mcmc_mix1: Markov chain Monte Carlo for TZP-power-law mixture

In clement-lee/rackage: Network Analysis of Dependencies of CRAN Packages

Markov chain Monte Carlo for TZP-power-law mixture

Description

mcmc_mix1 returns the posterior samples of the parameters, for fitting the TZP-power-law mixture distribution. The samples are obtained using Markov chain Monte Carlo (MCMC).

Usage

mcmc_mix1(
  x,
  count,
  u_set,
  u,
  alpha1,
  theta1,
  alpha2,
  a_psiu,
  b_psiu,
  a_alpha1,
  b_alpha1,
  a_theta1,
  b_theta1,
  a_alpha2,
  b_alpha2,
  positive,
  iter,
  thin,
  burn,
  freq,
  invt,
  mc3_or_marg,
  x_max
)

Arguments

x	Vector of the unique values (positive integers) of the data
count	Vector of the same length as x that contains the counts of each unique value in the full data, which is essentially rep(x, count)
u_set	Positive integer vector of the values u will be sampled from
u	Positive integer, initial value of the threshold
alpha1	Real number, initial value of the parameter
theta1	Real number in (0, 1], initial value of the parameter
alpha2	Real number greater than 1, initial value of the parameter
a_psiu, b_psiu, a_alpha1, b_alpha1, a_theta1, b_theta1, a_alpha2, b_alpha2	Scalars, real numbers representing the hyperparameters of the prior distributions for the respective parameters. See details for the specification of the priors.
positive	Boolean, is alpha positive (TRUE) or unbounded (FALSE)?
iter	Positive integer representing the length of the MCMC output
thin	Positive integer representing the thinning in the MCMC
burn	Non-negative integer representing the burn-in of the MCMC
freq	Positive integer representing the frequency of the sampled values being printed
invt	Vector of the inverse temperatures for Metropolis-coupled MCMC
mc3_or_marg	Boolean, is invt for parallel tempering / Metropolis-coupled MCMC (TRUE, default) or marginal likelihood via power posterior (FALSE)?
x_max	Scalar, positive integer limit for computing the normalising constant

Details

In the MCMC, a componentwise Metropolis-Hastings algorithm is used. The threshold u is treated as a parameter and therefore sampled. The hyperparameters are used in the following priors: u is such that the implied unique exceedance probability psiu ~ Uniform(a_psi, b_psi); alpha1 ~ Normal(mean = a_alpha1, sd = b_alpha1); theta1 ~ Beta(a_theta1, b_theta1); alpha2 ~ Normal(mean = a_alpha2, sd = b_alpha2)

Value

A list: $pars is a data frame of iter rows of the MCMC samples, $fitted is a data frame of length(x) rows with the fitted values, amongst other quantities related to the MCMC

See Also

mcmc_pol, mcmc_mix2 and mcmc_mix3 for MCMC for the Zipf-polylog, and 2-component and 3-component discrete extreme value mixture distributions, respectively.

clement-lee/rackage documentation built on July 3, 2025, 7:30 p.m.