A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.