MixPY2 function

Pitman-Yor process mixture of Type II

This function calls the PYdensity function from package BNPmix, to allow fitting a Pitman-Yor process mixture to the data.

MixPY2(
  x,
  probs = c(0.025, 0.5, 0.975),
  Alpha = 1,
  Gama = 0.4,
  asigma = 2,
  bsigma = 1/var(x),
  Nx = 100,
  Nit = 1500,
  Pbi = 0.5,
  epsilon = NULL,
  printtime = TRUE,
  extras = TRUE
)

Arguments

• x: Numeric vector. Data set to which the density is fitted.
• probs: Numeric vector. Desired quantiles of the density estimates.
• Alpha: Numeric constant. Total mass of the centering measure. See
• Gama: Numeric constant. c("$0 <= Gama <=\n$", "$1$"). See details.
• asigma: Numeric positive constant. Shape parameter of the gamma prior on the standard deviation of the mixture kernel. Default value suggested by package BNPmix.
• bsigma: Numeric positive constant. Rate parameter of the gamma prior on the standard deviation of the mixture kernel. Default value suggested by package BNPmix.
• Nx: Integer constant. Number of grid points for the evaluation of the density estimate.
• Nit: Integer constant. Number of MCMC iterations.
• Pbi: Numeric constant. Burn-in period proportion of Nit.
• epsilon: Numeric constant. Extension to the evaluation grid range. See details.
• printtime: Logical. If TRUE, prints out the execution time.
• extras: Logical. If TRUE, gives additional objects: means and weights

Returns

The function returns a MixPY2 object. It is based on a list with the following components: - xx: Numeric vector. Evaluation grid.

• qx: Numeric array. Matrix of dimension c("$Nx x\n$", "$(length(probs)+1)$") with the posterior mean and the desired quantiles input in probs.

• R: Numeric vector of length(Nit*(1-Pbi)) with the number of mixtures components (clusters).

• Allocs: List of length(Nit*(1-Pbi)) with the clustering allocations.

• means: List of length(Nit*(1-Pbi)) with the cluster means (locations). Only if extras = TRUE.

• sigmas: List of length(Nit*(1-Pbi)) with the cluster standard deviations (scales). Only if extras = TRUE.

• weights: List of length(Nit*(1-Pbi)) with the mixture weights. Only if extras = TRUE.

• Nit: Integer constant. Number of MCMC iterations.

• Pbi: Numeric constant. Burn-in period proportion of Nit.

• distr.k: Integer corresponding to the kernel chosen for the mixture. Always 1, since the Pitman-Yor process is only written to work with Gaussian kernels.

• data: Data used for the fit

• PY_params: A named list with the parameters of the Pitman-Yor process

Examples

# Data
data(acidity)
x <- acidity
# Fitting the model under default specifications
out <- MixPY2(x)
# Plotting density estimate + 95% credible interval
plot(out)