11am - 11:30am
Speaker: Md Rashedul (Rashed) Hoque
Title: Approximation of the Formal Bayesian Model Comparison using the Extended Conditional Predictive Ordinate Criterion
Abstract: The optimal method for Bayesian model comparison is the formal Bayes factor (BF), according to decision theory. The formal BF is computationally troublesome for more complex models. If predictive distributions under the competing models do not have a closed form, a cross-validation idea, called the conditional predictive ordinate (CPO) criterion, can be used. In the cross-validation sense, this is a “leave-out one” approach. CPO can be calculated directly from the Monte Carlo (MC) outputs, and the resulting Bayesian model comparison is called the pseudo Bayes factor (PBF). We can get closer to the formal Bayesian model comparison by increasing the “leave-out size”, and at “leave-out all” we recover the formal BF. But, the MC error increases with increasing `leave-out size'. In this study, we examine this for linear and logistic regression models.
Our study reveals that the Bayesian model comparison can favor a different model for PBF compared to BF when comparing two close linear models. So, larger “leave-out sizes” are preferred which provide result close to the optimal BF. On the other hand, MC samples based formal Bayesian model comparisons are computed with more MC error for increasing “leave-out sizes”; this is observed by comparing with the available closed form results. Still, considering a reasonable error, we can use “leave-out size” more than one instead of fixing it at one. These findings can be extended to logistic models where closed form solution is unavailable.
11:30am - 12:00pm
Speaker: Derek Cho
Title: Prediction of Indian reserve populations in Canada using administrative data sources
Abstract: Statistics Canada has recently been interested in using administrative data to construct models for predictive purposes. One such application is to use data from the Indian Register to predict populations of Indian reserves where Census collection is not possible for the 2016 Census of Population. Using a naïve robust mixed effects model, we can predict the populations of non-enumerated Indian reserves. In addition, I will also go over some of my other work at Statistics Canada last summer including work done with the Immigration Database and Census coding.