Flexible negative binomial mixtures for credible mode inference in heterogeneous count data from finance, economics and bioinformatics

In several scientific fields, such as finance, economics and bioinformatics, important theoretical and practical issues exist involving multimodal and asymmetric count data distributions due to heterogeneity of the underlying population. For accurate approximation of such distributions we introduce a novel class of flexible mixtures consisting of shifted negative binomial distributions, which accommodates a wide range of shapes that are commonly seen in these data. We further introduce a convenient reparameterization which is more closely related to a moment interpretation and facilitates the specification of prior information and the Monte Carlo simulation of the posterior. This mixture process is estimated by the sparse finite mixture Markov chain Monte method since it can handle a flexible number of nonempty components. Given loan payment, inflation expectation and DNA count data, we find coherent evidence on number and location of modes, fat tails and implied uncertainty measures, in contrast to conflicting evidence obtained from well-known frequentist tests. The proposed methodology may lead to more accurate measures of uncertainty and risk which improves prediction and policy analysis using multimodal and asymmetric count data.