mcmc_pol: Markov chain Monte Carlo for Zipf-polylog distribution

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

Markov chain Monte Carlo for Zipf-polylog distribution

Description

mcmc_pol returns the samples from the posterior of alpha and theta, for fitting the Zipf-polylog distribution to the data x. The samples are obtained using Markov chain Monte Carlo (MCMC). In the MCMC, a Metropolis-Hastings algorithm is used.

Usage

mcmc_pol(
  x,
  count,
  alpha,
  theta,
  a_alpha,
  b_alpha,
  a_theta,
  b_theta,
  a_pseudo,
  b_pseudo,
  pr_power,
  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)
alpha	Real number greater than 1, initial value of the parameter
theta	Real number in (0, 1], initial value of the parameter
a_alpha	Real number, mean of the prior normal distribution for alpha
b_alpha	Positive real number, standard deviation of the prior normal distribution for alpha
a_theta	Positive real number, first parameter of the prior beta distribution for theta; ignored if pr_power = 1.0
b_theta	Positive real number, second parameter of the prior beta distribution for theta; ignored if pr_power = 1.0
a_pseudo	Positive real number, first parameter of the pseudoprior beta distribution for theta in model selection; ignored if pr_power = 1.0
b_pseudo	Positive real number, second parameter of the pseudoprior beta distribution for theta in model selection; ignored if pr_power = 1.0
pr_power	Real number in [0, 1], prior probability of the discrete power law
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

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_mix2 and mcmc_mix3 for MCMC for the 2-component and 3-component discrete extreme value mixture distributions, respectively.

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