Added routines for Dynamic Striated Metropolis Hastings.
parent
8f56574464
commit
109fc28dd4
|
@ -0,0 +1,118 @@
|
|||
function [ ix2, temperedlogpost, loglik, ModelName, MetropolisFolder, npar, NumberOfParticles, bayestopt_] = ...
|
||||
DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
|
||||
% function [ ix2, ilogpo2, ModelName, MetropolisFolder, FirstBlock, FirstLine, npar, NumberOfParticles, bayestopt_] = ...
|
||||
% DSMH_initialization(TargetFun, xparam1, mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
|
||||
% Dynamic Striated Metropolis-Hastings initialization.
|
||||
%
|
||||
% INPUTS
|
||||
% o TargetFun [char] string specifying the name of the objective
|
||||
% function (tempered posterior kernel and likelihood).
|
||||
% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
|
||||
% o mh_bounds [double] (p*2) matrix defining lower and upper bounds for the parameters.
|
||||
% o dataset_ data structure
|
||||
% o dataset_info dataset info structure
|
||||
% o options_ options structure
|
||||
% o M_ model structure
|
||||
% o estim_params_ estimated parameters structure
|
||||
% o bayestopt_ estimation options structure
|
||||
% o oo_ outputs structure
|
||||
%
|
||||
% OUTPUTS
|
||||
% o ix2 [double] (NumberOfParticles*npar) vector of starting points for different chains
|
||||
% o ilogpo2 [double] (NumberOfParticles*1) vector of initial posterior values for different chains
|
||||
% o iloglik2 [double] (NumberOfParticles*1) vector of initial likelihood values for different chains
|
||||
% o ModelName [string] name of the mod-file
|
||||
% o MetropolisFolder [string] path to the Metropolis subfolder
|
||||
% o npar [scalar] number of parameters estimated
|
||||
% o NumberOfParticles [scalar] Number of particles requested for the parameters distributions
|
||||
% o bayestopt_ [structure] estimation options structure
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
% None.
|
||||
|
||||
% Copyright (C) 2006-2017 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
%Initialize outputs
|
||||
ix2 = [];
|
||||
ilogpo2 = [];
|
||||
iloglik2 = [];
|
||||
ModelName = [];
|
||||
MetropolisFolder = [];
|
||||
npar = [];
|
||||
NumberOfParticles = [];
|
||||
|
||||
ModelName = M_.fname;
|
||||
if ~isempty(M_.bvar)
|
||||
ModelName = [ModelName '_bvar'];
|
||||
end
|
||||
|
||||
MetropolisFolder = CheckPath('dsmh',M_.dname);
|
||||
BaseName = [MetropolisFolder filesep ModelName];
|
||||
|
||||
NumberOfParticles = options_.dsmh.number_of_particles; %Number of particles for the parameters
|
||||
npar = length(xparam1);
|
||||
|
||||
% Here we start a new DS Metropolis-Hastings, previous draws are discarded.
|
||||
disp('Estimation::dsmh: Initialization...')
|
||||
% Delete old dsmh files if any...
|
||||
files = dir([BaseName '_dsmh*_blck*.mat']);
|
||||
%if length(files)
|
||||
% delete([BaseName '_dsmh*_blck*.mat']);
|
||||
% disp('Estimation::smc: Old dsmh-files successfully erased!')
|
||||
%end
|
||||
% Delete old log file.
|
||||
file = dir([ MetropolisFolder '/dsmh.log']);
|
||||
%if length(file)
|
||||
% delete([ MetropolisFolder '/dsmh.log']);
|
||||
% disp('Estimation::dsmh: Old dsmh.log file successfully erased!')
|
||||
% disp('Estimation::dsmh: Creation of a new dsmh.log file.')
|
||||
%end
|
||||
fidlog = fopen([MetropolisFolder '/dsmh.log'],'w');
|
||||
fprintf(fidlog,'%% DSMH log file (Dynare).\n');
|
||||
fprintf(fidlog,['%% ' datestr(now,0) '.\n']);
|
||||
fprintf(fidlog,' \n\n');
|
||||
fprintf(fidlog,'%% Session 1.\n');
|
||||
fprintf(fidlog,' \n');
|
||||
prior_draw(bayestopt_,options_.prior_trunc);
|
||||
% Find initial values for the NumberOfParticles chains...
