected to minimize the free energy expected in the future. This assumption generalizes risk-sensitive control and expected utility theory to include epistemic value; namely, the value (or salience) of information inherent in resolving uncertainty about the causes of ambiguous cues or outcomes. Here, we apply active inference to saccadic searches of a visual scene. We consider the (difficult) problem of categorizing a scene, based on the spatial relationship among visual objects where, crucially, visual cues are sampled myopically through a sequence of saccadic eye movements. This means that evidence for competing hypotheses about the scene has to be accumulated sequentially, calling upon both prediction (planning) and postdiction (memory). Our aim is to highlight some simple but fundamental aspects of the requisite functional anatomy; namely, the link between approximate Bayesian inference under mean field assumptions and functional segregation in the visual cortex. This link rests upon the (neurobiologically plausible) process theory that accompanies the normative formulation of active inference for Markov decision processes. In future work, we hope to use this scheme to model empirical saccadic searches and identify the prior beliefs that underwrite intersubject variability in the way people forage for information in visual scenes (e.g., in schizophrenia). PMID:27378899
Scene Construction, Visual Foraging, and Active Inference.
Mirza, M Berk; Adams, Rick A; Mathys, Christoph D; Friston, Karl J
2016-01-01
This paper describes an active inference scheme for visual searches and the perceptual synthesis entailed by scene construction. Active inference assumes that perception and action minimize variational free energy, where actions are selected to minimize the free energy expected in the future. This assumption generalizes risk-sensitive control and expected utility theory to include epistemic value; namely, the value (or salience) of information inherent in resolving uncertainty about the causes of ambiguous cues or outcomes. Here, we apply active inference to saccadic searches of a visual scene. We consider the (difficult) problem of categorizing a scene, based on the spatial relationship among visual objects where, crucially, visual cues are sampled myopically through a sequence of saccadic eye movements. This means that evidence for competing hypotheses about the scene has to be accumulated sequentially, calling upon both prediction (planning) and postdiction (memory). Our aim is to highlight some simple but fundamental aspects of the requisite functional anatomy; namely, the link between approximate Bayesian inference under mean field assumptions and functional segregation in the visual cortex. This link rests upon the (neurobiologically plausible) process theory that accompanies the normative formulation of active inference for Markov decision processes. In future work, we hope to use this scheme to model empirical saccadic searches and identify the prior beliefs that underwrite intersubject variability in the way people forage for information in visual scenes (e.g., in schizophrenia). PMID:27378899
Inferring learners' knowledge from their actions.
Rafferty, Anna N; LaMar, Michelle M; Griffiths, Thomas L
2015-04-01
Watching another person take actions to complete a goal and making inferences about that person's knowledge is a relatively natural task for people. This ability can be especially important in educational settings, where the inferences can be used for assessment, diagnosing misconceptions, and providing informative feedback. In this paper, we develop a general framework for automatically making such inferences based on observed actions; this framework is particularly relevant for inferring student knowledge in educational games and other interactive virtual environments. Our approach relies on modeling action planning: We formalize the problem as a Markov decision process in which one must choose what actions to take to complete a goal, where choices will be dependent on one's beliefs about how actions affect the environment. We use a variation of inverse reinforcement learning to infer these beliefs. Through two lab experiments, we show that this model can recover people's beliefs in a simple environment, with accuracy comparable to that of human observers. We then demonstrate that the model can be used to provide real-time feedback and to model data from an existing educational game. PMID:25155381
Chorin, Alexandre J.
2007-12-12
A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the Edwards-Anderson spin glass in three dimensions.
Dopamine, reward learning, and active inference
FitzGerald, Thomas H. B.; Dolan, Raymond J.; Friston, Karl
2015-01-01
Temporal difference learning models propose phasic dopamine signaling encodes reward prediction errors that drive learning. This is supported by studies where optogenetic stimulation of dopamine neurons can stand in lieu of actual reward. Nevertheless, a large body of data also shows that dopamine is not necessary for learning, and that dopamine depletion primarily affects task performance. We offer a resolution to this paradox based on an hypothesis that dopamine encodes the precision of beliefs about alternative actions, and thus controls the outcome-sensitivity of behavior. We extend an active inference scheme for solving Markov decision processes to include learning, and show that simulated dopamine dynamics strongly resemble those actually observed during instrumental conditioning. Furthermore, simulated dopamine depletion impairs performance but spares learning, while simulated excitation of dopamine neurons drives reward learning, through aberrant inference about outcome states. Our formal approach provides a novel and parsimonious reconciliation of apparently divergent experimental findings. PMID:26581305
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.
Sezer, Deniz; Freed, Jack H; Roux, Benoit
2008-09-01
Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine alpha helix in explicit solvent. PMID:18698714