bayes_mixture {BayesMultiMode}

Creating a S3 object of class bayes_mixture

Description

Creates an object of class bayes_mixture which can subsequently be used as argument in bayes_mode(). This function is useful for users who want to use the mode inference capabilities of BayesMultiMode with mixture estimated using external software.

Usage

bayes_mixture(
  mcmc,
  data,
  burnin = 0,
  dist = NA_character_,
  pdf_func = NULL,
  dist_type = NA_character_,
  loglik = NULL,
  vars_to_keep = NA_character_,
  vars_to_rename = NA_character_,
  loc = NA_character_
)

Arguments

mcmc

A matrix of MCMC draws with one column per variable, e.g. eta1, eta2, ..., mu1, mu2, etc...

data

Vector of observation used for estimating the model.

burnin

Number of draws to discard as burnin; default is 0.

dist

Distribution family of the mixture components supported by the package (i.e. "normal", "student", "skew_normal" or "shifted_poisson"). If left unspecified, pdf_func is required.

pdf_func

(function) Pdf or pmf of the mixture components; this input is used only if dist is left unspecified. pdf_func should have two arguments : (i) the observation where the pdf is evaluated; (ii) a named vector representing the function parameters. For instance a normal pdf would take the form: pdf_func <- function(x, pars) dnorm(x, pars['mu'], pars['sigma']). The names of pars should correspond to variables in mcmc, e.g. "mu1", "mu2" etc...

dist_type

Either "continuous" or "discrete".

loglik

Vector showing the log likelihood at each MCMC draw.

vars_to_keep

(optional) Character vector containing the names of the variables to keep in mcmc, e.g. c("eta", "mu", "sigma").

vars_to_rename

(optional) Use for renaming variables/parameters in mcmc. A named character vector where the names are the new variable names and the elements the variables in mcmc, e.g. c("new_name" = "old_name").

loc

(for continuous mixtures other than Normal mixtures) String indicating the location parameter of the distribution; the latter is used to initialise the MEM algorithm.

Value

A list of class bayes_mixture containing:

data

Same as argument.

mcmc

Matrix of MCMC draws where the rows corresponding to burnin have been discarded;

mcmc_all

Matrix of MCMC draws.

loglik

Log likelihood at each MCMC draw.

K

Number of components.

dist

Same as argument.

pdf_func

The pdf/pmf of the mixture components.

dist_type

Type of the distribution, i.e. continuous or discrete.

pars_names

Names of the mixture components' parameters.

loc

Name of the location parameter of the mixture components.

nb_var

Number of parameters in the mixture distribution.

Examples

# Example with a Student t ================================================

# Constructing synthetic mcmc output
mu = c(0.5,6)
mu_mat = matrix(rep(mu, 100) + rnorm(200, 0, 0.1),
            ncol = 2, byrow = TRUE)

omega = c(1,2)
sigma_mat = matrix(rep(omega, 100) + rnorm(200, 0, 0.1),
            ncol = 2, byrow = TRUE)

nu = c(5,5)
nu_mat = matrix(rep(nu, 100) + rnorm(200, 0, 0.1),
            ncol = 2, byrow = TRUE)

eta = c(0.8,0.2)
eta_mat = matrix(rep(eta[1], 100) + rnorm(100, 0, 0.05),
            ncol = 1)
eta_mat = cbind(eta_mat,1-eta_mat)

xi_mat = matrix(0,100,2)

fit = cbind(eta_mat, mu_mat, sigma_mat, nu_mat, xi_mat)
colnames(fit) = c("eta1", "eta2", "mu1", "mu2",
                  "omega1", "omega2", "nu1", "nu2", "xi1", "xi2")
                  
# sampling observations
data = c(sn::rst(eta[1]*1000, mu[1], omega[1], nu = nu[1]),
        sn::rst(eta[2]*1000, mu[2], omega[2], nu = nu[2]))
        
pdf_func = function(x, pars) {
  sn::dst(x, pars["mu"], pars["sigma"], pars["xi"], pars["nu"])
}

dist_type = "continuous"

BM = bayes_mixture(fit, data, burnin = 50,
pdf_func = pdf_func, dist_type = dist_type,
vars_to_rename = c("sigma" = "omega"), loc = "xi")
# plot(BM)