| Title: | demc2 implements adaptive MCMC on real parameter spaces via Differential Evolution Markov Chain |
|---|---|
| Description: | The package implements both the origal Markovian demc version of ter Braak (2006) and the egodic demc-zc version of ter Braak & Vrugt (2008) using learning from the past and the snooker update. Convergence can be checked with coda. The demc package allows restarts. |
| Authors: | Cajo J.F. ter Braak |
| Maintainer: | Cajo J.F. ter Braak <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0 |
| Built: | 2025-01-30 05:22:01 UTC |
| Source: | https://github.com/CajoterBraak/demc2 |
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).
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, ...)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, ...)
X |
matrix of initial values or |
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. |
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.
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.
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
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).
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, ...)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, ...)
Nchain |
number of (parallel) chains. |
Z |
matrix of initial values or |
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 |
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. |
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.
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.
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
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).
demc_zs_p(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, pClust = NULL, ...)demc_zs_p(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, pClust = NULL, ...)
Nchain |
number of (parallel) chains. |
Z |
matrix of initial values or |
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). |
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. |
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.
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.
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
demc2 implements both the origal Markovian demc version of ter Braak (2006) and
the egodic demc_zc version of ter Braak & Vrugt (2008) using learning from the past and the snooker update.
Convergence can be checked with coda.
The demc package allows restarts.
The functions that you're likely need from demc are
demc and demc_zs for generating samples and
as.coda to be able to use package coda for convergence checks
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 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
Extracts the draws from a demc object
draws.demc(object, keep.all = 0.9, thin = 1)draws.demc(object, keep.all = 0.9, thin = 1)
object |
|
keep.all |
logical or fraction of draws to keep. If fraction, the one-complement is discarded as burnin. If logical the first half of the draws are discarded. Default 0.9. |
thin |
integer (default 1), keep every thin-th draw |
a dataframe with parameters as variables and as rows the kept samples
Summarizes a demc object
## S3 method for class 'demc' summary(a, trans = NULL, keep.all = 0.9, Rupper.keep = FALSE)## S3 method for class 'demc' summary(a, trans = NULL, keep.all = 0.9, Rupper.keep = FALSE)
trans |
a vector of length k (default NULL): "" if no transformation, or "log" or "logit" |
keep.all |
logical or fraction of draws to keep. If fraction, the one-complement is discarded as burnin. If logical the first half of the draws are discarded. Default 0.9. |
Rupper.keep |
logical (default FALSE); if TRUE: keep Rupper, (Otherwise don't display it.) |
object |
|
The summary is adapted from the monitor function written by Andrew Gelman.
an S3 object of class demc which is a list with
$summary $accept.prob.mat