Performs Bayesian probability mass function estimation under nonparametric mixture of rounded of Gaussian kernels.
rmg(ydis, k=length(ydis), nrep, nb, alpha=1, theta=alpha, sigma=0,
mixing_hyperprior= FALSE, basemeasure_hyperprior = FALSE, mixing_type="DP", algo="slice",
mu0=mean(ydis), kap=var(ydis),
atau=1, btau=2, a_a=1, b_a=1, lb=NULL, ub=NULL, print = 1, ndisplay = nrep/4,
plot.it = FALSE, pdfwrite = FALSE, ...)dpmrg(ydis, k, nrep, nb, alpha, alpha_r = FALSE, mu0 = mean(ydis), kap = var(ydis),
atau, btau, a_a = 1, b_a = 1, lb = NULL, ub = NULL,
print = 1, ndisplay = nrep/4,
plot.it = FALSE, pdfwrite = FALSE, ...)
Name of the model
Name of the mixing prior
Quantities about MCMC sampling
MCMC chains of the parameters
A list containing several quantities related to the probability mass function (emprical pmf, posterior mean pmf and pointwise 95% credible intervals) computed for the values from lb to ub
A list containing the posterior mean of the cluster specific parameters (be careful of label-switching problems)
A list containing posterior quantities related to the clustering structure of the data
Vector of count data
Truncation level for the number of cluster in the mixture. Default is length(ydis).
Number of MCMC iterations
Number of burn-in iteration in the MCMC to discard
Value of the precision parameter of the Dirichlet process prior
Value of the strength parameter of the Two-parameters-Poisson-Dirichlet process prior
Value of the discount parameter of the Two-parameters-Poisson-Dirichlet process prior
Logical. If TRUE alpha is random with gamma hyperprior
Logical. If TRUE alpha is random with gamma hyperprior
Logical. If TRUE also the parameters of the base measure are random, see details below.
Type of mixing distribution. Default is "DP" for Dirichlet process but also "2PD" for Two-parameters-Poisson-Dirichlet process is allowed.
Type of algorithm. Current choices are: slice sampler (algo="slice") or polya-urn-type sampler (algo="polya-urn").
Location hyperparameter for the latent rounded Gaussian base measure
Precision hyperparameter for the latent rounded Gaussian base measure
Shape hyperparameter for the Gamma distribution
Scale hyperparameter for the Gamma distribution
Shape hyperparameter for the Gamma distribution for alpha
Scale hyperparameter for the Gamma distribution for alpha
Scalar integer. Lower bound for the argument of the pmf. Default is max(0,min(ydis)-10).
Scalar integer. Upper bound for the argument of the pmf. Default is max(ydis)+10.
Vector of integers (from 1 to 6) indicating whether to print each step of the Gibbs sampler. Specifically, 1 for current iteration, 2 for the data augmentation step simulating the latent continuous variables, 3 for the DP cluster allocation, 4 for the posterior parameters of the mixture components, 5 for the precision of the DP, 6 for the posterior pmf.
Scalar integer. It gives the number of iterations to be displayed on screen (the function reports on the screen when every ndisplay iterations have been carried out)
Logical, default FALSE. If TRUE a plot with empirical and estimated posterior probability mass functions is plotted.
Logical, default FALSE. If TRUE a pdf file is written in the current working directory. Traceplots and other posterior quantities are drown.
Additional arguments (for future implemetantions).
R code and porting by A. Canale, C code by A. Canale with minor contributions by N. Lunardon.
The rmg function performs Bayesian probability mass function estimation under the mixture model of Canale and Dunson (2011) with Dirichlet process or Two-parameters-Poisson-Dirichlet process as prior for the mixing measure. The model is
$$y_i \mid \mu_i, \tau_i \sim \mbox{RG}(\mu_i, \tau_i), i=1, \dots, n$$
$$(\mu_i, \tau_i) \mid G \sim G$$
$$G \sim \Pi(P_0),$$
where \(\Pi\) is the Dirichlet process or the Two-parameters-Poisson-Dirichlet process with base measure \(P_0\) and \(RG(\mu, \tau)\) is a rounded Gaussian kernel with location \(\mu\) and precision \(\tau\) and tresholds \(-\infty, 1, 2, \dots\).
The function dpmrg is a wrapper to rmg with mixing_type="DP" for back portability with version 1.0 of the package.
The main part of the code is written in C language to gain computational speed. Plots and posterior summaries are in plain R code. From version 2.0 on, the blocked gibbs sampler has been removed in place of slice samper (Kalli et al., 2011) and polya-urn sampler.
Canale, A. and Dunson, D. B. (2011), "Bayesian Kernel Mixtures for Counts", Journal of American Statistical Association, 106, 1528-1539.
Kalli, M., Griffin, J., and Walker, S. (2011), "Slice sampling mixture models," Statistics and Computing, 21, 93-105.
dpmpoiss
# \donttest{
data(ethylene)
y <- tapply(ethylene$impl,FUN=mean,INDEX=ethylene$id)
z <- tapply(ethylene$dose,FUN=mean,INDEX=ethylene$id)
# Estimate the pmf of the number of implants in the control group
y0 <- y[z==0]
pmf.control = rmg(y0, k=20, nrep=11000, nb=1000, alpha=1, atau=1, btau=1,
lb=5, ub=24, plot.it= TRUE)
# }
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