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제안 방법
- Again, in our study we did not account for common environment related covariates to analyze the reason behind the variations in θt’s but, one can easily incorporate covariates such as economic climate and seasonal variables in the model for further analysis.
- Harvey and Fernandes [9] develop a recursionalgorithm similar to Kalman filter methods to construct the likelihood function. In their study, they assume a Gamma process on the stochastic evolution of the latent mean and extend their model to include explanatory variables as well as handling other count related models such as multinomial and binomial models. Wedel et al.
- In this paper, we address the above problem with a Bayesian Poisson model for multivariate count data using multiplicative rates, meaning that we compose the parameter for overall arrival rates by the product of common effect and individual effect. It is a simple idea but, this type of formulation allows the researcher to specifically analyze two different forms of effects separately and produce a more robust result.
- In this study, we consider the Bayesian multi-variate model for count data with common and individual effects on the arrival rates. We first presented the basic model for Bayesian analysis of univariate count data and showed the extension for the multivariate model and also showed an application of the model using real customer arrival data for a large retail store.
- Of the said dataset, we are interested in multivariate count data, i.e. customer arrivals, and hence we merged customer arrivals by the day of the week, i.e. Monday, Tuesday, …, Sunday, and created 7 different Poisson time series for our Bayesian multivariate count analysis.
- First of all, the differences in individual arrival rates identify the busy days for store operation. The store manager could devise an efficient staff schedule by incorporating the findings from the Bayesian multivariate count data analysis. Furthermore, the store manager may devise some type of promotional strategy to lure customers into the store on days when the individual arrival rates are low.
- It is a simple idea but, this type of formulation allows the researcher to specifically analyze two different forms of effects separately and produce a more robust result. Therefore, the Bayesian multivariate Poisson model presented in this paper contribute to the current literature on multivariate count models, by introducing a simple method for analyzing a complicated problem as well as being able to provide intuitive interpretation of results. We highlight the properties and possible applications of the Bayesian multivariate Poisson model with an example, analyzing real data involving customer arrivals to a retail store.
이론/모형
- Estimation of the parameters is straightforward using the MCMC procedure, where one can take advantage of the forward filtering backward sampling (FFBS) suggested by Fruhwirth-Schnatter [8] with an added Gibbs sampler step for the λi’s.
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