|
||||
set_dynare_seed('default');
|
||||
fprintf(fidlog,[' Initial values of the parameters:\n']);
|
||||
disp('Estimation::dsmh: Searching for initial values...');
|
||||
ix2 = zeros(npar,NumberOfParticles);
|
||||
temperedlogpost = zeros(NumberOfParticles,1);
|
||||
loglik = zeros(NumberOfParticles,1);
|
||||
%stderr = sqrt(bsxfun(@power,mh_bounds.ub-mh_bounds.lb,2)/12)/10;
|
||||
for j=1:NumberOfParticles
|
||||
validate = 0;
|
||||
while validate == 0
|
||||
candidate = prior_draw()';
|
||||
% candidate = xparam1(:) + 0.001*randn(npar,1);%bsxfun(@times,stderr,randn(npar,1)) ;
|
||||
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
|
||||
ix2(:,j) = candidate ;
|
||||
[temperedlogpost(j),loglik(j)] = tempered_likelihood(TargetFun,candidate,0.0,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
|
||||
if isfinite(loglik(j)) % if returned log-density is Inf or Nan (penalized value)
|
||||
validate = 1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
fprintf(fidlog,' \n');
|
||||
disp('Estimation::dsmh: Initial values found!')
|
||||
skipline()
|
||||
|
||||
|
|
@ -0,0 +1,303 @@
|
|||
function DSMH_sampler(TargetFun,xparam1,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
|
||||
% function DSMH_sampler(TargetFun,ProposalFun,xparam1,sampler_options,mh_bounds,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_)
|
||||
% Dynamic Striated Metropolis-Hastings algorithm.
|
||||
%
|
||||
% INPUTS
|
||||
% o TargetFun [char] string specifying the name of the objective
|
||||
% function (posterior kernel).
|
||||
% o ProposalFun [char] string specifying the name of the proposal
|
||||
% density
|
||||
% o xparam1 [double] (p*1) vector of parameters to be estimated (initial values).
|
||||
% o sampler_options structure
|
||||
% .invhess [double] (p*p) matrix, posterior covariance matrix (at the mode).
|
||||
% o mh_bounds [double] (p*2) matrix defining lower and upper bounds for the parameters.
|
||||
% o dataset_ data structure
|
||||
% o dataset_info dataset info structure
|
||||
% o options_ options structure
|
||||
% o M_ model structure
|
||||
% o estim_params_ estimated parameters structure
|
||||
% o bayestopt_ estimation options structure
|
||||
% o oo_ outputs structure
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
% None.
|
||||
%
|
||||
% PARALLEL CONTEXT
|
||||
% The most computationally intensive part of this function may be executed
|
||||
% in parallel. The code suitable to be executed in
|
||||
% parallel on multi core or cluster machine (in general a 'for' cycle)
|
||||
% has been removed from this function and been placed in the posterior_sampler_core.m funtion.
|
||||
%
|
||||
% The DYNARE parallel packages comprise a i) set of pairs of Matlab functions that can be executed in
|
||||
% parallel and called name_function.m and name_function_core.m and ii) a second set of functions used
|
||||
% to manage the parallel computations.
|
||||
%
|
||||
% This function was the first function to be parallelized. Later, other
|
||||
% functions have been parallelized using the same methodology.
|
||||
% Then the comments write here can be used for all the other pairs of
|
||||
% parallel functions and also for management functions.
|
||||
|
||||
% Copyright (C) 2006-2017 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
|
||||
lambda = exp(bsxfun(@minus,options_.dsmh.H,1:1:options_.dsmh.H)/(options_.dsmh.H-1)*log(options_.dsmh.lambda1));
|
||||
c = 55 ;
|
||||
|
||||
% Step 0: Initialization of the sampler
|
||||
[ param, tlogpost_iminus1, loglik, ~, ~, npar, nparticles, bayestopt_] = ...
