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Merge pull request #998 from JohannesPfeifer/prior_distributions 

Prior distributions
time-shift
MichelJuillard 2015-07-27 21:53:19 +02:00
parent 7541cf0132 19fdb309ac
commit fb77b447bd
3 changed files with 386 additions and 5 deletions
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4
matlab/distributions/compute_prior_mode.m
View File

@ -22,7 +22,7 @@ function m = compute_prior_mode(hyperparameters,shape)
% [3] The uniform distribution has an infinity of modes. In this case the function returns the prior mean.
% [4] For the beta distribution we can have 1, 2 or an infinity of modes.
% Copyright (C) 2009 Dynare Team
% Copyright (C) 2009-2015 Dynare Team
%
% This file is part of Dynare.
%
@ -74,7 +74,7 @@ switch shape
m = m + hyperparameters(3);
end
case 5
m = .5*(hyperparameters(2)-hyperparameters(1)) ;
m = hyperparameters(1);
case 6
% s = hyperparameters(1)
% nu = hyperparameters(2)

378
matlab/prior_draw.m
View File

@ -1,4 +1,4 @@
function pdraw = prior_draw(init,uniform)
function pdraw = prior_draw(init,uniform) % --*-- Unitary tests --*--
% This function generate one draw from the joint prior distribution.
%
% INPUTS
@ -15,7 +15,7 @@ function pdraw = prior_draw(init,uniform)
% NOTE 1. Input arguments 1 an 2 are only needed for initialization.
% NOTE 2. A given draw from the joint prior distribution does not satisfy BK conditions a priori.
% Copyright (C) 2006-2010 Dynare Team
% Copyright (C) 2006-2015 Dynare Team
%
% This file is part of Dynare.
%
@ -93,6 +93,11 @@ end
if uniform_draws
pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
while ~isempty(out_of_bound),
pdraw(uniform_index) = rand(length(uniform_index),1).*(p4(uniform_index)-p3(uniform_index)) + p3(uniform_index);
out_of_bound = find( (pdraw(uniform_index)'>ub(uniform_index)) | (pdraw(uniform_index)'<lb(uniform_index)));
end
end
if gaussian_draws
@ -139,7 +144,374 @@ if inverse_gamma_2_draws
out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
while ~isempty(out_of_bound),
pdraw(inverse_gamma_2_index(out_of_bound)) = ...
sqrt(1./gamrnd(p7(inverse_gamma_2_index(out_of_bound))/2,2./p6(inverse_gamma_2_index(out_of_bound))))+p3(inverse_gamma_2_index(out_of_bound));
1./gamrnd(p7(inverse_gamma_2_index(out_of_bound))/2,2./p6(inverse_gamma_2_index(out_of_bound)))+p3(inverse_gamma_2_index(out_of_bound));
out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
end
end
%@test:1
%$ %% Initialize required structures
%$ options_.prior_trunc=0;
%$ options_.initialize_estimated_parameters_with_the_prior_mode=0;
%$
%$ M_.dname='test';
%$ M_.param_names = 'alp';
%$ ndraws=100000;
%$ global estim_params_
%$ estim_params_.var_exo = [];
%$ estim_params_.var_endo = [];
%$ estim_params_.corrx = [];
%$ estim_params_.corrn = [];
%$ estim_params_.param_vals = [];
%$ estim_params_.param_vals = [1, NaN, (-Inf), Inf, 1, 0.356, 0.02, NaN, NaN, NaN ];
%$
%$ %% beta
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 1;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<0) || any(pdraw_vec>1)
%$ error('Beta prior wrong')
%$ end
%$
%$
%$ %% Gamma
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 2;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<0)
%$ error('Gamma prior wrong')
%$ end
%$
%$ %% Normal
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 3;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4
%$ error('Normal prior wrong')
%$ end
%$
%$ %% inverse gamma distribution (type 1)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 4;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<0)
%$ error('inverse gamma distribution (type 1) prior wrong')
%$ end
%$
%$ %% Uniform
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 5;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=sqrt(12)^(-1)*(1-0);
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-2 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-3 || any(pdraw_vec<0) || any(pdraw_vec>1)
%$ error('Uniform prior wrong')
%$ end
%$
%$ %% inverse gamma distribution (type 2)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 6;%Shape
%$ estim_params_.param_vals(1,6)=0.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<0)
%$ error('inverse gamma distribution (type 2) prior wrong')
%$ end
%$
%$
%$ %%%%%%%%%%%%%%%%%%%%%% Generalized distributions %%%%%%%%%%%%%%%%%%%%%
%$
%$ %% beta
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 1;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=3;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<estim_params_.param_vals(1,3)) || any(pdraw_vec>estim_params_.param_vals(1,4))
%$ error('Beta prior wrong')
%$ end
%$
%$ %% Gamma
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 2;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<estim_params_.param_vals(1,8))
%$ error('Gamma prior wrong')
%$ end
%$
%$ %% inverse gamma distribution (type 1)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 4;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<estim_params_.param_vals(1,8))
%$ error('inverse gamma distribution (type 1) prior wrong')
%$ end
%$
%$ %% Uniform
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 5;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<estim_params_.param_vals(1,3)) || any(pdraw_vec>estim_params_.param_vals(1,4))
%$ error('Uniform prior wrong')
%$ end
%$
%$ %% inverse gamma distribution (type 2)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 6;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>1e-4 || abs(std(pdraw_vec)-estim_params_.param_vals(1,7))>1e-4 || any(pdraw_vec<estim_params_.param_vals(1,8))
%$ error('inverse gamma distribution (type 2) prior wrong')
%$ end
%$
%$ %%%%%%%%%%%% With prior truncation
%$ options_.prior_trunc=.4;
%$
%$ %% beta
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 1;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=3;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$ bounds = prior_bounds(bayestopt_,options_)';
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>5e-3 || any(pdraw_vec<bounds.lb) || any(pdraw_vec>bounds.ub)
%$ error('Beta prior wrong')
%$ end
%$
%$ %% Gamma
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 2;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$ bounds = prior_bounds(bayestopt_,options_)';
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>5e-3 || any(pdraw_vec<bounds.lb) || any(pdraw_vec>bounds.ub)
%$ error('Gamma prior wrong')
%$ end
%$
%$ %% inverse gamma distribution (type 1)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 4;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$ bounds = prior_bounds(bayestopt_,options_)';
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>5e-3 || any(pdraw_vec<bounds.lb) || any(pdraw_vec>bounds.ub)
%$ error('inverse gamma distribution (type 1) prior wrong')
%$ end
%$
%$ %% Uniform
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 5;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=NaN;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$ bounds = prior_bounds(bayestopt_,options_)';
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>5e-3 || any(pdraw_vec<bounds.lb) || any(pdraw_vec>bounds.ub)
%$ error('Uniform prior wrong')
%$ end
%$
%$
%$ %% inverse gamma distribution (type 2)
%$ estim_params_.param_vals(1,3)= -Inf;%LB
%$ estim_params_.param_vals(1,4)= +Inf;%UB
%$ estim_params_.param_vals(1,5)= 6;%Shape
%$ estim_params_.param_vals(1,6)=1.5;
%$ estim_params_.param_vals(1,7)=0.01;
%$ estim_params_.param_vals(1,8)=1;
%$ estim_params_.param_vals(1,9)=NaN;
%$
%$ [xparam1, estim_params_, bayestopt_, lb, ub, M_]=set_prior(estim_params_, M_, options_);
%$ bounds = prior_bounds(bayestopt_,options_)';
%$
%$ pdraw = prior_draw(1,0);
%$ pdraw_vec=NaN(ndraws,1);
%$ for ii=1:ndraws
%$ pdraw_vec(ii)=prior_draw(0,0);
%$ end
%$
%$ if abs(mean(pdraw_vec)-estim_params_.param_vals(1,6))>5e-3 || any(pdraw_vec<bounds.lb) || any(pdraw_vec>bounds.ub)
%$ error('inverse gamma distribution (type 2) prior wrong')
%$ end
%$
%@eof:1

