Organizer: Hedibert Freitas Lopes, Insper, Brasil
Spatio-temporal factor model with non-linear interactions for cluster analysis
In this study, we develop a factor model to explore areal data collected in space and time. The main goal is to incorporate the factor model with non-linear interactions (proposed in 2013) to handle a spatio-temporal random effect in the structure of a logistic regression. The spatial dependence between regions is established through the CAR model specified for each column of the loadings matrix. Temporal dependence is considered to associate the columns of the factor scores matrix. The presence of non-linear interactions is intended to improve cluster detection, since new types of groups can emerge as a combination of main factor effects and the interaction effect. In terms of application, this study is motivated by the analysis of a electrocardiogram data set obtained between 2013 and 2016 in the Telessaude System of the Hospital das Clinicas at the Federal University of Minas Gerais in Brazil.
Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to allow for evolution of the intensity function over discrete time. The novelty of the method lies on the fact that no discretisation error is involved despite the non-tractability of the likelihood function and infinite dimensionality of the problem. The method is based on a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the parameters and latent variables of the model. The models are defined in a general and flexible way but they are amenable to direct sampling from the relevant distributions, due to careful characterisation of its components. The models also allow for the inclusion of regression covariates and/or temporal components to explain the variability of the intensity function. These components may be subject to relevant interaction with space and/or time. Real and simulated examples illustrate the methodology, followed by concluding remarks.
ABC-CDE: Towards Approximate Bayesian Computation with Complex High-Dimensional Data and Limited Simulations
Approximate Bayesian computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some applications. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC-–CDE, help address three nontrivial challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC-CDE procedures that directly estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate.