mpost: M-Posterior Algorithm for Parameter Estimation

In JacobRaymond/ConquerMCMC: Divide and Conquer Algorithms for Markov Chain Monte Carlo

Description

This function estimates the parameters of a model using the M-posterior method developped by Minsker et al. (2014). It models the subposterior of subset X_k as

π_k(θ | X_k) ∝ π(θ) (∏ p(x|θ))^K

Parameter estimates are subsequently weighted according to their geometric mean.

Usage

mpost(
  chains,
  para,
  startval,
  niter,
  X,
  prior,
  likelihood,
  propvar = NULL,
  burn.rate = 0.1,
  random = T
)

Arguments

chains	Number of subsets in the simulation. Used when a divide-and-conquer algorithm is employed.
para	Parameters to be estimated.
startval	Initial value of the chain.
niter	Number of iterations (including burned iterations).
X	Matrix of observations from the underlying data set.
prior	Prior function for the parameters.
likelihood	Likelihood function.
propvar	The diagonal of the variance matrix for the proposal distribution. If no value is specified, the identify matrix is used.
burn.rate	The percentage of iterations to be burned.
random	If true, the rows of X are shuffled prior to the split.

Value

A list with the following items:

Chains

A list of dataframes, one for each subset, containing the generated Markov chains.

Estimate

The parameter estimate obtained using the M-posterior method.

References

Stanislav Minsker, Sanvesh Srivastava, Lizhen Lin, and David B. Dunson. Scalable and robust bayesian inference via the median posterior. In Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32, ICML’14, page II–1656–II–1664. JMLR.org, 2014.

Examples

#Parameter estimation for data from a Weibull distribution

#Prior
prior<-function(param){
  ifelse(all(param>0), 1, 0)
}

#Likelihood
weibull.likelihood<-function(X, param){
  shape=param[1]
  scale=param[2]
  sum(dweibull(x=X, shape, scale, log=TRUE))
}

#Simulate data
X<-rweibull(100, 2, 1.2)

#Parameters
chains<-10
para<-c("shape", "scale")
niter<-10000
startval<-c(1.5, 1)
likelihood=weibull.likelihood

df<-mpost(chains, para, startval, niter, X, prior, likelihood,
          propvar=NULL, burn.rate=0.1, random=TRUE)

JacobRaymond/ConquerMCMC documentation built on May 12, 2020, 1:03 a.m.