Run a Bayesian functional data model under a GP prior whose parameters employ a DP prior

Description

An internal function to gpdpgrow

Usage

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gpdpbPost(y, ipr, Omega_t, Omega_s, gp_mod, jitter, b_move, gp_shape, gp_rate,
  noise_shape, noise_rate, lower, upper, w_star, w, n_slice_iter, y_index,
  n.iter, n.burn, n.thin, n.tune, M_init, dp_shape, dp_rate, progress)

Arguments

y

An N x T matrix of N observations of T x 1 functions. y may\ have intermittant missing values. They should be input with NA.

ipr

An optional input vector of inclusion probabilities for each observation unit in the case the observed data were acquired through an informative sampling design, so that unbiased inference about the population requires adjustments to the observed sample. Defaults to ipr = rep(1,nrow(y)) indicating an iid sample.

Omega_t

A T x T matrix of squared Eucidean distances for T time points

Omega_s

A list object of length L_s, where each contains the T x T matrix of Euclidean distances associated to each seasonal covariance term.

gp_mod

An L x 1 numeric vector denoting the selected covariance function for each of L terms. gp_mod = 1 is "rq". gp_mod = 2 is "se". gp_mod = 3 is "sn".

jitter

Numeric value added to diagonals of GP covariance matrix to stabilize inversion.

b_move

An indicator in {0,1} denoting whether to sample GP functions, (bb_i) in a T x 1 Gibbs step or through elliptical slice sampling. b_move = 1 samples in a Gibbs step. Defaults to b_move = 1.

gp_shape

The shape parameter of the Gamma base distribution for the kappa_star locations used to sample the DP prior on the P GP covariance parameters, kappa, for each experimental unit.

gp_rate

The rate parameter of the Gamma base distribution for the kappa_star locations used to sample the DP prior on the P GP covariance parameters, kappa, for each experimental unit.

noise_shape

The shape parameter of the Gamma base distribution on tau_e, the model noise precision parameter. Defaults to noise_shape = 3.

noise_rate

The rate parameter of the Gamma base distribution on tau_e, the model noise precision parameter. Defaults to noise_rate = 1.

lower

Minimum in range of support for GP covariance parameters, kappa.

upper

Maximum in range of support for GP covariance parameters, kappa.

w_star

Tuning parameter for number of locations to sample not linked to observations in the auxiliary Gibbs sampler for cluster assignments.

w

Tuning parameter for slice sampling interval width used for GP covariance parameters, kappa.

n_slice_iter

Maximum number of steps to widen slice samplind width for GP covariance parameters, kappa.

y_index

List object where each contains index of time points to use in n progressively coarser distribution for sampling kappa in tempered update steps.

n.iter

The number of MCMC sampling iterations

n.burn

The number of warm-up iterations to discard

n.thin

The interval or step size of post-burn-in samples to return

n.tune

The number of tuning iterations to update the slice sampler width, w.

M_init

Starting value of number of clusters for sampling cluster assignments.

dp_shape

The shape parameter for the Γ prior on the DP concentration parameter. The rate parameter is set of 1.

dp_rate

The rate parameter for the Γ prior on the DP concentration parameter. Default value is 1.

progress

An indicator in {0,1} denoting whether to display a progress bar during model execution. progress = 1 displays a progress bar. Defaults to progress = 1.

Value

res A list object containing MCMC runs for all model parameters.

Note

Intended as an internal function for gpdpgrow

Author(s)

Terrance Savitsky tds151@gmail.com

See Also

gpdpgrow

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