9
matlab/set_prior.m
View File

@ -196,6 +196,9 @@ k2 = find(isnan(bayestopt_.p4(k)));
bayestopt_.p3(k(k1)) = zeros(length(k1),1);
bayestopt_.p4(k(k2)) = Inf(length(k2),1);
for i=1:length(k)
if (bayestopt_.p1(k(i))<bayestopt_.p3(k(i))) || (bayestopt_.p1(k(i))>bayestopt_.p4(k(i)))
error(['The prior mean of ' bayestopt_.name{k(i)} ' has to be above the lower (' num2str(bayestopt_.p3(k(i))) ') bound of the Gamma prior density!']);
end
if isinf(bayestopt_.p2(k(i)))
error(['Infinite prior standard deviation for parameter ' bayestopt_.name{k(i)} ' is not allowed (Gamma prior)!'])
end
@ -224,6 +227,9 @@ k2 = find(isnan(bayestopt_.p4(k)));
bayestopt_.p3(k(k1)) = zeros(length(k1),1);
bayestopt_.p4(k(k2)) = Inf(length(k2),1);
for i=1:length(k)
if (bayestopt_.p1(k(i))<bayestopt_.p3(k(i))) || (bayestopt_.p1(k(i))>bayestopt_.p4(k(i)))
error(['The prior mean of ' bayestopt_.name{k(i)} ' has to be above the lower (' num2str(bayestopt_.p3(k(i))) ') bound of the Inverse Gamma prior density!']);
end
[bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),1,0) ;
bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 4) ;
@ -246,6 +252,9 @@ k2 = find(isnan(bayestopt_.p4(k)));
bayestopt_.p3(k(k1)) = zeros(length(k1),1);
bayestopt_.p4(k(k2)) = Inf(length(k2),1);
for i=1:length(k)
if (bayestopt_.p1(k(i))<bayestopt_.p3(k(i))) || (bayestopt_.p1(k(i))>bayestopt_.p4(k(i)))
error(['The prior mean of ' bayestopt_.name{k(i)} ' has to be above the lower (' num2str(bayestopt_.p3(k(i))) ') bound of the Inverse Gamma II prior density!']);
end
[bayestopt_.p6(k(i)),bayestopt_.p7(k(i))] = ...
inverse_gamma_specification(bayestopt_.p1(k(i))-bayestopt_.p3(k(i)),bayestopt_.p2(k(i)),2,0);
bayestopt_.p5(k(i)) = compute_prior_mode([ bayestopt_.p6(k(i)) , bayestopt_.p7(k(i)) , bayestopt_.p3(k(i)) ], 6) ;