|
||||
DSMH_initialization(TargetFun, xparam1, mh_bounds, dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,oo_);
|
||||
|
||||
ESS = zeros(options_.dsmh.H,1) ;
|
||||
zhat = 1 ;
|
||||
|
||||
% The DSMH starts here
|
||||
for i=1:options_.dsmh.H
|
||||
disp('');
|
||||
disp('Tempered iteration');
|
||||
disp(i) ;
|
||||
% Step 1: sort the densities and compute IS weigths
|
||||
[tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param) ;
|
||||
[tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS) ;
|
||||
% Step 2: tune c_i
|
||||
c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
|
||||
% Step 3: Metropolis step
|
||||
[param,tlogpost_iminus1,loglik] = mutation_DSMH(TargetFun,param,tlogpost_i,tlogpost_iminus1,loglik,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
|
||||
end
|
||||
|
||||
weights = exp(loglik*(lambda(end)-lambda(end-1)));
|
||||
weights = weights/sum(weights);
|
||||
indx_resmpl = DSMH_resampling(weights,rand(1,1),nparticles);
|
||||
distrib_param = param(:,indx_resmpl);
|
||||
|
||||
%% Plot parameters densities
|
||||
TeX = options_.TeX;
|
||||
|
||||
[nbplt,nr,nc,lr,lc,nstar] = pltorg(npar);
|
||||
|
||||
if TeX
|
||||
fidTeX = fopen([M_.fname '_param_density.tex'],'w');
|
||||
fprintf(fidTeX,'%% TeX eps-loader file generated by DSMH.m (Dynare).\n');
|
||||
fprintf(fidTeX,['%% ' datestr(now,0) '\n']);
|
||||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
|
||||
number_of_grid_points = 2^9; % 2^9 = 512 !... Must be a power of two.
|
||||
bandwidth = 0; % Rule of thumb optimal bandwidth parameter.
|
||||
kernel_function = 'gaussian'; % Gaussian kernel for Fast Fourier Transform approximation.
|
||||
for plt = 1:nbplt,
|
||||
if TeX
|
||||
NAMES = [];
|
||||
TeXNAMES = [];
|
||||
end
|
||||
hh = dyn_figure(options_.nodisplay,'Name','Parameters Densities');
|
||||
for k=1:min(nstar,npar-(plt-1)*nstar)
|
||||
subplot(nr,nc,k)
|
||||
kk = (plt-1)*nstar+k;
|
||||
[name,texname] = get_the_name(kk,TeX,M_,estim_params_,options_);
|
||||
if TeX
|
||||
if isempty(NAMES)
|
||||
NAMES = name;
|
||||
TeXNAMES = texname;
|
||||
else
|
||||
NAMES = char(NAMES,name);
|
||||
TeXNAMES = char(TeXNAMES,texname);
|
||||
end
|
||||
end
|
||||
optimal_bandwidth = mh_optimal_bandwidth(distrib_param(kk,:)',nparticles,bandwidth,kernel_function);
|
||||
[density(:,1),density(:,2)] = kernel_density_estimate(distrib_param(kk,:)',number_of_grid_points,...
|
||||
nparticles,optimal_bandwidth,kernel_function);
|
||||
plot(density(:,1),density(:,2));
|
||||
hold on
|
||||
title(name,'interpreter','none')
|
||||
hold off
|
||||
axis tight
|
||||
drawnow
|
||||
end
|
||||
dyn_saveas(hh,[ M_.fname '_param_density' int2str(plt) ],options_.nodisplay,options_.graph_format);
|
||||
if TeX
|
||||
% TeX eps loader file
|
||||
fprintf(fidTeX,'\\begin{figure}[H]\n');
|
||||
for jj = 1:min(nstar,length(x)-(plt-1)*nstar)
|
||||
fprintf(fidTeX,'\\psfrag{%s}[1][][0.5][0]{%s}\n',deblank(NAMES(jj,:)),deblank(TeXNAMES(jj,:)));
|
||||
end
|
||||
fprintf(fidTeX,'\\centering \n');
|
||||
fprintf(fidTeX,'\\includegraphics[scale=0.5]{%s_ParametersDensities%s}\n',M_.fname,int2str(plt));
|
||||
fprintf(fidTeX,'\\caption{ParametersDensities.}');
|
||||
