1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
|
function pdraw = prior_draw(bayestopt_, prior_trunc, uniform)
% pdraw = prior_draw(bayestopt_, prior_trunc, uniform)
% This function generate one draw from the joint prior distribution and
% allows sampling uniformly from the prior support (uniform==1 when called with init==1)
%
% INPUTS
% o init [integer] scalar equal to:
% 1: first call to set up persistent variables
% describing the prior
% 0: subsequent call to get prior
% draw
% o uniform [integer] scalar used in initialization (init=1), equal to:
% 1: sample uniformly from prior
% support (overwrites prior shape used for sampling within this function)
% 0: sample from joint prior distribution
%
% OUTPUTS
% o pdraw [double] 1*npar vector, draws from the joint prior density.
%
%
% SPECIAL REQUIREMENTS
% none
%
% NOTE 1. Input arguments 1 and 2 are only needed for initialization.
% NOTE 2. A given draw from the joint prior distribution does not satisfy BK conditions a priori.
%
% Copyright © 2006-2023 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 <https://www.gnu.org/licenses/>.
persistent p6 p7 p3 p4 lb ub
persistent uniform_index gaussian_index gamma_index beta_index inverse_gamma_1_index inverse_gamma_2_index weibull_index
persistent uniform_draws gaussian_draws gamma_draws beta_draws inverse_gamma_1_draws inverse_gamma_2_draws weibull_draws
if nargin>0
p6 = bayestopt_.p6;
p7 = bayestopt_.p7;
p3 = bayestopt_.p3;
p4 = bayestopt_.p4;
bounds = prior_bounds(bayestopt_, prior_trunc);
lb = bounds.lb;
ub = bounds.ub;
number_of_estimated_parameters = length(p6);
if nargin>2 && uniform
prior_shape = repmat(5,number_of_estimated_parameters,1);
else
prior_shape = bayestopt_.pshape;
end
beta_index = find(prior_shape==1);
if isempty(beta_index)
beta_draws = false;
else
beta_draws = true;
end
gamma_index = find(prior_shape==2);
if isempty(gamma_index)
gamma_draws = false;
else
gamma_draws = true;
end
gaussian_index = find(prior_shape==3);
if isempty(gaussian_index)
gaussian_draws = false;
else
gaussian_draws = true;
end
inverse_gamma_1_index = find(prior_shape==4);
if isempty(inverse_gamma_1_index)
inverse_gamma_1_draws = false;
else
inverse_gamma_1_draws = true;
end
uniform_index = find(prior_shape==5);
if isempty(uniform_index)
uniform_draws = false;
else
uniform_draws = true;
end
inverse_gamma_2_index = find(prior_shape==6);
if isempty(inverse_gamma_2_index)
inverse_gamma_2_draws = false;
else
inverse_gamma_2_draws = true;
end
weibull_index = find(prior_shape==8);
if isempty(weibull_index)
weibull_draws = false;
else
weibull_draws = true;
end
pdraw = NaN(number_of_estimated_parameters,1);
return
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
pdraw(gaussian_index) = randn(length(gaussian_index),1).*p7(gaussian_index) + p6(gaussian_index);
out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
while ~isempty(out_of_bound)
pdraw(gaussian_index(out_of_bound)) = randn(length(gaussian_index(out_of_bound)),1).*p7(gaussian_index(out_of_bound)) + p6(gaussian_index(out_of_bound));
out_of_bound = find( (pdraw(gaussian_index)'>ub(gaussian_index)) | (pdraw(gaussian_index)'<lb(gaussian_index)));
end
end
if gamma_draws
pdraw(gamma_index) = gamrnd(p6(gamma_index),p7(gamma_index))+p3(gamma_index);
out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
while ~isempty(out_of_bound)
pdraw(gamma_index(out_of_bound)) = gamrnd(p6(gamma_index(out_of_bound)),p7(gamma_index(out_of_bound)))+p3(gamma_index(out_of_bound));
out_of_bound = find( (pdraw(gamma_index)'>ub(gamma_index)) | (pdraw(gamma_index)'<lb(gamma_index)));
end
end
if beta_draws
pdraw(beta_index) = (p4(beta_index)-p3(beta_index)).*betarnd(p6(beta_index),p7(beta_index))+p3(beta_index);
out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
while ~isempty(out_of_bound)
pdraw(beta_index(out_of_bound)) = (p4(beta_index(out_of_bound))-p3(beta_index(out_of_bound))).*betarnd(p6(beta_index(out_of_bound)),p7(beta_index(out_of_bound)))+p3(beta_index(out_of_bound));
out_of_bound = find( (pdraw(beta_index)'>ub(beta_index)) | (pdraw(beta_index)'<lb(beta_index)));
end
end
if inverse_gamma_1_draws
pdraw(inverse_gamma_1_index) = ...
sqrt(1./gamrnd(p7(inverse_gamma_1_index)/2,2./p6(inverse_gamma_1_index)))+p3(inverse_gamma_1_index);
out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
while ~isempty(out_of_bound)
pdraw(inverse_gamma_1_index(out_of_bound)) = ...
sqrt(1./gamrnd(p7(inverse_gamma_1_index(out_of_bound))/2,2./p6(inverse_gamma_1_index(out_of_bound))))+p3(inverse_gamma_1_index(out_of_bound));
out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
end
end
if inverse_gamma_2_draws
pdraw(inverse_gamma_2_index) = ...
