BayesMultiMode

An R package for detecting multimodality in discrete data using Bayesian techniques. The approach works in two stages. First, a mixture distribution is fitted on the data using a Sparse Finite Mixture (SFM) MCMC algorithm. The number of mixture components does not have to be specified; it is estimated simultaneously with the mixture weights and components through the SFM approach. Second, the resulting MCMC output is used to calculate the number of modes and their locations. Posterior probabilities are retrieved for both of these quantities providing a powerful tool for mode inference. Currently the package supports a flexible mixture of shifted Poisson distributions. The shifted Poisson is a two-parameter generalisation of the Poisson distribution where the mean can diverge from the variance. More distributions (discrete and continuous) are in the pipeline.

Installing BayesMultiMode

# Installing from github :
# install.packages("devtools") # if devtools is not installed 
devtools::install_github("paullabonne/BayesMultiMode")

Loading the package

library(BayesMultiMode)

Generating data

set.seed(1)
p1 = 0.3
p2 = 1-p1
kap1 = 3
kap2 = 0
lam1 = 1
lam2 = 0.5
length_data = 70
simulated_data <- c(rpois(length_data*p1, lam1)+kap1, rpois(length_data*p2, lam2)+kap2)

Choosing either simulated or DNA data

# Select DNA data :
data("d4z4")
y = d4z4

# Or select simulated data :
# y = simulated_data

Setting parameters for SFM MCMC estimation

# Number of MCMC iterations 
M = 5000 

# Proportion of draws to discard as burnin
S = 0.5 

# Maximum number of mixture components 
Jmax = 6

Estimation with SFM MCMC

#Bayesian estimation
sfm_mcmc = sfm_mcmc_spmix(y=y,Jmax=Jmax, M=M)

## 10  % draws finished. Accept. prob of e0 = 9 percent
## 20  % draws finished. Accept. prob of e0 = 8 percent
## 30  % draws finished. Accept. prob of e0 = 8 percent
## 40  % draws finished. Accept. prob of e0 = 9 percent
## 50  % draws finished. Accept. prob of e0 = 9 percent
## 60  % draws finished. Accept. prob of e0 = 9 percent
## 70  % draws finished. Accept. prob of e0 = 9 percent
## 80  % draws finished. Accept. prob of e0 = 9 percent
## 90  % draws finished. Accept. prob of e0 = 9 percent
## 100  % draws finished. Accept. prob of e0 = 9 percent

#Plots of the estimation output
graphs = plots_mcmc(sfm_mcmc,S)
graphs[[3]]

graphs[[4]]

## Warning: Removed 41 rows containing missing values (position_stack).

Post-processing : burn-in and discarding empty components

post_sfmmcmc = post_sfm_mcmc(sfm_mcmc,S)

Mode inference

sfm_mcmc_modes = bayes_mode(post_sfmmcmc$theta_draws_slim,y)
sfm_mcmc_modes$graphs

References

(Basturk, Hoogerheide, and Dijk 2021) (Malsiner-Walli, Fruhwirth-Schnatter, and Grun 2016) (Schaap et al. 2013)