bic_vmf_mix {DirStats}

Fitting mixtures of von Mises–Fisher distributions

Description

Fitting mixtures of von Mises–Fisher distributions by the Expectation-Maximization algorithm, with determination of the optimal number of mixture components.

Usage

bic_vmf_mix(data, M_bound = ceiling(log(nrow(data))), M_neig = 3,
  crit = "BIC", iterative = TRUE, plot_it = FALSE, verbose = FALSE,
  kappa_max = 250)

Arguments

data

directional data, a matrix of size c(n, q + 1).

M_bound

bound for the number of components in the mixtures. If it is not enough, the search for the mixture with minimum crit will continue from M_bound + 1 if iterative = TRUE. Defaults to ceiling(log(nrow(data))).

M_neig

number of neighbors explored around the optimal number of mixture components. Defaults to 3.

crit

information criterion employed, either "BIC" (default), "AICc" or "AIC".

iterative

keep exploring higher number of components if the optimum is attained at M_bound? Defaults to TRUE.

plot_it

display an informative plot on the optimization's grid search? Defaults to FALSE.

verbose

display fitting progress? Defaults to FALSE.

kappa_max

maximum value of allowed concentrations, to avoid numerical instabilities. Defaults to 250.

Details

See Algorithm 3 in García-Portugués (2013). The Expectation-Maximization fit is performed with movMF.

Value

A list with entries:

• best_fit: a list with estimated mixture parameters mu_hat, kappa_hat, and p_hat of the best-fitting mixture according to crit.

• fit_mixs: a list with of the fitted mixtures.

• BICs: a vector with the BICs (or other information criterion) of the fitted mixtures.

References

García-Portugués, E. (2013). Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electronic Journal of Statistics, 7:1655–1685. doi:10.1214/13-ejs821

Hornik, K. and Grün, B. (2014). movMF: An R Package for Fitting Mixtures of von Mises–Fisher Distributions. Journal of Statistical Software, 58(10):1–31. doi:10.18637/jss.v058.i10

Examples

# Sample
q <- 2
n <- 300
set.seed(42)
samp <- rbind(rotasym::r_vMF(n = n / 3, mu = c(rep(0, q), 1), kappa = 5),
              rotasym::r_vMF(n = n / 3, mu = c(rep(0, q), -1), kappa = 5),
              rotasym::r_vMF(n = n / 3, mu = c(1, rep(0, q)), kappa = 5))

# Mixture fit
bic_vmf_mix(data = samp, plot_it = TRUE, verbose = TRUE)