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.
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…
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
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.
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.
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.
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.
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.
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 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
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.
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…
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…
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…
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.
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
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
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
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.
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
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)
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).
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
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.
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
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.
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.
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.
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
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.
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.
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.
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
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…
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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
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
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
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
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
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.
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
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.
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.
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
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)
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.
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.
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.
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
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
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)
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
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)
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
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.
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
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.
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 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
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.
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.
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.
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
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
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.
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
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
A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
NASA Astrophysics Data System (ADS)
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
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)
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
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.
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)
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''.
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)
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
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
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.
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)
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
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)
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.
NASA Astrophysics Data System (ADS)
Jalayer, Fatemeh; Ebrahimian, Hossein
2014-05-01
Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the
NASA Astrophysics Data System (ADS)
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.
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.
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
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
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…
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.
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 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.
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.
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.
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.
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.
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
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…
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…
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
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.
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.
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
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.
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.
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)
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...
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
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
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
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.
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.
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
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.
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.
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
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.
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
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.
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.
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.
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…
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…
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
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.
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
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
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.
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
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.
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.
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.
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
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling
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.
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.
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.
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.
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.
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…
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.
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
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.
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
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.
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...
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.
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.
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…
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.
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
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
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...
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.
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.
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.
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 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.
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
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
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
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.
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.
Blennow, Mattias
2010-03-30
We introduce the software package MonteCUBES, which is designed to easily and effectively perform Markov Chain Monte Carlo simulations for analyzing neutrino oscillation experiments. We discuss the methods used in the software as well as why we believe that it is particularly useful for simulating new physics effects.
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.
Short-term droughts forecast using Markov chain model in Victoria, Australia
NASA Astrophysics Data System (ADS)
Rahmat, Siti Nazahiyah; Jayasuriya, Niranjali; Bhuiyan, Muhammed A.
2016-04-01
A comprehensive risk management strategy for dealing with drought should include both short-term and long-term planning. The objective of this paper is to present an early warning method to forecast drought using the Standardised Precipitation Index (SPI) and a non-homogeneous Markov chain model. A model such as this is useful for short-term planning. The developed method has been used to forecast droughts at a number of meteorological monitoring stations that have been regionalised into six (6) homogenous clusters with similar drought characteristics based on SPI. The non-homogeneous Markov chain model was used to estimate drought probabilities and drought predictions up to 3 months ahead. The drought severity classes defined using the SPI were computed at a 12-month time scale. The drought probabilities and the predictions were computed for six clusters that depict similar drought characteristics in Victoria, Australia. Overall, the drought severity class predicted was quite similar for all the clusters, with the non-drought class probabilities ranging from 49 to 57 %. For all clusters, the near normal class had a probability of occurrence varying from 27 to 38 %. For the more moderate and severe classes, the probabilities ranged from 2 to 13 % and 3 to 1 %, respectively. The developed model predicted drought situations 1 month ahead reasonably well. However, 2 and 3 months ahead predictions should be used with caution until the models are developed further.
NASA Astrophysics Data System (ADS)
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