Conditional Autoregressive (CAR) Model

Abstract

Conditional autoregressive (CAR) models are useful to obtain a multivariate joint distributions of a random vector based on univariate conditional specifications. These conditional specifications are based on Markovian properties such that the conditional distribution of a component of the random vector depends only on a set of neighbors. Conditional autoregressive models are particular cases of Markov random fields. CAR models have been applied in different areas of science; some examples are image analysis, epidemiology, and agriculture. Typically, Gaussian CAR specifications are used as latent structures in hierarchical models for areal level data. In this case, the region of interest is divided into a set of disjoint areas and a CAR random effect is used to account for possible correlation among observations made across the different areas.

D-Optimal Design for Network A/B Testing

“…In this paper, we focus on the construction of A/B testing experimental designs for network-correlated outcomes when users who are connected in a network share some common social and demographic backgrounds. We propose a spatial network model for A/B testing, called conditional auto-regressive model or CAR (Schmidt and Nobre, 2014) to incorporate the correlated network structure in the analysis. To accurately estimate the treatment effect, we use the D-optimal criterion (Sitter and Torsney, 1995), which seeks to maximize the determinant of the information matrix of the linear regression model of the response with respect to the treatment effects and other potential variables.…”