Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based method

In this paper we develop an inverse Bayesian approach to find the value of the unknown model parameter vector that supports the real (or test) data, where the data comprises measurements of a matrix-variate variable. The method is illustrated via the estimation of the unknown Milky Way feature parameter vector, using available test and simulated (training) stellar velocity data matrices. The data is represented as an unknown function of the model parameters, where this high-dimensional function is modelled using a high-dimensional Gaussian Process (GP). The model for this function is trained using available training data and inverted by Bayesian means, to estimate the sought value of the model parameter vector at which the test data is realised. We achieve a closed-form expression for the posterior of the unknown parameter vector and the parameters of the invoked GP, given test and training data. We perform model fitting by comparing the observed data with predictions made at different summaries of the posterior probability of the model parameter vector. As a supplement, we undertake a leave-one-out cross validation of our method

Bayesian nonparametric dynamic state space modeling with circular latent states

<p>State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in comparison. In this article we propose a novel Bayesian nonparametric approach to state space modeling, assuming that both the observational and evolutionary functions are unknown and are varying with time; crucially, we assume that the unknown evolutionary equation describes dynamic evolution of some latent circular random variable. Based on appropriate kernel convolution of the standard Weiner process, we model the time-varying observational and evolutionary functions as suitable Gaussian processes that take both linear and circular variables as arguments. Additionally, for the time-varying evolutionary function, we wrap the Gaussian process thus constructed around the unit circle to form an appropriate circular Gaussian process. We show that our process thus created satisfies desirable properties.</p> <p>For the purpose of inference we develop a Markov-chain Monte Carlo (MCMC)-based methodology combining Gibbs sampling and Metropolis–Hastings algorithms. Applications to a simulated data set, a real wind speed data set, and a real ozone data set demonstrated quite encouraging performances of our model and methodologies.</p

An efficient Bayesian meta-analysis approach for studying cross-phenotype genetic associations

<div><p>Simultaneous analysis of genetic associations with multiple phenotypes may reveal shared genetic susceptibility across traits (pleiotropy). For a locus exhibiting overall pleiotropy, it is important to identify which specific traits underlie this association. We propose a Bayesian meta-analysis approach (termed CPBayes) that uses summary-level data across multiple phenotypes to simultaneously measure the evidence of aggregate-level pleiotropic association and estimate an optimal subset of traits associated with the risk locus. This method uses a unified Bayesian statistical framework based on a spike and slab prior. CPBayes performs a fully Bayesian analysis by employing the Markov Chain Monte Carlo (MCMC) technique Gibbs sampling. It takes into account heterogeneity in the size and direction of the genetic effects across traits. It can be applied to both cohort data and separate studies of multiple traits having overlapping or non-overlapping subjects. Simulations show that CPBayes can produce higher accuracy in the selection of associated traits underlying a pleiotropic signal than the subset-based meta-analysis ASSET. We used CPBayes to undertake a genome-wide pleiotropic association study of 22 traits in the large Kaiser GERA cohort and detected six independent pleiotropic loci associated with at least two phenotypes. This includes a locus at chromosomal region 1q24.2 which exhibits an association simultaneously with the risk of five different diseases: Dermatophytosis, Hemorrhoids, Iron Deficiency, Osteoporosis and Peripheral Vascular Disease. We provide an R-package ‘CPBayes’ implementing the proposed method.</p></div

Simulation study results: Comparison of the accuracy of selection of associated traits by different methods for multiple overlapping case-control studies.

<p>The total number of studies is denoted by <i>K</i> and <i>m</i> denotes the minor allele frequency at the risk SNP. denotes the number of positively associated traits and denotes the number of negatively associated traits. Different type of points present different configurations of the number of associated traits and the number of positively and negatively associated traits.</p

Simulation results: The number of true positives and false positives detected by CPBayes at different significance levels of locFDR.

<p>Simulation results: The number of true positives and false positives detected by CPBayes at different significance levels of locFDR.</p

Forest plot for pleiotropic signal at rs10455872 on chromosome 6 contrasting the selection of traits by CPBayes and ASSET.

<p>Phenotypes selected by either of the two methods are plotted. Blue diamonds present the trait-specific univariate log odds ratio estimate with the corresponding 95% confidence interval. Red diamonds present the posterior mean and 95% credible interval of the trait-specific log odds ratio obtained by CPBayes. The CPBayes locFDR and ASSET p-value (ASTpv) are provided. The association status of a phenotype detected by a method is denoted by null (not associated), positive or negative (associated). The trait-specific univariate association p-values are also provided.</p

Simulation study results: Partial receiver operating characteristic (ROC) curves for CPBayes and ASSET.

<p>Number of true positives detected by CPBayes and ASSET at the expense of committing a given number of false positives are plotted. The number of false positives is varied across a range: 0, 1, …, 500. In each simulation scenario, 50 replications are performed to compute the mean number of true and false positives detected by each method.</p

A circos plot presenting the pairwise trait-trait pleiotropic signals detected by CPBayes in GERA cohort.

<p>A circos plot presenting the pairwise trait-trait pleiotropic signals detected by CPBayes in GERA cohort.</p

Simulation results: The number of true positives and false positives detected by CPBayes and ASSET at different significance levels of FDR.

<p>Simulation results: The number of true positives and false positives detected by CPBayes and ASSET at different significance levels of FDR.</p

Independent pleiotropic SNPs detected by CPBayes which are associated with at least two phenotypes.

<p>Independent pleiotropic SNPs detected by CPBayes which are associated with at least two phenotypes.</p