Empirical analysis of Bayesian kernel methods for modeling count data

Abstract

Bayesian models are used for estimation and forecasting in a wide range of application areas. One extension of such methods is the Bayesian kernel model, which integrate the Bayesian conjugate prior with kernel functions. This paper empirically analyzes the performance of Bayesian kernel models when applied to count data. The analysis is performed with several data sets with different characteristics regarding the numbers of observations and predictors. While the size of the data and number of predictors is changing across data sets, the predictors are all continuous in this study. The Poisson Bayesian kernel model is applied to each data set and compared to the Poisson generalized linear model. The measures of goodness of fit used are the deviance and the log-likelihood functional value, and the computation is done by dividing the data into training and testing sets, for the Bayesian kernel model, a tuning set is used to optimize the parameters of the kernel function. The Bayesian kernel approach tends to outperform classical count data models for smaller data sets with a small number of predictors. The analysis conducted in this paper is an initial step towards the validation of the Poisson Bayesian kernel model. This type of model can be useful in risk analysis applications in which data sources are scarce and can help in analytical and data-driven decision making.