Using Thermodynamic Integration to Calculate the Posterior Probability in Bayesian Model Selection Problems

Goggans, Paul M.

doi:10.1063/1.1751356

Cited by 37 publications

(31 citation statements)

References 5 publications

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“…The calculations presented here extend the Bayesian/McMC approach (22) to simultaneously estimate the posterior probability of diffusion anisotropy model parameters and compare the relative probabilities of various model expressions against each other. The latter part of the calculation is referred to as “model selection.” Model selection is a simple conceptual extension of parameter estimation whereby a model parameter is assigned as an index that specifies which expression from a set is used to represent the data (23, 24). The posterior probability for this index therefore indicates the relative probabilities of the model expressions.…”

Section: Methodsmentioning

confidence: 99%

Divergent roles of the DEAD-box protein BS-PL10, the urochordate homologue of human DDX3 and DDX3Y proteins, in colony astogeny and ontogeny

2006

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Proteins of the highly conserved PL-10 (Ded1P) subfamily of DEAD-box family, participate in a wide variety of biological functions. However, the entire spectrum of their functions in both vertebrates and invertebrates is still unknown. Here, we isolated the Botryllus schlosseri (Urochordata) homologue, BS-PL10, revealing its distributions and functions in ontogeny and colony astogeny. In botryllid ascidians, the colony grows by increasing the number of modular units (each called a zooid) through a whole colony synchronized and weekly cyclical astogenic budding process (blastogenesis). At the level of the colony, both BS-PL10 mRNA and its protein (

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Section: Methodsmentioning

confidence: 99%

Divergent roles of the DEAD-box protein BS-PL10, the urochordate homologue of human DDX3 and DDX3Y proteins, in colony astogeny and ontogeny

2006

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“…For more information on Markov chain Monte Carlo, see (6,7), and for more details on how to implement model selection within simulated annealing, see (8,9).…”

Section: Exponential Model Selection (In Nmr) Using Bayesian Probabilmentioning

confidence: 99%

“…[9], into the posterior probability for the model indicator, Eq. [7], gives P͑u͉DI͒ ϰ P͑u͉I͒ ͵ d⌿ u P͑⌿ u ͉uI͒ P͑D͉⌿ u uI͒.…”

Section: Theorymentioning

confidence: 99%

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Exponential model selection (in NMR) using Bayesian probability theory

Bretthorst

Hutton

Garbow

et al. 2005

Concepts Magn. Reson.

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ABSTRACT:In a companion article in this issue, parameter estimation using exponential models was addressed when the form of the model is known (i.e., when the number of exponentials and whether a constant offset is present are known). In this article, we apply Bayesian probability theory to the problem of determining the functional form of the model. The calculations are implemented using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for the parameters and the functional form of the model. Monte Carlo integration is then used to approximate the marginal posterior probabilities for all the parameters, including the number of exponentials and whether a constant offset is present. Examples using empirical data are given to illustrate the calculations.

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“…where p(·) is the prior distribution and L(· | D, M k ) is the likelihood under model k. These posterior evidence integrals are approximated using emcee's (Foreman-Mackey et al, 2013) implementation of an approach using thermodynamic integration (see Goggans and Chi, 2004).…”

Section: Inferencementioning

confidence: 99%

A population phylogenetic view of mitochondrial heteroplasmy

Wilton

Zaidi

Makova

et al. 2017

Preprint

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The mitochondrion has recently emerged as an active player in a myriad of cellular processes. Additionally, it was recently shown that more than 200 diseases are known to be linked to variants in mitochondrial DNA or in nuclear genes interacting with mitochondria. This has reinvigorated interest in its biology and population genetics. Mitochondrial heteroplasmy, or genotypic variation of mitochondria within an individual, is now understood to be common in humans and important in human health. However, it is still not possible to make quantitative predictions about the inheritance of heteroplasmy and its proliferation within the body, partly due to the lack of an appropriate model. Here, we present a population-genetic framework for modeling mitochondrial heteroplasmy as a process that occurs on an ontogenetic phylogeny, with genetic drift and mutation changing heteroplasmy frequencies during the various developmental processes represented in the phylogeny. Using this framework, we develop a Bayesian inference method for inferring rates of mitochondrial genetic drift and mutation at different stages of human life. Applying the method to previously published heteroplasmy frequency data, we demonstrate a severe effective germline bottleneck comprised of the cumulative genetic drift occurring between the divergence of germline and somatic cells in the mother and the separation of germ layers in the offspring. Additionally, we find that the two somatic tissues we analyze here undergo tissue-specific bottlenecks during embryogenesis, less severe than the effective germline bottleneck, and that these somatic tissues experience little additional genetic drift during adulthood. We conclude with a discussion of possible extensions of the ontogenetic phylogeny framework and its possible applications to other ontogenetic processes in addition to mitochondrial heteroplasmy.

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Using Thermodynamic Integration to Calculate the Posterior Probability in Bayesian Model Selection Problems

Cited by 37 publications

References 5 publications

Divergent roles of the DEAD-box protein BS-PL10, the urochordate homologue of human DDX3 and DDX3Y proteins, in colony astogeny and ontogeny

Divergent roles of the DEAD-box protein BS-PL10, the urochordate homologue of human DDX3 and DDX3Y proteins, in colony astogeny and ontogeny

Exponential model selection (in NMR) using Bayesian probability theory

A population phylogenetic view of mitochondrial heteroplasmy

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