BayesMultiMode : Bayesian Mode Inference in R

Journal of Statistical Software, vol. 116

Abstract

Multimodal univariate distributions arise in many fields such as astrophysics, bioinformatics, climatology and economics due to the heterogeneity of the underlying populations. Mixture processes are a popular tool for accurate approximation of such distributions and implied mode detection. Using Bayesian univariate mixture models and methods, BayesMultiMode estimates posterior probabilities of the number of modes, their locations and uncertainty, yielding a powerful tool for mode inference. The approach follows Cross, Hoogerheide, Labonne, and Van Dijk (2024) and works in two stages. First, a flexible mixture with an unknown number of components is estimated using a Bayesian Markov chain Monte Carlo (MCMC) method due to Malsiner-Walli, Frühwirth-Schnatter, and Grün (2016). Second, suitable detection algorithms are employed to estimate modes for continuous and discrete probability distributions. Given these mode estimates, posterior probabilities for the number of modes, their locations and uncertainties are constructed. BayesMultiMode supports a range of mixture processes, complementing and extending existing software for mixture modeling. The mode detection algorithms implemented in BayesMultiMode also support MCMC draws for mixture estimation generated with external software. The package uses for illustrative purposes both continuous and discrete empirical distributions from the four listed fields yielding reliable multiple mode detection with substantial posterior probability where frequentist tests fail to reject the null hypothesis of unimodality.

Authors 6

1. Nalan Baştürk

   Maastricht University

   Affiliation as printed

   Maastricht University

2. Jamie L. Cross

   The University of Melbourne

   Affiliation as printed

   Melbourne Business School, University of Melbourne

3. Peter de Knijff Aachen

   Leiden University · Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Centre

4. Lennart F. Hoogerheide

   Vrije Universiteit Amsterdam

   Affiliation as printed

   Vrije Universiteit Amsterdam

5. Paul Labonne

   Bank of England

   Affiliation as printed

   Bank of England

6. Herman K. van Dijk

   Erasmus University Rotterdam

   Affiliation as printed

   Erasmus University Rotterdam