Package 'rmp' reference manual

Title:	Rounded Mixture Package
Description:	Performs univariate probability mass function estimation via Bayesian nonparametric mixtures of rounded kernels as in Canale and Dunson (2011) <doi:10.1198/jasa.2011.tm10552>.
Authors:	Antonio Canale [aut, cre], Nicola Lunardon [ctb]
Maintainer:	Antonio Canale <[email protected]>
License:	GPL-2
Version:	2.2
Built:	2024-12-08 06:51:20 UTC
Source:	CRAN

Posterior probability mass function estimation with DP prior

Description

Performs Bayesian probability mass function estimation under DP prior with Poisson base measure.

Usage

dp.post.est(x, y, alpha, lambda)
dp.post.est(x, y, alpha, lambda)

Arguments

`x`	Values on which to compute the pmf.
`y`	Vector of observed data.
`alpha`	DP precision parameter
`lambda`	Mean parameter for the Poisson base measure.

Details

Performs probability mass function estimation under th following model

$y_i \mid P \sim P, i=1, \dots, n$

$P \sim DP(\alpha, P_0),$

where $P_0$ is Poisson with mean lambda.

Value

A vector of size length(x) containing the probability masses

Author(s)

Antonio Canale

References

Carota, C., and Parmigiani, G. (2002), “Semiparametric Regression for Count Data,” Biometrika, 89, 265–281.

Examples

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 = dp.post.est(0:30, y0, alpha = 1)
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 = dp.post.est(0:30, y0, alpha = 1)

Developmental toxicity study of ethylene glycol in mice

Description

Data from the developmental toxicity study of ethylene glycol in mice conducted by the National Toxicology Program. Pregnant mice were assigned to dose groups of 0, 750, 1,500 or 3,000 mg/kg per day, with the number of implants measured for each mouse at the end of the experiment. Group sizes are 25, 24, 23 and 23, respectively.

Usage

data(ethylene)data(ethylene)

Format

A data frame with 1192 observations on the following 7 variables.

id: identifyer for pregnant mouse
dose: dose of ethylene glycol
weight: weight of the fetus
sex: sex of the fetus
impl: number of implants in the pregnant mouce
litsz: size of the relative litter
malf: presence of malformation in the fetus

References

Price, C. J., Kimmel, C. A., Tyl, R. W., and Marr, M. C. (1985) "The developemental toxicity of ethylene glycol in rats and mice" Toxicological and Applied Pharmacology 81, 113-127.

Examples

data(ethylene)
implants <- tapply(ethylene$impl, FUN=mean, INDEX=ethylene$id)

summary(implants)
m <- mean(implants)
v <- var(implants)
hist(implants, main=paste("Histogram of the number of implants (Mean = ",
round(m,2), ", Var = ", round(v,2),")"))
data(ethylene)
implants <- tapply(ethylene$impl, FUN=mean, INDEX=ethylene$id)

summary(implants)
m <- mean(implants)
v <- var(implants)
hist(implants, main=paste("Histogram of the number of implants (Mean = ",
round(m,2), ", Var = ", round(v,2),")"))

DP mixtures of Poissons

Description

Performs probability mass function estimation under nonparametric mixture of Poisson kernels.

Usage

npmp(y, k, nrep, nb, alpha=1, theta=alpha, sigma=0, 
mixing_hyperprior= FALSE, basemeasure_hyperprior = FALSE, mixing_type="DP", 
algo="slice",  prior="gamma", a, b, a_a=1, b_a=1, lb=NULL, ub=NULL, 
print = 1, ndisplay = nrep/4, plot.it = FALSE, pdfwrite = FALSE, ... )

dpmpoiss(y, k, nrep, nb, alpha = 1, a, b, lb = NULL, ub = NULL, print = 1,
ndisplay = nrep/4, plot.it = FALSE, pdfwrite = FALSE, ...)
npmp(y, k, nrep, nb, alpha=1, theta=alpha, sigma=0, 
mixing_hyperprior= FALSE, basemeasure_hyperprior = FALSE, mixing_type="DP", 
algo="slice",  prior="gamma", a, b, a_a=1, b_a=1, lb=NULL, ub=NULL, 
print = 1, ndisplay = nrep/4, plot.it = FALSE, pdfwrite = FALSE, ... )

dpmpoiss(y, k, nrep, nb, alpha = 1, a, b, lb = NULL, ub = NULL, print = 1,
ndisplay = nrep/4, plot.it = FALSE, pdfwrite = FALSE, ...)

