Date & Time: Wednesday, July 21 at 12:00PM (Noon) EST
Prior distributions for covariance matrices are a well-studied topic in Bayesian modeling. The most popular priors, such as inverse Wishart, require a completely unrestricted covariance matrix, which is not satisfied in some structural equation models. In these models, the covariance matrices are “structured”: certain covariances in the matrix are fixed to 0 or constrained to be equal. While some prior distributions exist for this situation, the parameterizations are relatively complicated, making it difficult for researchers to meaningfully specify their priors. For example, previous approaches include transforming the covariance matrix to spherical coordinates or placing prior distributions on partial correlations.
In this project, we explore the “naive” way of placing priors on structured covariance matrices. These involve prior distributions for standard deviations separately from correlations, with a univariate distribution placed on each parameter. While these priors provide interpretable parameterizations and allow for varying degrees of informativeness, they are deceiving because they allow for covariance matrices that are not positive definite. This means that if we only consider positive definite covariance matrices under these priors, the priors are more informative than we might naively expect. We discuss a method for generating only positive definite covariance matrices from these naive prior distributions, study the amount of information actually implied by the priors, and provide results on the resulting MCMC algorithms’ calibration. We seek to answer the question, “what exactly do you get when placing naive priors on covariance matrices?”
About the Speaker
Oludare Ariyo is a lecturer at the department of the Statistics Federal University of Agriculture, Abeokuta (FUNAAB) Nigeria and a postdoctoral Postdoctoral Researcher at University of Missouri-Columbia. He received his PhD (Biostatistics) at the KU Leuven Belgium on Bayesian model selection for longitudinal random-effects models. He has gained expertise in various statistical topics with research interests, including Bayesian methods, longitudinal analysis, statistical modelling, missing data/ survival analysis, and Mixed models / random-effects models / multilevel models. His research has led to several papers in highly qualified international Journals.
Before his appointment in FUNAAB, Dr Ariyo has worked as a Data Analyst at the Crop-Utilization Units, IITA, Ibadan, Nigeria and as a Senior statistician at National Horticultural Research Institutes (NIHORT), Ibadan. For over six years of working with these research institutes, Dr Ariyo had gain experience in applying Statistical methodology to real-life problems, especially in Agriculture. During his four and half years of stay at the Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Leuven, Belgium, Dr Ariyo further gained clinical trials experience and applied statistical methodology in Medical studies.
Dr Ariyo is an experienced R user with two R functions (https://github.com/OludareAriyo/Bayesselect and https://github.com/OludareAriyo/BayesselectGLMM) and currently working on an R package. Besides, he has an excellent working knowledge of the following software: SAS, JAGS, STAN, SPSS, Epi Info, etc.
He is a member of many professional bodies, has presented papers in international conferences across continents, and has received several grants. He currently the coordinator of FUNAAB-LISA (FUNAAB-Laboratory for Interdisciplinary Statistical Analysis) and an advisor to Overleaf ( a collaborative cloud-based LaTeX editor used for writing, editing and publishing scientific documents.)