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Reversible Jump Markov Chain (reversible + jump_markov_chain)

Distribution by Scientific Domains
Mathematics and Statistics91%

Selected Abstracts

A Bayesian approach to inverse modelling of stratigraphy, part 1: method

BASIN RESEARCH, Issue 1 2009
Karl Charvin
ABSTRACT The inference of ancient environmental conditions from their preserved response in the sedimentary record still remains an outstanding issue in stratigraphy. Since the 1970s, conceptual stratigraphic models (e.g. sequence stratigraphy) based on the underlying assumption that accommodation space is the critical control on stratigraphic architecture have been widely used. Although these methods considered more recently other possible parameters such as sediment supply and transport efficiency, they still lack in taking into account the full range of possible parameters, processes, and their complex interactions that control stratigraphic architecture. In this contribution, we present a new quantitative method for the inference of key environmental parameters (specifically sediment supply and relative sea level) that control stratigraphy. The approach combines a fully non-linear inversion scheme with a ,process,response' forward model of stratigraphy. We formulate the inverse problem using a Bayesian framework in order to sample the full range of possible solutions and explicitly build in prior geological knowledge. Our methodology combines Reversible Jump Markov chain Monte Carlo and Simulated Tempering algorithms which are able to deal with variable-dimensional inverse problems and multi-modal posterior probability distributions, respectively. The inverse scheme has been linked to a forward stratigraphic model, BARSIM (developed by Joep Storms, University of Delft), which simulates shallow-marine wave/storm-dominated systems over geological timescales. This link requires the construction of a likelihood function to quantify the agreement between simulated and observed data of different types (e.g. sediment age and thickness, grain size distributions). The technique has been tested and validated with synthetic data, in which all the parameters are specified to produce a ,perfect' simulation, although we add noise to these synthetic data for subsequent testing of the inverse modelling approach. These tests addressed convergence and computational-overhead issues, and highlight the robustness of the inverse scheme, which is able to assess the full range of uncertainties on the inferred environmental parameters and facies distributions. [source]

Capture,Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

BIOMETRICS, Issue 2 2010
Richard Arnold
Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture,recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood-based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set. [source]

Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2000
C. P. Robert
Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism. [source]

Segmenting bacterial and viral DNA sequence alignments with a trans-dimensional phylogenetic factorial hidden Markov model

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 3 2009
Wolfgang P. Lehrach
Summary., The traditional approach to phylogenetic inference assumes that a single phylogenetic tree can represent the relationships and divergence between the taxa. However, taxa sequences exhibit varying levels of conservation, e.g. because of regulatory elements and active binding sites. Also, certain bacteria and viruses undergo interspecific recombination, where different strains exchange or transfer DNA subsequences, leading to a tree topology change. We propose a phylogenetic factorial hidden Markov model to detect recombination and rate variation simultaneously. This is applied to two DNA sequence alignments: one bacterial (Neisseria) and another of type 1 human immunodeficiency virus. Inference is carried out in the Bayesian framework, using reversible jump Markov chain Monte Carlo sampling. [source]

Motor unit number estimation using reversible jump Markov chain Monte Carlo methods

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 3 2007
P. G. Ridall
Summary., We present an application of reversible jump Markov chain Monte Carlo sampling from the field of neurophysiology where we seek to estimate the number of motor units within a single muscle. Such an estimate is needed for monitoring the progression of neuromuscular diseases such as amyotrophic lateral sclerosis. Our data consist of action potentials that were recorded from the surface of a muscle in response to stimuli of different intensities applied to the nerve supplying the muscle. During the gradual increase in intensity of the stimulus from the threshold to supramaximal, all motor units are progressively excited. However, at any given submaximal intensity of stimulus, the number of units that are excited is variable, because of random fluctuations in axonal excitability. Furthermore, the individual motor unit action potentials exhibit variability. To account for these biological properties, Ridall and co-workers developed a model of motor unit activation that is capable of describing the response where the number of motor units, N, is fixed. The purpose of this paper is to extend that model so that the possible number of motor units, N, is a stochastic variable. We illustrate the elements of our model, show that the results are reproducible and show that our model can measure the decline in motor unit numbers during the course of amyotrophic lateral sclerosis. Our method holds promise of being useful in the study of neurogenic diseases. [source]