1./gamrnd(p7(inverse_gamma_2_index)/2,2./p6(inverse_gamma_2_index))+p3(inverse_gamma_2_index);
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)) = ...
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
if weibull_draws
pdraw(weibull_index) = wblrnd(p7(weibull_index), p6(weibull_index)) + p3(weibull_index);
out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
while ~isempty(out_of_bound)
pdraw(weibull_index(out_of_bound)) = wblrnd(p7(weibull_index(out_of_bound)),p6(weibull_index(out_of_bound)))+p3(weibull_index(out_of_bound));
out_of_bound = find( (pdraw(weibull_index)'>ub(weibull_index)) | (pdraw(weibull_index)'<lb(weibull_index)));
end
end
return % --*-- Unit tests --*--
%@test:1
% Fill global structures with required fields...
prior_trunc = 1e-10;
p0 = repmat([1; 2; 3; 4; 5; 6; 8], 2, 1); % Prior shape
p1 = .4*ones(14,1); % Prior mean
p2 = .2*ones(14,1); % Prior std.
p3 = NaN(14,1);
p4 = NaN(14,1);
p5 = NaN(14,1);
p6 = NaN(14,1);
p7 = NaN(14,1);
for i=1:14
switch p0(i)
case 1
% Beta distribution
p3(i) = 0;
p4(i) = 1;
[p6(i), p7(i)] = beta_specification(p1(i), p2(i)^2, p3(i), p4(i));
p5(i) = compute_prior_mode([p6(i) p7(i)], 1);
case 2
% Gamma distribution
p3(i) = 0;
p4(i) = Inf;
[p6(i), p7(i)] = gamma_specification(p1(i), p2(i)^2, p3(i), p4(i));
p5(i) = compute_prior_mode([p6(i) p7(i)], 2);
case 3
% Normal distribution
p3(i) = -Inf;
p4(i) = Inf;
p6(i) = p1(i);
p7(i) = p2(i);
p5(i) = p1(i);
case 4
% Inverse Gamma (type I) distribution
p3(i) = 0;
p4(i) = Inf;
[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 1, false);
p5(i) = compute_prior_mode([p6(i) p7(i)], 4);
case 5
% Uniform distribution
[p1(i), p2(i), p6(i), p7(i)] = uniform_specification(p1(i), p2(i), p3(i), p4(i));
p3(i) = p6(i);
p4(i) = p7(i);
p5(i) = compute_prior_mode([p6(i) p7(i)], 5);
case 6
% Inverse Gamma (type II) distribution
p3(i) = 0;
p4(i) = Inf;
[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 2, false);
p5(i) = compute_prior_mode([p6(i) p7(i)], 6);
case 8
% Weibull distribution
p3(i) = 0;
p4(i) = Inf;
[p6(i), p7(i)] = weibull_specification(p1(i), p2(i)^2, p3(i));
p5(i) = compute_prior_mode([p6(i) p7(i)], 8);
otherwise
error('This density is not implemented!')
end
end
bayestopt_.pshape = p0;
bayestopt_.p1 = p1;
bayestopt_.p2 = p2;
bayestopt_.p3 = p3;
bayestopt_.p4 = p4;
bayestopt_.p5 = p5;
bayestopt_.p6 = p6;
bayestopt_.p7 = p7;
ndraws = 1e5;
m0 = bayestopt_.p1; %zeros(14,1);
v0 = diag(bayestopt_.p2.^2); %zeros(14);
% Call the tested routine
try
% Initialization of prior_draws.
prior_draw(bayestopt_, prior_trunc, false);
% Do simulations in a loop and estimate recursively the mean and teh variance.
for i = 1:ndraws
draw = transpose(prior_draw());
m1 = m0 + (draw-m0)/i;
m2 = m1*m1';
v0 = v0 + ((draw*draw'-m2-v0) + (i-1)*(m0*m0'-m2'))/i;
m0 = m1;
end
t(1) = true;
catch
t(1) = false;
end
if t(1)
t(2) = all(abs(m0-bayestopt_.p1)<3e-3);
t(3) = all(all(abs(v0-diag(bayestopt_.p2.^2))<5e-3));
end
T = all(t);
%@eof:1
|
