demc_zs: 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_zs implements multi-chain adaptive MCMC on real parameter spaces via Differential Evolution Markov Chain with learning from the past and the snooker update. It allows restart from a previous run. Required input: starting position for each chain (X) and a unnormalized logposterior function (FUN).

Usage

demc_zs(Nchain = 3, Z, FUN, X, blocks, f = 2.38, pSnooker = 0.1,
  p.f.is.1 = 0.1, n.generation = 1000, n.thin, n.burnin = 0,
  eps.mult = 0.2, eps.add = 0, verbose = FALSE, logfitness_X, ...)

Arguments

Nchain	number of (parallel) chains.
Z	matrix of initial values or demc object resulting from a previous run. If matrix, initial parameter values for N chains (columns) for each of the parameters (rows). 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.
X	optional matrix of initial values (d x Nchain); default: X.final of a previous run or the first Nchain columns of Z if Z is a matrix. If matrix, initial parameter values for N chains (columns) for each of the parameters (rows). See Details for choice of N.
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 (default 2.38). The scale used is f/sqrt(2k), where k the number of parameters in a block (k=d if there only one block) in the parallel update and k = 1 in the snooker update. f can be a vector of length(blocks) to set differential scaling factors for blocks.
pSnooker	probability of snooker update (default 0.1); 1-pSnooker: prob of the differential evolution (parallel) update
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.
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). In demc_zs and demc_zs_p this value should be set as large as possible, because of autocorrelation that makes the method to adapt to quickly/to the wrong scale and orientation as the many correlated samples overrule any decent initial sample
n.burnin	integer, number of initial generations that is not stored (default 0).
eps.mult	real value (default 0.2). It adds scaled uncorrelated noise to the proposal, by multiplying the scale of the update with a d-dimension uniform variate [1-eps,1+eps].
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).
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_zs This function implements the method of ter Braak & Vrugt (2008) using learning of the past, the differential evolution (parelle direction) update and the snooker update. The number of initial positions (N, columns of Z) should be much larger than the number of paramaters (d) in each block. The advice is N=10d. So fewer initial values 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., and Vrugt J. A. (2008). Differential Evolution Markov Chain with snooker updater and fewer chains. Statistics and Computing, 18 (4), 435-446. http://dx.doi.org/10.1007/s11222-008-9104-9

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