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Bayesian constraint relaxation.

ABSTRACT: Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.

SUBMITTER: Duan LL

PROVIDER: S-EPMC7017863 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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Publications

Bayesian constraint relaxation.

Duan Leo L LL Young Alexander L AL Nishimura Akihiko A Dunson David B DB

Biometrika 20191224 1

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator functi ...[more]

PMID: 32089562

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Project description:Bayesian gene networks are powerful for modelling causal relationships and incorporating prior knowledge for making inferences about relationships. We used three algorithms to construct Bayesian gene networks around genes expressed in the bovine uterus and compared the efficacies of the algorithms. Dataset GSE33030 from the Gene Expression Omnibus (GEO) repository was analyzed using different algorithms for hub gene expression due to the effect of progesterone on bovine endometrial tissue following conception. Six different algorithms (grow-shrink, max-min parent children, tabu search, hill-climbing, max-min hill-climbing and restricted maximum) were compared in three higher categories, including constraint-based, score-based and hybrid algorithms. Gene network parameters were estimated using the bnlearn bundle, which is a Bayesian network structure learning toolbox implemented in R. The results obtained indicated the tabu search algorithm identified the highest degree between genes (390), Markov blankets (25.64), neighborhood sizes (8.76) and branching factors (4.38). The results showed that the highest number of shared hub genes (e.g., proline dehydrogenase 1 (PRODH), Sam-pointed domain containing Ets transcription factor (SPDEF), monocyte-to-macrophage differentiation associated 2 (MMD2), semaphorin 3E (SEMA3E), solute carrier family 27 member 6 (SLC27A6) and actin gamma 2 (ACTG2)) was seen between the hybrid and the constraint-based algorithms, and these genes could be recommended as central to the GSE33030 data series. Functional annotation of the hub genes in uterine tissue during progesterone treatment in the pregnancy period showed that the predicted hub genes were involved in extracellular pathways, lipid and protein metabolism, protein structure and post-translational processes. The identified hub genes obtained by the score-based algorithms had a role in 2-arachidonoylglycerol and enzyme modulation. In conclusion, different algorithms and subsequent topological parameters were used to identify hub genes to better illuminate pathways acting in response to progesterone treatment in the bovine uterus, which should help with our understanding of gene regulatory networks in complex trait expression.

Dataset Information

Bayesian constraint relaxation.

Publications

Bayesian constraint relaxation.

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