fprintf(fidTeX,'\\label{Fig:ParametersDensities:%s}\n',int2str(plt));
|
||||
fprintf(fidTeX,'\\end{figure}\n');
|
||||
fprintf(fidTeX,' \n');
|
||||
end
|
||||
end
|
||||
|
||||
function indx = DSMH_resampling(weights,noise,number)
|
||||
indx = zeros(number,1);
|
||||
cumweights = cumsum(weights);
|
||||
randvec = (transpose(1:number)-1+noise(:))/number;
|
||||
j = 1;
|
||||
for i=1:number
|
||||
while (randvec(i)>cumweights(j))
|
||||
j = j+1;
|
||||
end
|
||||
indx(i) = j;
|
||||
end
|
||||
|
||||
function [tlogpost_iminus1,loglik,param] = sort_matrices(tlogpost_iminus1,loglik,param)
|
||||
[~,indx_ord] = sortrows(tlogpost_iminus1);
|
||||
tlogpost_iminus1 = tlogpost_iminus1(indx_ord);
|
||||
param = param(:,indx_ord);
|
||||
loglik = loglik(indx_ord);
|
||||
|
||||
function [tlogpost_i,weights,zhat,ESS,mu,Omegachol] = compute_IS_weights_and_moments(param,tlogpost_iminus1,loglik,lambda,i,zhat,ESS)
|
||||
if i==1
|
||||
tlogpost_i = tlogpost_iminus1 + loglik*lambda(i);
|
||||
else
|
||||
tlogpost_i = tlogpost_iminus1 + loglik*(lambda(i)-lambda(i-1));
|
||||
end
|
||||
weights = exp(tlogpost_i-tlogpost_iminus1);
|
||||
zhat = (mean(weights))*zhat ;
|
||||
weights = weights/sum(weights);
|
||||
ESS(i) = 1/sum(weights.^2);
|
||||
% estimates of mean and variance
|
||||
mu = param*weights;
|
||||
z = bsxfun(@minus,param,mu);
|
||||
Omega = z*diag(weights)*z';
|
||||
Omegachol = chol(Omega)';
|
||||
|
||||
function c = tune_c(TargetFun,param,tlogpost_i,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
|
||||
disp('tuning c_i...');
|
||||
disp('Initial value =');
|
||||
disp(c) ;
|
||||
npar = size(param,1);
|
||||
lower_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^5;
|
||||
upper_prob = (.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))^(1/5);
|
||||
stop=0 ;
|
||||
while stop==0
|
||||
acpt = 0.0;
|
||||
indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
|
||||
param0 = param(:,indx_resmpl);
|
||||
tlogpost0 = tlogpost_i(indx_resmpl);
|
||||
for j=1:options_.dsmh.G
|
||||
for l=1:options_.dsmh.K
|
||||
validate = 0;
|
||||
while validate == 0
|
||||
candidate = param0(:,j) + sqrt(c)*Omegachol*randn(npar,1);
|
||||
if all(candidate >= mh_bounds.lb) && all(candidate <= mh_bounds.ub)
|
||||
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,lambda(i),dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
|
||||
if isfinite(loglikx) % if returned log-density is not Inf or Nan (penalized value)
|
||||
validate = 1;
|
||||
if rand(1,1)<exp(tlogpostx-tlogpost0(j)) % accept
|
||||
acpt = acpt + 1/(options_.dsmh.G*options_.dsmh.K);
|
||||
param0(:,j)= candidate;
|
||||
tlogpost0(j) = tlogpostx;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
disp('Acceptation rate =') ;
|
||||
disp(acpt) ;
|
||||
if options_.dsmh.alpha0<=acpt && acpt<=options_.dsmh.alpha1
|
||||
disp('done!');
|
||||
stop=1;
|
||||
else
|
||||
if acpt<lower_prob
|
||||
c = c/5;
|
||||
elseif lower_prob<=acpt && acpt<=upper_prob
|
||||
c = c*log(.5*(options_.dsmh.alpha0+options_.dsmh.alpha1))/log(acpt);
|
||||
else
|
||||
c = 5*c;
|
||||
end
|
||||
disp('Trying with c= ') ;
|
||||
disp(c)
|
||||
end
|
||||
end
|
||||
|
||||
