A Bayesian Test for Multimodality with Applications to DNA and Economic Data

In several applications the data comes from a non-standard, multimodal distribution. In such cases, standard exploratory data analysis can be misleading since possible multimodality is not taken into account. This paper proposes a Bayesian approach for detecting the number of distinct modes in the data. The proposed method is also suitable to estimate quantiles of the data distribution. A mixture of shifted Poisson distributions and a mixture of normal distributions are proposed to estimate the probability of multimodality in discrete and continuous data, respectively. The method is illustrated with simulation studies and applied to three datasets, namely DNA tandem repeats' data, number of defaulted installments in a financial institution in Spain and cross-country economic growth data. The results are compared with those of the standard frequentist tests.

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