semiparamDPE

array of subset posterior samples of the dimension c(d,sampT,M). Here d is the dimension of the parameter space, sampT is the number of samples, and M is the number of subposterior datasets.

subchain

bandwidth vector of the length d=dim(subchain)[1]. It is a vector of tuning parameters used in kernel density approximation employed by the semiparametric method. When anneal=TRUE then one of the choices for bandw could be the vector consisting of standard deviations for each of the d parameters. When anneal=FALSE then one of the choices for bandw could be the diagonal of the optimal bandwidth matrix obtained via Silverman's rule of thumb; see Examples. By default bandw=rep(1.0,d).

bandw

logical; if TRUE, the bandwidth bandw (instead of being fixed) is annealed as bandw*i^(-1/(4+d)); here i is the index corresponding to a sample; see References.

anneal

logical; if TRUE, each of the M subsets of d dimensional parameters in subchain is shuffled.

shuff

The function uses the Semiparametric Density Product Estimator method introduced by Neiswanger et al. (see References) to combine the independent subset posterior samples subchains into the set of samples that estimate the posterior density given the full data set. The semiparametric density product estimator method uses kernel smoothing techniques to estimate each subset posterior density; the subposterior densities are then multiplied together to approximate the posterior density based on the full data set.

combine

consensus

subposterior

posterior

See Miroshnikov and Conlon (2014) <doi:10.1371/journal.pone.0108425>. Recent Bayesian Markov chain Monto Carlo (MCMC) methods have been developed for big data sets that are too large to be analyzed using traditional statistical methods. These methods partition the data into non-overlapping subsets, and perform parallel independent Bayesian MCMC analyses on the data subsets, creating independent subposterior samples for each data subset. These independent subposterior samples are combined through four functions in this package, including averaging across subset samples, weighted averaging across subsets samples, and kernel smoothing across subset samples. The four functions assume the user has previously run the Bayesian analysis and has produced the independent subposterior samples outside of the package; the functions use as input the array of subposterior samples. The methods have been demonstrated to be useful for Bayesian MCMC models including Bayesian logistic regression, Bayesian Gaussian mixture models and Bayesian hierarchical Poisson-Gamma models. The methods are appropriate for Bayesian hierarchical models with hyperparameters, as long as data values in a single level of the hierarchy are not split into subsets.

Erin Conlon

parallelMCMCcombine

Combining Subset MCMC Samples to Estimate a Posterior Density

semiparamDPE function

Semiparametric Density Product Estimator Method — semiparamDPE

Semiparametric Density Product Estimator Method

Recent Bayesian Markov chain Monto Carlo (MCMC) methods have been developed for big data sets that are too large to be analyzed using traditional statistical methods. These methods partition the data into non-overlapping subsets, and perform parallel independent Bayesian MCMC analyses on the data subsets, creating independent subposterior samples for each data subset. These independent subposterior samples are combined through four functions in this package, including averaging across subset samples, weighted averaging across subsets samples, and kernel smoothing across subset samples. The four functions assume the user has previously run the Bayesian analysis and has produced the independent subposterior samples outside of the package; the functions use as input the array of subposterior samples. The methods have been demonstrated to be useful for Bayesian MCMC models including Bayesian logistic regression, Bayesian Gaussian mixture models and Bayesian hierarchical Poisson-Gamma models. The methods are appropriate for Bayesian hierarchical models with hyperparameters, as long as data values in a single level of the hierarchy are not split into subsets.

semiparamDPE: Semiparametric Density Product Estimator Method

Description

Usage

Arguments

Value

References

Examples