mcmc_mix2 | R Documentation |
mcmc_mix2
returns the posterior samples of the parameters, for fitting the 2-component discrete extreme value mixture distribution. The samples are obtained using Markov chain Monte Carlo (MCMC).
mcmc_mix2(
x,
count,
u_set,
u,
alpha,
theta,
shape,
sigma,
a_psiu,
b_psiu,
a_alpha,
b_alpha,
a_theta,
b_theta,
m_shape,
s_shape,
a_sigma,
b_sigma,
positive,
a_pseudo,
b_pseudo,
pr_power,
iter,
thin,
burn,
freq,
invt
)
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 |
alpha |
Real number greater than 1, initial value of the parameter |
theta |
Real number in (0, 1], initial value of the parameter |
shape |
Real number, initial value of the parameter |
sigma |
Positive real number, initial value of the parameter |
a_psiu, b_psiu, a_alpha, b_alpha, a_theta, b_theta, m_shape, s_shape, a_sigma, b_sigma |
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)? |
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 (below u) |
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; default c(1.0) i.e. no Metropolis-coupling |
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); alpha ~ Normal(mean = a_alpha, sd = b_alpha); theta ~ Beta(a_theta, b_theta); shape ~ Normal(mean = m_shape, sd = s_shape); sigma ~ Gamma(a_sigma, scale = b_sigma). If pr_power = 1.0, the discrete power law (below u) is assumed, and the samples of theta will be all 1.0. If pr_power is in (0.0, 1.0), model selection between the polylog distribution and the discrete power law will be performed within the MCMC.
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
mcmc_pol
and mcmc_mix3
for MCMC for the Zipf-polylog and 3-component discrete extreme value mixture distributions, respectively.
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