Arguments

`y`	Vector of count data
`k`	Truncation level for the number of cluster in the mixture. Default is `length(ydis)`.
`nrep`	Number of MCMC iterations
`nb`	Number of burn-in iteration in the MCMC to discard
`alpha`	Value of the precision parameter of the Dirichlet process prior
`theta`	Value of the strength parameter of the Two-parameters-Poisson-Dirichlet process prior
`sigma`	Value of the discount parameter of the Two-parameters-Poisson-Dirichlet process prior
`mixing_hyperprior`	Logical. If TRUE `alpha` is random with gamma hyperprior
`basemeasure_hyperprior`	Logical. If TRUE also the parameters of the base measure are random, see details below.
`mixing_type`	Type of mixing distribution. Default is "DP" for Dirichlet process but also "2PD" for Two-parameters-Poisson-Dirichlet process is allowed.
`algo`	Type of algorithm. Current choices are: slice sampler (`algo="slice"`) or polya-urn-type sampler (`algo="polya-urn"`).
`prior`	String for the base measure prior. Default is "gamma" for lambda ~ Gamma(a,b). The other choice is "normal" for exp(lambda) ~ N(a,b)
`a`	Shape (mean) hyperparameter for the gamma (normal) base measure
`b`	Scale (sd) hyperparameter for the gamma (normal) prior
`a_a`	Shape hyperparameter for `alpha`
`b_a`	Scale hyperparameter for `alpha`
`lb`	Scalar integer. Lower bound for the argument of the pmf. Default is `max(0,min(ydis)-10)`.
`ub`	Scalar integer. Upper bound for the argument of the pmf. Default is `max(ydis)+10`.
`print`	Vector of integers (from 1 to 5) indicating whether to print each step of the Gibbs sampler. Specifically, 1 for current iteration, 2 for the DP cluster allocation, 3 for the posterior parameters of the mixture components, 4 for the precision of the DP, 5 for the posterior pmf.
`ndisplay`	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)
`plot.it`	Logical, default FALSE. If TRUE a plot with empirical and estimated posterior probability mass functions is plotted.
`pdfwrite`	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).

Details

The function npmp performs probability mass function estimation under nonparametric mixture of Poisson kernels, i.e.

$y_i \mid \lambda_i \sim \mbox{Poi}(\lambda_i), i=1, \dots, n$

$\lambda_i \mid G \sim G$

$G \sim \Pi(P_0),$

where $\Pi$ is a nonparametric prior (Dirichlet process or Two-parameters-Poisson-Dirichlet process) with base measure $P_0$ . The function dppoiss is a wrapper to npmp 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. Two different base measures $P_0$ are implemented: prior="gamma" and prior="normal" for

$\lambda_h \sim \mbox{Gamma}(a,b), \log(\lambda_h) \sim N(a,b), h=1,\dots$

respectively.

Value

`name`	Name of the model
`mixing_type`	Name of the mixing prior
`mcmc`	Quantities about MCMC sampling
`mcmc.chains`	MCMC chains of the parameters
`pmf`	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`
`parameters`	A list containing the posterior mean of the cluster specific parameters (be careful of label-switching problems)
`clustering`	A list containing posterior quantities related to the clustering structure of the data

Author(s)

R code and porting by A. Canale, C code by A. Canale with minor contributions by N. Lunardon.

References

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.

Examples


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 = dpmpoiss(y0, k=20, nrep=11000, nb=1000, alpha=1, a=1, b=1,
lb=5, ub=24, plot.it=TRUE)

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 = dpmpoiss(y0, k=20, nrep=11000, nb=1000, alpha=1, a=1, b=1,
lb=5, ub=24, plot.it=TRUE)

Nonparametric mixture of rounded Gaussians

Description

Performs Bayesian probability mass function estimation under nonparametric mixture of rounded of Gaussian kernels.

Usage

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, ...)

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, ...)

Arguments

`ydis`	Vector of count data
`k`	Truncation level for the number of cluster in the mixture. Default is `length(ydis)`.
`nrep`	Number of MCMC iterations
`nb`	Number of burn-in iteration in the MCMC to discard
`alpha`	Value of the precision parameter of the Dirichlet process prior
`theta`	Value of the strength parameter of the Two-parameters-Poisson-Dirichlet process prior
`sigma`	Value of the discount parameter of the Two-parameters-Poisson-Dirichlet process prior
`mixing_hyperprior`	Logical. If TRUE `alpha` is random with gamma hyperprior
`alpha_r`	Logical. If TRUE `alpha` is random with gamma hyperprior
`basemeasure_hyperprior`	Logical. If TRUE also the parameters of the base measure are random, see details below.
`mixing_type`	Type of mixing distribution. Default is "DP" for Dirichlet process but also "2PD" for Two-parameters-Poisson-Dirichlet process is allowed.
`algo`	Type of algorithm. Current choices are: slice sampler (`algo="slice"`) or polya-urn-type sampler (`algo="polya-urn"`).
`mu0`	Location hyperparameter for the latent rounded Gaussian base measure
`kap`	Precision hyperparameter for the latent rounded Gaussian base measure
`atau`	Shape hyperparameter for the Gamma distribution
`btau`	Scale hyperparameter for the Gamma distribution
`a_a`	Shape hyperparameter for the Gamma distribution for `alpha`
`b_a`	Scale hyperparameter for the Gamma distribution for `alpha`
`lb`	Scalar integer. Lower bound for the argument of the pmf. Default is `max(0,min(ydis)-10)`.
`ub`	Scalar integer. Upper bound for the argument of the pmf. Default is `max(ydis)+10`.
`print`	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.
`ndisplay`	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)
`plot.it`	Logical, default FALSE. If TRUE a plot with empirical and estimated posterior probability mass functions is plotted.
`pdfwrite`	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).

Details

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.

Value

`name`	Name of the model
`mixing_type`	Name of the mixing prior
`mcmc`	Quantities about MCMC sampling
`mcmc.chains`	MCMC chains of the parameters
`pmf`	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`
`parameters`	A list containing the posterior mean of the cluster specific parameters (be careful of label-switching problems)
`clustering`	A list containing posterior quantities related to the clustering structure of the data

Author(s)

R code and porting by A. Canale, C code by A. Canale with minor contributions by N. Lunardon.

References

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.

Examples


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)

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)

Package 'rmp'

Help Index

Posterior probability mass function estimation with DP prior

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Developmental toxicity study of ethylene glycol in mice

Description

Usage

Format

References

Examples

DP mixtures of Poissons

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Nonparametric mixture of rounded Gaussians

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples