Exact Bayesian designs for count time series

Abstract

Exact D-optimal Bayesian designs for time series experiments are discussed in this article. This work is motivated by an RNA sequencing experiment and two disease surveillance studies, where the response is count type and has a correlated structure over time points. The conditional distribution of the count responses given a weakly stationary latent process is assumed to follow a log-linear model. The latent process allows for both overdispersion and autocorrelation in the responses. Linear predictor with the trend and seasonal components are studied. An estimating approach based on only the first two moments of the responses is used for parameter estimation. The D-optimality criterion based on minimization of the log determinant of the variance–covariance matrix of the parameter estimates is used for choosing the exact designs. To address the dependency of the design selection criterion on the unknown parameter values, prior distributions are assumed on the parameters. From the numerical results, it is noted that for linear predictors with only trend component, the optimal design is very close to the equispaced design for high correlation values. However, when the linear predictor has both the trend and seasonal components, the two designs are similar for smaller correlations.