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
|
function [a, b] = beta_specification(mu, sigma2, lb, ub, name) % --*-- Unitary tests --*--
% Returns the hyperparameters of the beta distribution given the expectation and variance.
%
% INPUTS
% - mu [double] Expectation of the Gamma random variable.
% - sigma2 [double] Variance of the Gamma random variable.
% - lb [double] Lower bound of the domain (default is zero).
% - ub [double] Upper bound of the domain (default is one).
%
% OUTPUTS
% - a [double] First hyperparameter of the Beta density.
% - b [double] Second hyperparameter of the Beta density.
% Copyright (C) 2015-2017 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/>.
if nargin<3
lb = 0;
ub = 1;
end
if nargin<4
ub = 1;
end
if nargin>4 && ~isempty(name)
name1 = sprintf('of %s ', name);
name2 = sprintf(' (for %s)', name);
else
name1 = '';
name2 = '';
end
if mu<lb
error(['The prior expectation (%f) %scannot be smaller than the lower bound of the Beta distribution (%f)!'], mu, name1, lb)
end
if mu>ub
error('The prior expectation (%f) %scannot be greater than the upper bound of the Beta distribution (%f)!', mu, name1, ub)
end
len = ub-lb;
mu = (mu-lb)/len;
sigma2 = sigma2/(len*len);
if sigma2>(1-mu)*mu
error('Beta prior%s. Given the declared prior expectation, prior lower and upper bounds, the prior std. has to be smaller than %f.',name2,sqrt((1-mu)*mu))
end
a = (1-mu)*mu*mu/sigma2-mu;
b = a*(1/mu-1);
%@test:1
%$ try
%$ [a, b] = beta_specification(.5, .05);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = abs(0.5-a/(a+b))<1e-12;
%$ t(3) = abs(0.05-a*b/((a+b)^2*(a+b+1)))<1e-12;
%$ end
%$ T = all(t);
%@eof:1
%@test:2
%$ try
%$ [a, b] = beta_specification(0.5, .05, 1, 2);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:2
%@test:3
%$ try
%$ [a, b] = beta_specification(2.5, .05, 1, 2);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:3
%@test:4
%$ try
%$ [a, b] = beta_specification(.4, .6*.4+1e-4);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:4
%@test:5
%$ try
%$ [a, b] = beta_specification(.4, .6*.4+1e-6);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$ try
%$ [a, b] = beta_specification(.4, .6*.4-1e-6);
%$ t(2) = true;
%$ catch
%$ t(2) = false;
%$ end
%$
%$ T = all(t);
%@eof:5
|