function [out_param,out_tlogpost_iminus1,out_loglik] = mutation_DSMH(TargetFun,param,tlogpost_i,tlogpost_iminus1,loglik,lambda,i,c,Omegachol,weights,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_)
|
||||
indx_levels = (1:1:options_.dsmh.M-1)*options_.dsmh.N*options_.dsmh.G/options_.dsmh.M;
|
||||
npar = size(param,1) ;
|
||||
p = 1/(10*options_.dsmh.tau);
|
||||
disp('Metropolis step...');
|
||||
% build the dynamic grid of levels
|
||||
levels = [0.0;tlogpost_iminus1(indx_levels)];
|
||||
% initialize the outputs
|
||||
out_param = param;
|
||||
out_tlogpost_iminus1 = tlogpost_i;
|
||||
out_loglik = loglik;
|
||||
% resample and initialize the starting groups
|
||||
indx_resmpl = DSMH_resampling(weights,rand(1,1),options_.dsmh.G);
|
||||
param0 = param(:,indx_resmpl);
|
||||
tlogpost_iminus10 = tlogpost_iminus1(indx_resmpl);
|
||||
tlogpost_i0 = tlogpost_i(indx_resmpl);
|
||||
loglik0 = loglik(indx_resmpl);
|
||||
% Start the Metropolis
|
||||
for l=1:options_.dsmh.N*options_.dsmh.tau
|
||||
for j=1:options_.dsmh.G
|
||||
u1 = rand(1,1);
|
||||
u2 = rand(1,1);
|
||||
if u1<p
|
||||
k=1 ;
|
||||
for m=1:options_.dsmh.M-1
|
||||
if levels(m)<=tlogpost_iminus10(j) && tlogpost_iminus10(j)<levels(m+1)
|
||||
k = m+1;
|
||||
break
|
||||
end
|
||||
end
|
||||
indx = floor( (k-1)*options_.dsmh.N*options_.dsmh.G/options_.dsmh.M+1 + u2*(options_.dsmh.N*options_.dsmh.G/options_.dsmh.M-1) );
|
||||
if i==1
|
||||
alp = (loglik(indx)-loglik0(j))*lambda(i);
|
||||
else
|
||||
alp = (loglik(indx)-loglik0(j))*(lambda(i)-lambda(i-1));
|
||||
end
|
||||
if u2<exp(alp)
|
||||
param0(:,j) = param(:,indx);
|
||||
tlogpost_i0(j) = tlogpost_i(indx);
|
||||
loglik0(j) = loglik(indx);
|
||||
tlogpost_iminus10(j) = tlogpost_iminus1(indx);
|
||||
end
|
||||
else
|
||||
validate= 0;
|
||||
while validate==0
|
||||
candidate = param0(:,j) + sqrt(c)*Omegachol*randn(npar,1);
|
||||
if all(candidate(:) >= mh_bounds.lb) && all(candidate(:) <= mh_bounds.ub)
|
||||
[tlogpostx,loglikx] = tempered_likelihood(TargetFun,candidate,lambda(i),dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,mh_bounds,oo_);
|
||||
if isfinite(loglikx) % if returned log-density is not Inf or Nan (penalized value)
|
||||
validate = 1;
|
||||
if u2<exp(tlogpostx-tlogpost_i0(j)) % accept
|
||||
param0(:,j) = candidate;
|
||||
tlogpost_i0(j) = tlogpostx;
|
||||
loglik0(j) = loglikx;
|
||||
if i==1
|
||||
tlogpost_iminus10(j) = tlogpostx-loglikx*lambda(i);
|
||||
else
|
||||
tlogpost_iminus10(j) = tlogpostx-loglikx*(lambda(i)-lambda(i-1));
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
if mod(l,options_.dsmh.tau)==0
|
||||
rang = (l/options_.dsmh.tau-1)*options_.dsmh.G+1:l*options_.dsmh.G/options_.dsmh.tau;
|
||||
out_param(:,rang) = param0;
|
||||
out_tlogpost_iminus1(rang) = tlogpost_i0;
|
||||
out_loglik(rang) = loglik0;
|
||||
end
|
||||
end
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
function [tlogpostkern,loglik] = tempered_likelihood(TargetFun,xparam1,lambda,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_)
|
||||
logpostkern = -feval(TargetFun,xparam1,dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_);
|
||||
logprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||||
loglik = logpostkern-logprior ;
|
||||
tlogpostkern = lambda*loglik + logprior;
|
Loading…
Reference in New Issue