Training samples in objective Bayesian model selection

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal training samples. When data can vary widely in terms of either information content or impact on the improper priors, use of minimal training samples can be inadequate. Important examples include certain cases of discrete data, the presence of censored observations, and certain situations involving linear models and explanatory variables. Such situations require more sophisticated methods of choosing training samples. A variety of such methods are developed in this paper, and successfully applied in challenging situations

The matrix-F prior for estimating and testing covariance matrices

The matrix-F distribution is presented as prior for covariance matrices as an alternative to the conjugate inverted Wishart distribution. A special case of the univariate F distribution for a variance parameter is equivalent to a half-t distribution for a standard deviation, which is becoming increasingly popular in the Bayesian literature. The matrix-F distribution can be conveniently modeled as a Wishart mixture of Wishart or inverse Wishart distributions, which allows straightforward implementation in a Gibbs sampler. By mixing the covariance matrix of a multivariate normal distribution with a matrix-F distribution, a multivariate horseshoe type prior is obtained which is useful for modeling sparse signals. Furthermore, it is shown that the intrinsic prior for testing covariance matrices in non-hierarchical models has a matrix-F distribution. This intrinsic prior is also useful for testing inequality constrained hypotheses on variances. Finally through simulation it is shown that the matrix-variate F distribution has good frequentist properties as prior for the random effects covariance matrix in generalized linear mixed models

Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection

Gaussian graphical models are commonly used to characterize conditional (in)dependence structures (i.e., partial correlation networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various subpopulations. The focus is primarily to detect differences or demonstrate replicability. We introduce two novel Bayesian methods for comparing networks that explicitly address these aims. The first is based on the posterior predictive distribution, with a symmetric version of Kullback-Leibler divergence as the discrepancy measure, that tests differences between two (or more) multivariate normal distributions. The second approach makes use of Bayesian model comparison, with the Bayes factor, and allows for gaining evidence for invariant network structures. This overcomes limitations of current approaches in the literature that use classical hypothesis testing, where it is only possible to determine whether groups are significantly different from each other. With simulation we show the posterior predictive method is approximately calibrated under the null hypothesis (alpha = .05) and has more power to detect differences than alternative approaches. We then examine the necessary sample sizes for detecting invariant network structures with Bayesian hypothesis testing, in addition to how this is influenced by the choice of prior distribution. The methods are applied to posttraumatic stress disorder symptoms that were measured in 4 groups. We end by summarizing our major contribution, that is proposing 2 novel methods for comparing Gaussian graphical models (GGMs), which extends beyond the social-behavioral sciences. The methods have been implemented in the R package BGGM. Translational Abstract Gaussian graphical models are becoming popular in the social-behavioral sciences. Recently attention has shifted from estimating single networks to those from various subpopulations (e.g., males vs. females). We introduce Bayesian methodology for comparing networks estimated from any number of groups. The first approach is based on the posterior predictive distribution and it allows for determining whether networks are different from one another. This is ideal for testing the null hypothesis of group equality, say, in the context of testing for network replicability (or lack thereof). The second approach is based on Bayesian hypothesis testing and it allows for gaining evidence for network invariances or equality of partial correlations for any number of groups. This is ideal for focusing on specific aspects of the network such as individual partial correlations. In a series of simulations and illustrative examples we demonstrate the utility of the proposed methodology for comparing Gaussian graphical models. The methods have been implemented in the R package BGGM

Prior-based Bayesian information criterion

We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one overall sample size n). We also consider a modification of PBIC which is more favourable to complex models

Walls talk: Microbial biogeography of homes spanning urbanization.

Westernization has propelled changes in urbanization and architecture, altering our exposure to the outdoor environment from that experienced during most of human evolution. These changes might affect the developmental exposure of infants to bacteria, immune development, and human microbiome diversity. Contemporary urban humans spend most of their time indoors, and little is known about the microbes associated with different designs of the built environment and their interaction with the human immune system. This study addresses the associations between architectural design and the microbial biogeography of households across a gradient of urbanization in South America. Urbanization was associated with households' increased isolation from outdoor environments, with additional indoor space isolation by walls. Microbes from house walls and floors segregate by location, and urban indoor walls contain human bacterial markers of space use. Urbanized spaces uniquely increase the content of human-associated microbes-which could increase transmission of potential pathogens-and decrease exposure to the environmental microbes with which humans have coevolved

Incidence, in-hospital case-fatality rates, and management practices in Puerto Ricans hospitalized with acute myocardial infarction

