BayesMultiMode is an R package for detecting and exploring
multimodality using Bayesian techniques. The approach works in two
stages. First, a mixture distribution is fitted on the data using a
sparse finite mixture Markov chain Monte Carlo (SFM MCMC) algorithm. The
number of mixture components does not have to be known; the size of the
mixture is estimated endogenously through the SFM approach. Second, the
modes of the estimated mixture in each MCMC draw are retrieved using
algorithms specifically tailored for mode detection. These estimates are
then used to construct posterior probabilities for the number of modes,
their locations and uncertainties, providing a powerful tool for mode
inference. See Basturk et al. (2023) and Cross et al. (2024) for more
details.
install.packages("BayesMultiMode")# install.packages("devtools") # if devtools is not installed
devtools::install_github("paullabonne/BayesMultiMode")library(BayesMultiMode)BayesMultiMode provides a very flexible and efficient MCMC estimation
approach : it handles mixtures with unknown number of components through
the sparse finite mixture approach of Malsiner-Walli,
Fruhwirth-Schnatter, and Grun (2016) and supports a comprehensive range
of mixture distributions, both continuous and discrete.
set.seed(123)
# retrieve galaxy data
y = galaxy
# estimation
bayesmix = bayes_fit(data = y,
K = 10,
dist = "normal",
nb_iter = 2000,
burnin = 1000,
print = F)
plot(bayesmix, draws = 200)
# mode estimation
bayesmode = bayes_mode(bayesmix)
plot(bayesmode)
summary(bayesmode)## Posterior probability of multimodality is 0.993
##
## Inference results on the number of modes:
## p_nb_modes (matrix, dim 4x2):
## number of modes posterior probability
## [1,] 1 0.007
## [2,] 2 0.133
## [3,] 3 0.840
## [4,] 4 0.020
##
## Inference results on mode locations:
## p_loc (matrix, dim 252x2):
## mode location posterior probability
## [1,] 9.2 0.021
## [2,] 9.3 0.000
## [3,] 9.4 0.000
## [4,] 9.5 0.083
## [5,] 9.6 0.132
## [6,] 9.7 0.117
## ... (246 more rows)
BayesMultiMode also works on MCMC output generated using external
software. The function bayes_mixture() creates an object of class
bayes_mixture which can then be used as input in the mode inference
function bayes_mode(). Here is an example using cyclone intensity data
(Knapp et al. 2018) and the BNPmix package for estimation. More
examples can be found
here.
library(BNPmix)
library(dplyr)
y = cyclone %>%
filter(BASIN == "SI",
SEASON > "1981") %>%
dplyr::select(max_wind) %>%
unlist()
## estimation
PY_result = PYdensity(y,
mcmc = list(niter = 2000,
nburn = 1000,
print_message = FALSE),
output = list(out_param = TRUE))mcmc_py = list()
for (i in 1:length(PY_result$p)) {
k = length(PY_result$p[[i]][, 1])
draw = c(PY_result$p[[i]][, 1],
PY_result$mean[[i]][, 1],
sqrt(PY_result$sigma2[[i]][, 1]),
i)
names(draw)[1:k] = paste0("eta", 1:k)
names(draw)[(k+1):(2*k)] = paste0("mu", 1:k)
names(draw)[(2*k+1):(3*k)] = paste0("sigma", 1:k)
names(draw)[3*k + 1] = "draw"
mcmc_py[[i]] = draw
}
mcmc_py = as.matrix(bind_rows(mcmc_py))py_BayesMix = bayes_mixture(mcmc = mcmc_py,
data = y,
burnin = 0, # the burnin has already been discarded
dist = "normal",
vars_to_keep = c("eta", "mu", "sigma"))plot(py_BayesMix)
# mode estimation
bayesmode = bayes_mode(py_BayesMix)
# plot
plot(bayesmode)
# Summary
summary(bayesmode)## Posterior probability of multimodality is 1
##
## Inference results on the number of modes:
## p_nb_modes (matrix, dim 2x2):
## number of modes posterior probability
## [1,] 2 0.897
## [2,] 3 0.103
##
## Inference results on mode locations:
## p_loc (matrix, dim 793x2):
## mode location posterior probability
## [1,] 40.2 0.001
## [2,] 40.3 0.000
## [3,] 40.4 0.000
## [4,] 40.5 0.001
## [5,] 40.6 0.000
## [6,] 40.7 0.000
## ... (787 more rows)
It is possible to use BayesMultiMode to find modes in mixtures
estimated using maximum likelihood and the EM algorithm. Below is an
example using the popular package mclust. More examples can be found
here.
set.seed(123)
library(mclust)
y = cyclone %>%
filter(BASIN == "SI",
SEASON > "1981") %>%
dplyr::select(max_wind) %>%
unlist()
fit = Mclust(y)
pars = c(eta = fit$parameters$pro,
mu = fit$parameters$mean,
sigma = sqrt(fit$parameters$variance$sigmasq))
mix = mixture(pars, dist = "normal", range = c(min(y), max(y))) # create new object of class Mixture
modes = mix_mode(mix) # estimate modes
plot(modes)
summary(modes)## Modes of a normal mixture with 3 components.
## - Number of modes found: 3
## - Mode estimation technique: fixed-point algorithm
## - Estimates of mode locations:
## mode_estimates (numeric vector, dim 3):
## [1] 41 60 110
Basturk, Nalan, Jamie L. Cross, Peter de Knijff, Lennart Hoogerheide, Paul Labonne, and Herman K. van Dijk. 2023. “BayesMultiMode: Bayesian Mode Inference in r.” Tinbergen Institute Discussion Paper TI 2023-041/III.
Cross, Jamie L., Lennart Hoogerheide, Paul Labonne, and Herman K. van Dijk. 2024. “Bayesian Mode Inference for Discrete Distributions in Economics and Finance.” Economics Letters 235 (February): 111579. https://doi.org/10.1016/j.econlet.2024.111579.
Knapp, Kenneth R., Howard J. Diamond, Kossin J. P., Michael C. Kruk, and C. J. Schreck. 2018. “International Best Track Archive for Climate Stewardship (IBTrACS) Project, Version 4.” NOAA National Centers for Environmental Information. https://doi.org/10.1175/2009BAMS2755.1.
Malsiner-Walli, Gertraud, Sylvia Fruhwirth-Schnatter, and Bettina Grun. 2016. “Model-Based Clustering Based on Sparse Finite Gaussian Mixtures.” Statistics and Computing 26 (1): 303–24. https://doi.org/10.1007/s11222-014-9500-2.