demc: generates MCMC samples using Differential Evolution Markov...

In CajoterBraak/demc2: demc2 implements adaptive MCMC on real parameter spaces via Differential Evolution Markov Chain

Description

demc implements multi-chain adaptive MCMC on real parameter spaces via Differential Evolution Markov Chain. It allows restart from a previous run. It is the only (?) adaptive MCMC method that is really Markovian and not just ergodic. Required input: starting position for each chain (X) and a unnormalized logposterior function (FUN).

Usage

demc(X, FUN, blocks, f = 2.38, n.generation = 1000, n.thin = 1,
  n.burnin = 0, eps.add = 0, p.f.is.1 = 0.1, verbose = FALSE,
  logfitness_X, ...)

Arguments

X	matrix of initial values or demc object resulting from a previous run. If matrix, initial parameter values for N chains (rows) for each of the parameters (columns). See Details for choice of N.
FUN	function specifying the (unnormalized) logposterior or target. FUN(theta ,...) with theta a d vector of parameter values and ... other arguments to FUN (e.g. NULL, data, ..). The value of FUN should a single numeric value.
blocks	list of sets of parameters, where each set contains the indices (or names if X has rownames) of variables in theta that are updated jointly, e.g. blocks= list(); blocks[[1]] = c(1,3); blocks[[2]] = c(2,4). The default uses a single block (joint update of all parameters).
f	value specifying the scale of the updates. The scale used is f/sqrt(2k), where k the number of parameters in a block (k=d if there only one block); f can be a vector of length(blocks) to set differential scaling factors for blocks.
n.generation	integer, number of generations, each one generating ncol(X) samples.
n.thin	integer, thinning number, e.g 3 stores every 3rd generation (default 1, no thinning).
n.burnin	integer, number of initial generations that is not stored (default 0).
eps.add	real value . Standard deviation of the (additive) independent random normal step added to the DE update. that guarantees that all parameter values can be reached. Must be postive to garantee that all positions in the space can be reached. For targets (posteriors) without gaps, it can set small or even to 0 (default 0).
p.f.is.1	probability (default 0.1) of using scale 0.98 in the parallel update instead of f/sqrt(2d). Allows exploration of multi-modal posteriors.
verbose	logical (default FALSE). No used currently
logfitness_X	Can be missing. If set, logposterior values for the columns of X; can save some computation if known.

Details

demc This function implements the method of ter Braak (2006) using the differential evolution update (also known as the paralled direction sampling update). See also demc_zs for an egodic variant with learning from the past. The number of initial positions (N, columns of X) should be larger than the number of paramaters (d) in each block. The advice is N=2d. So fewer starting positions are required by specifying blocks with few (or even single) parameters in each block.

Value

an S3 object of class demc which is a list with

$Draws d x (Nchain*n) matrix with n the number of retained simulations [post process with summary or as.coda]. matrix(Draws[p,],nrow= Nchain) is an Nchain x n array (for each parameter p in 1:d)

$accept.prob.mat accept probability matrix of blocks by chains.

$X.final matrix of parameter values of the last generation (same shape as initial X).

$logfitness.X.final vector of logposterior values for columns of X.final (useful for restarting).

$Nchain number of chains.

$demc_zs logical set of FALSE.

References

ter Braak, C. J. F. (2006). A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces. Statistics and Computing, 16, 239-249.http://edepot.wur.nl/26336

CajoterBraak/demc2 documentation built on Dec. 16, 2019, 10:48 p.m.