OBJECTIVE: There are extremely limited data on minority populations, especially Hispanics, describing the clinical epidemiology of acute coronary disease. The aim of this study is to examine the incidence rate of acute myocardial infarction (AMI), in-hospital case-fatality rate (CFR), and management practices among residents of greater San Juan (Puerto Rico) who were hospitalized with an initial AMI. METHODS: Our trained study staff reviewed and independently validated the medical records of patients who had been hospitalized with possible AMI at any of the twelve hospitals located in greater San Juan during calendar year 2007. RESULTS: The incidence rate (# per 100,000 population) of 1,415 patients hospitalized with AMI increased with advancing age and were significantly higher for older patients for men (198) than they were for women (134). The average age of the study population was 64 years, and women comprised 45% of the study sample. Evidence-based cardiac therapies, e.g., aspirin, beta blockers, ACE inhibitors/angiotensin receptor blockers, and statins, were used with 60% of the hospitalized patients, and women were less likely than men to have received these therapies (59% vs. 65%) or to have undergone interventional cardiac procedures (47% vs. 59%) (p \u3c 0.05). The in-hospital CFR increased with advancing age and were higher for women (8.6%) than they were for men (6.0%) (p \u3c 0.05). CONCLUSION: Efforts are needed to reduce the magnitude of AMI, enhance the use of evidence-based cardiac therapies, reduce possible gender disparities, and improve the short-term prognoses of Puerto Rican patients hospitalized with an initial AMI

Amerindian Helicobacter pylori Strains Go Extinct, as European Strains Expand Their Host Range

We studied the diversity of bacteria and host in the H. pylori-human model. The human indigenous bacterium H. pylori diverged along with humans, into African, European, Asian and Amerindian groups. Of these, Amerindians have the least genetic diversity. Since niche diversity widens the sets of resources for colonizing species, we predicted that the Amerindian H. pylori strains would be the least diverse. We analyzed the multilocus sequence (7 housekeeping genes) of 131 strains: 19 cultured from Africans, 36 from Spanish, 11 from Koreans, 43 from Amerindians and 22 from South American Mestizos. We found that all strains that had been cultured from Africans were African strains (hpAfrica1), all from Spanish were European (hpEurope) and all from Koreans were hspEAsia but that Amerindians and Mestizos carried mixed strains: hspAmerind and hpEurope strains had been cultured from Amerindians and hpEurope and hpAfrica1 were cultured from Mestizos. The least genetically diverse H. pylori strains were hspAmerind. Strains hpEurope were the most diverse and showed remarkable multilocus sequence mosaicism (indicating recombination). The lower genetic structure in hpEurope strains is consistent with colonization of a diversity of hosts. If diversity is important for the success of H. pylori, then the low diversity of Amerindian strains might be linked to their apparent tendency to disappear. This suggests that Amerindian strains may lack the needed diversity to survive the diversity brought by non-Amerindian hosts

Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection.

Gaussian graphical models are commonly used to characterize conditional (in)dependence structures (i.e., partial correlation networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various subpopulations. The focus is primarily to detect differences or demonstrate replicability. We introduce two novel Bayesian methods for comparing networks that explicitly address these aims. The first is based on the posterior predictive distribution, with a symmetric version of Kullback-Leibler divergence as the discrepancy measure, that tests differences between two (or more) multivariate normal distributions. The second approach makes use of Bayesian model comparison, with the Bayes factor, and allows for gaining evidence for invariant network structures. This overcomes limitations of current approaches in the literature that use classical hypothesis testing, where it is only possible to determine whether groups are significantly different from each other. With simulation we show the posterior predictive method is approximately calibrated under the null hypothesis (α = .05) and has more power to detect differences than alternative approaches. We then examine the necessary sample sizes for detecting invariant network structures with Bayesian hypothesis testing, in addition to how this is influenced by the choice of prior distribution. The methods are applied to posttraumatic stress disorder symptoms that were measured in 4 groups. We end by summarizing our major contribution, that is proposing 2 novel methods for comparing Gaussian graphical models (GGMs), which extends beyond the social-behavioral sciences. The methods have been implemented in the R package BGGM. (PsycInfo Database Record (c) 2020 APA, all rights reserved)

From <i>p</i>-Values to Posterior Probabilities of Null Hypotheses

Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis, in particular the bound −e·p·log(p). This bound is easy to compute and explain; however, it does not behave as a Bayes factor. For example, it does not change with the sample size. This is a very serious defect, particularly for moderate to large sample sizes, which is precisely the situation in which p-values are the most problematic. In this article, we propose adjusting this minimum Bayes factor with the information to approximate an exact Bayes factor, not only when p is a p-value but also when p is a pseudo-p-value. Additionally, we develop a version of the adjustment for linear models using the recent refinement of the Prior-Based BIC