Modeling a sequence of multinomial data with randomly varying probabilities
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We consider a sequence of variables having multinomial distribution with the number of trials corresponding to these variables being large and possibly different. The multinomial probabilities of the categories are assumed to vary randomly depending on batches. The proposed framework is interesting from the perspective of various applications in practice such as predicting the winner of an election, forecasting the market share of different brands etc. In this work, first we derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities, and corresponding suitable transformations. Then, we consider a Bayesian setting to implement our model. We consider hierarchical priors using multivariate normal and inverse Wishart distributions, and establish the posterior consistency. Based on this result and following appropriate Gibbs sampling algorithms, we can infer about aggregate data. The methodology is illustrated in detail with two real life applications, in the contexts of political election and sales forecasting. Additional insights of effectiveness are also derived through a simulation study.
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