  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.
