Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

2010 ◽  
Vol 37 (2) ◽  
pp. 135-155 ◽  
Author(s):  
Satoshi Usami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Individual Differences ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Reversible Jump

scholarly journals Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

2016 ◽  
Vol 9 (9) ◽  
pp. 3213-3229 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Spatial Domain ◽  
Monte Carlo Algorithm ◽  
Trace Gas ◽  
Reversible Jump ◽  
Pseudo Data ◽  
Atmospheric Trace Gas

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.

scholarly journals Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

2008 ◽  
Vol 363 (1512) ◽  
pp. 3955-3964 ◽  
Author(s):  
Mark Pagel ◽  
Andrew Meade
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mixture Model ◽  
Branch Length ◽  
Monte Carlo Algorithm ◽  
Morphological Data ◽  
Reversible Jump ◽  
Rate Variation ◽  
Ancestral State

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon—known as heterotachy—can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our ‘pattern-heterogeneity’ mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of ‘significance’ such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

scholarly journals Bayesian estimation of a phenotype network structure using reversible jump Markov chain Monte Carlo

2021 ◽  
Author(s):  
◽  
Lisa Woods
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Network Structure ◽  
Monte Carlo Algorithm ◽  
Maximum Likelihood Estimates ◽  
Reversible Jump ◽  
Network Structures ◽  
Double Step ◽  
Phenotype Network

<p>In this thesis we aim to estimate the unknown phenotype network structure existing among multiple interacting quantitative traits, assuming the genetic architecture is known.  We begin by taking a frequentist approach and implement a score-based greedy hill-climbing search strategy using AICc to estimate an unknown phenotype network structure. This approach was inconsistent and overfitting was common, so we then propose a Bayesian approach that extends on the reversible jump Markov chain Monte Carlo algorithm. Our approach makes use of maximum likelihood estimates in the chain, so we have an efficient sampler using well-tuned proposal distributions. The common approach is to assume uniform priors over all network structures; however, we introduce a prior on the number of edges in the phenotype network structure, which prefers simple models with fewer directed edges. We determine that the relationship between the prior penalty and the joint posterior probability of the true model is not monotonic, there is some interplay between the two.  Simulation studies were carried out and our approach is also applied to a published data set. It is determined that larger trait-to-trait effects are required to recover the phenotype network structure; however, mixing is generally slow, a common occurrence with reversible jump Markov chain Monte Carlo methods. We propose the use of a double step to combine two steps that alter the phenotype network structure. This proposes larger steps than the traditional birth and death move types, possibly changing the dimension of the model by more than one. This double step helped the sampler move between different phenotype network structures in simulated data sets.</p>

scholarly journals A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data

2018 ◽  
Vol 113 ◽  
pp. 94-105 ◽  
Author(s):  
Eric Mandolesi ◽  
Xenia Ogaya ◽  
Joan Campanyà ◽  
Nicola Piana Agostinetti
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Reversible Jump ◽  
Magnetotelluric Data

scholarly journals Bayesian estimation of a phenotype network structure using reversible jump Markov chain Monte Carlo

2021 ◽  
Author(s):  
◽  
Lisa Woods
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Network Structure ◽  
Monte Carlo Algorithm ◽  
Maximum Likelihood Estimates ◽  
Reversible Jump ◽  
Network Structures ◽  
Double Step ◽  
Phenotype Network

<p>In this thesis we aim to estimate the unknown phenotype network structure existing among multiple interacting quantitative traits, assuming the genetic architecture is known.  We begin by taking a frequentist approach and implement a score-based greedy hill-climbing search strategy using AICc to estimate an unknown phenotype network structure. This approach was inconsistent and overfitting was common, so we then propose a Bayesian approach that extends on the reversible jump Markov chain Monte Carlo algorithm. Our approach makes use of maximum likelihood estimates in the chain, so we have an efficient sampler using well-tuned proposal distributions. The common approach is to assume uniform priors over all network structures; however, we introduce a prior on the number of edges in the phenotype network structure, which prefers simple models with fewer directed edges. We determine that the relationship between the prior penalty and the joint posterior probability of the true model is not monotonic, there is some interplay between the two.  Simulation studies were carried out and our approach is also applied to a published data set. It is determined that larger trait-to-trait effects are required to recover the phenotype network structure; however, mixing is generally slow, a common occurrence with reversible jump Markov chain Monte Carlo methods. We propose the use of a double step to combine two steps that alter the phenotype network structure. This proposes larger steps than the traditional birth and death move types, possibly changing the dimension of the model by more than one. This double step helped the sampler move between different phenotype network structures in simulated data sets.</p>

scholarly journals Estimation of trace gas fluxes with objectively determined basis functions using reversible jump Markov chain Monte Carlo

2016 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Spatial Domain ◽  
Monte Carlo Algorithm ◽  
Trace Gas ◽  
Reversible Jump ◽  
Pseudo Data ◽  
Atmospheric Trace Gas

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the size of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the the well-established reversible jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, it allows the uncertainty in our choice of aggregation to be carried through to the solution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allows methane emissions over north-west Europe to be resolved.

A Reversible Jump Markov Chain Monte Carlo Algorithm for Bacterial Promoter Motifs Discovery

2006 ◽  
Vol 13 (3) ◽  
pp. 651-667 ◽  
Author(s):  
Pierre Nicolas ◽  
Anne-Sophie Tocquet ◽  
Vincent Miele ◽  
Florence Muri
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Reversible Jump
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