Bayesian selection of threshold autoregressive models

JOURNAL OF TIME SERIES ANALYSIS, Issue 4 2004
Edward P. Campbell
Abstract., An approach to Bayesian model selection in self-exciting threshold autoregressive (SETAR) models is developed within a reversible jump Markov chain Monte Carlo (RJMCMC) framework. Our approach is examined via a simulation study and analysis of the Zurich monthly sunspots series. We find that the method converges rapidly to the optimal model, whilst efficiently exploring suboptimal models to quantify model uncertainty. A key finding is that the parsimony of the model selected is influenced by the specification of prior information, which can be examined and subjected to criticism. This is a strength of the Bayesian approach, allowing physical understanding to constrain the model selection algorithm. [source]

A bayesian estimator for the dependence function of a bivariate extreme-value distribution

THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2008
Simon Guillotte
Abstract Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme-value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set. Un estimateur bayésien de la fonction de dépendance d'une loi des valeurs extrêmes bivariée Toute loi bivariée continue peut s'écrire en fonction de ses marges et d'une copule unique. Dans le cas des lois des valeurs extrêmes, la copule est caractérisée par une fonction de dépendance tandis que chaque marge dépend de trois paramètres. Les auteurs proposent une approche bayésienne pour l'estimation simultanée de la fonction de dépendance et des paramètres définissant les marges. Ils décrivent un modèle non paramétrique pour la fonction de dépendance et un algorithme MCMC à sauts réversibles pour le calcul de l'estimateur bayésien. Ils montrent par simulation que l'erreur quadratique moyenne intégrée de leur estimateur est plus faible que celle des estimateurs classiques, surtout dans de petits échantillons. Ils illustrent leur propos à l'aide de données hydrologiques. [source]

REVERSIBLE JUMP MARKOV CHAIN MONTE CARLO METHODS AND SEGMENTATION ALGORITHMS IN HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2010
R. Paroli
Summary We consider hidden Markov models with an unknown number of regimes for the segmentation of the pixel intensities of digital images that consist of a small set of colours. New reversible jump Markov chain Monte Carlo algorithms to estimate both the dimension and the unknown parameters of the model are introduced. Parameters are updated by random walk Metropolis,Hastings moves, without updating the sequence of the hidden Markov chain. The segmentation (i.e. the estimation of the hidden regimes) is a further aim and is performed by means of a number of competing algorithms. We apply our Bayesian inference and segmentation tools to digital images, which are linearized through the Peano,Hilbert scan, and perform experiments and comparisons on both synthetic images and a real brain magnetic resonance image. [source]

Bayesian Adaptive Regression Splines for Hierarchical Data

BIOMETRICS, Issue 3 2007
Jamie L. Bigelow
Summary This article considers methodology for hierarchical functional data analysis, motivated by studies of reproductive hormone profiles in the menstrual cycle. Current methods standardize the cycle lengths and ignore the timing of ovulation within the cycle, both of which are biologically informative. Methods are needed that avoid standardization, while flexibly incorporating information on covariates and the timing of reference events, such as ovulation and onset of menses. In addition, it is necessary to account for within-woman dependency when data are collected for multiple cycles. We propose an approach based on a hierarchical generalization of Bayesian multivariate adaptive regression splines. Our formulation allows for an unknown set of basis functions characterizing the population-averaged and woman-specific trajectories in relation to covariates. A reversible jump Markov chain Monte Carlo algorithm is developed for posterior computation. Applying the methods to data from the North Carolina Early Pregnancy Study, we investigate differences in urinary progesterone profiles between conception and nonconception cycles. [source]

Model Selection for Integrated Recovery/Recapture Data

BIOMETRICS, Issue 4 2002
R. King
Summary. Catchpole et al. (1998, Biometrics 54, 33,46) provide a novel scheme for integrating both recovery and recapture data analyses and derive sufficient statistics that facilitate likelihood computations. In this article, we demonstrate how their efficient likelihood expression can facilitate Bayesian analyses of these kinds of data and extend their methodology to provide a formal framework for model determination. We consider in detail the issue of model selection with respect to a set of recapture/recovery histories of shags (Phalacrocorax aristotelis) and determine, from the enormous range of biologically plausible models available, which best describe the data. By using reversible jump Markov chain Monte Carlo methodology, we demonstrate how this enormous model space can be efficiently and effectively explored without having to resort to performing an infeasibly large number of pairwise comparisons or some ad hoc stepwise procedure. We find that the model used by Catchpole et al. (1998) has essentially zero posterior probability and that, of the 477,144 possible models considered, over 60% of the posterior mass is placed on three neighboring models with biologically interesting interpretations. [source]