An official website of the United States government
Abstract We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.
more »
« less
Bayes Factors for Mixed Models: a Discussion
Abstract van Doorn et al. (2021) outlined various questions that arise when conducting Bayesian model comparison for mixed effects models. Seven response articles offered their own perspective on the preferred setup for mixed model comparison, on the most appropriate specification of prior distributions, and on the desirability of default recommendations. This article presents a round-table discussion that aims to clarify outstanding issues, explore common ground, and outline practical considerations for any researcher wishing to conduct a Bayesian mixed effects model comparison.
more »
« less
- Award ID(s):
- 2145308
- PAR ID:
- 10397380
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Computational Brain & Behavior
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2522-0861
- Page Range / eLocation ID:
- p. 140-158
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We propose a new classified mixed model prediction (CMMP) procedure, called pseudo-Bayesian CMMP,that uses network information in matching the group index between the training data and new data, whosecharacteristics of interest one wishes to predict. The current CMMP procedures do not incorporate suchinformation; as a result, the methods are not consistent in terms of matching the group index. Although, asthe number of training data groups increases, the current CMMP method can predict the mixed effects ofinterest consistently, its accuracy is not guaranteed when the number of groups is moderate, as is the case inmany potential applications. The proposed pseudo-Bayesian CMMP procedure assumes a flexible workingprobability model for the group index of the new observation to match the index of a training data group,which may be viewed as a pseudo prior. We show that, given any working model satisfying mild conditions,the pseudo-Bayesian CMMP procedure is consistent and asymptotically optimal both in terms of matchingthe group index and in terms of predicting the mixed effect of interest associated with the new observations.The theoretical results are fully supported by results of empirical studies, including Monte-Carlo simulationsand real-data validation.more » « less
-
Abstract BackgroundGenome-wide association studies (GWAS) seek to identify single nucleotide polymorphisms (SNPs) that cause observed phenotypes. However, with highly correlated SNPs, correlated observations, and the number of SNPs being two orders of magnitude larger than the number of observations, GWAS procedures often suffer from high false positive rates. ResultsWe propose BGWAS, a novel Bayesian variable selection method based on nonlocal priors for linear mixed models specifically tailored for genome-wide association studies. Our proposed method BGWAS uses a novel nonlocal prior for linear mixed models (LMMs). BGWAS has two steps: screening and model selection. The screening step scans through all the SNPs fitting one LMM for each SNP and then uses Bayesian false discovery control to select a set of candidate SNPs. After that, a model selection step searches through the space of LMMs that may have any number of SNPs from the candidate set. A simulation study shows that, when compared to popular GWAS procedures, BGWAS greatly reduces false positives while maintaining the same ability to detect true positive SNPs. We show the utility and flexibility of BGWAS with two case studies: a case study on salt stress in plants, and a case study on alcohol use disorder. ConclusionsBGWAS maintains and in some cases increases the recall of true SNPs while drastically lowering the number of false positives compared to popular SMA procedures.more » « less
-
Abstract Simultaneous molecular dating of population and species divergences is essential in many biological investigations, including phylogeography, phylodynamics and species delimitation studies. In these investigations, multiple sequence alignments consist of both intra‐ and interspecies samples (mixed samples). As a result, the phylogenetic trees contain interspecies, interpopulation and within‐population divergences. Bayesian relaxed clock methods are often employed in these analyses, but they assume the same tree prior for both inter‐ and intraspecies branching processes and require specification of a clock model for branch rates (independent vs. autocorrelated rates models). We evaluated the impact of a single tree prior on Bayesian divergence time estimates by analysing computer‐simulated data sets. We also examined the effect of the assumption of independence of evolutionary rate variation among branches when the branch rates are autocorrelated. Bayesian approach with coalescent tree priors generally produced excellent molecular dates and highest posterior densities with high coverage probabilities. We also evaluated the performance of a non‐Bayesian method, RelTime, which does not require the specification of a tree prior or a clock model. RelTime's performance was similar to that of the Bayesian approach, suggesting that it is also suitable to analyse data sets containing both populations and species variation when its computational efficiency is needed.more » « less
-
Abstract The 1 January 2024, moment magnitude 7.5 Noto Peninsula earthquake ruptured in complex ways, challenging analysis of its tsunami generation. We present tsunami models informed by a 6‐subevent centroid moment tensor (CMT) model obtained through Bayesian inversion of teleseismic and strong motion data. We identify two distinct bilateral rupture episodes. Initial, onshore rupture toward the southwest is followed by delayed re‐nucleation at the hypocenter, likely aided by fault weakening, causing significant seafloor uplift to the northeast. We construct a complex multi‐fault uplift model, validated against geodetic observations, that aligns with known fault system geometries and is critical in modeling the observed tsunami. The simulations can explain tsunami wave amplitude, timing, and polarity of the leading wave, which are crucial for tsunami early warning. Upon comparison with alternative source models and analysis of 2000 multi‐CMT ensemble solutions, we highlight the importance of incorporating complex source effects for realistic tsunami simulations.more » « less
