DPP-package: Inference of Parameters of Normal Distributions from a...

In DPP: Inference of Parameters of Normal Distributions from a Mixture of Normals

Description

This MCMC method takes a data numeric vector (Y) and assigns the elements of Y to a (potentially infinite) number of normal distributions. The individual normal distributions from a mixture of normals can be inferred. Following the method described in Escobar (1994) <doi:10.2307/2291223> we use a Dirichlet Process Prior (DPP) to describe stochastically our prior assumptions about the dimensionality of the data.

Details

DPP implements a Bayesian method to get a posterior probability for k normal distributions form a vector of n numeric values. We implemented an MCMC method as described in Escobar (1994). Using a Dirichlet process prior we describe stochastically our prior assumptions about the dimensionality of the data without specifying a fix number of clusters k, allowing us to infer the number of normal distributions or categories from a potentially infinite number of categories. DPP is implemented in C++ and made available to used within the R statistical environment using Rcpp (Eddelbuettel and Francois, 2011).

Author(s)

Luis M. Avila, Michael R. May, Jeff Ross-Ibarra

Maintainer: Luis M. Avila <[e-mail]>

References

Ferguson, Thomas S. A Bayesian analysis of some nonparametric problems. The annals of statistics (1973): 209-230.

Antoniak, Charles E. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics (1974): 1152-1174.

Escobar, Michael D. Estimating Normal Means With a Dirichlet Process Prior. Journal of the American Statistical Association, 89(425), 1994.

Neal, Radford M. Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics 9.2 (2000): 249-265.

Eddelbuettel, Dirk and Romain Francois. Rcpp: Seamless R and C++ Integration. Journal Of Statistical Software, 40(8):1-18, 2011.

Examples

normal.model<-new(NormalModel,
                  mean_prior_mean=0.5,
                  mean_prior_sd=0.1,
                  sd_prior_shape=3,
                  sd_prior_rate=20,
                  estimate_concentration_parameter=TRUE,
                  concentration_parameter_alpha=10,
                  proposal_disturbance_sd=0.1)

 #simulating three normal distributions
 y <- c(rnorm(100,mean=0.2,sd=0.05), rnorm(100,0.7,0.05), rnorm(100,1.3,0.1))
 hist(y,breaks=30)

 #setwd("~/yourwd") #mcmc log files will be saved here
 my_dpp_analysis <- dppMCMC_C(data=y,
                              output = "output_prefix_",
                              model=normal.model,
                              num_auxiliary_tables=4,
                              expected_k=1.5,
                              power=1)
 #running the mcmc  , generations will be ignored because auto_stop=true
 ## Not run: 
 my_dpp_analysis$run(generations=1000,auto_stop=TRUE,max_gen = 10000,min_ess = 500)

 #we get rid of the first 25% of the output (burn-in)
 hist(my_dpp_analysis$getNumCategoryTrace(0.25))
 my_dpp_analysis$getNumCategoryProbabilities(0.25)
 
## End(Not run)

DPP documentation built on May 6, 2019, 1:10 a.m.