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function m = compute_prior_mode(hyperparameters,shape) % --*-- Unitary tests --*--
% This function computes the mode of the prior distribution given the (two, three or four) hyperparameters
% of the prior distribution.
%
% INPUTS
% hyperparameters [double] 1*n vector of hyper parameters.
% shape [integer] scalar specifying the prior shape:
% shape=1 => Beta distribution,
% shape=2 => Gamma distribution,
% shape=3 => Gaussian distribution,
% shape=4 => Inverse Gamma (type 1) distribution,
% shape=5 => Uniform distribution,
% shape=6 => Inverse Gamma (type 2) distribution,
% shape=8 => Weibull distribution.
%
% OUTPUTS
% m [double] scalar or 2*1 vector, the prior mode.
%
% REMARKS
% [1] The size of the vector of hyperparameters is 3 when the Gamma or Inverse Gamma is shifted and 4 when
% the support of the Beta distribution is not [0,1].
% [2] The hyperparameters of the uniform distribution are the lower and upper bounds.
% [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) 2009-2017 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 <https://www.gnu.org/licenses/>.
m = NaN ;
switch shape
case 1
if (hyperparameters(1)>1 && hyperparameters(2)>1)
m = (hyperparameters(1)-1)/(hyperparameters(1)+hyperparameters(2)-2) ;
elseif (hyperparameters(1)<1 && hyperparameters(2)<1)
m = [ 0 ; 1 ] ;
elseif ( hyperparameters(1)<1 && hyperparameters(2)>1-eps ) || ( abs(hyperparameters(1)-1)<2*eps && hyperparameters(2)>1 )
m = 0;
elseif ( hyperparameters(1)>1 && hyperparameters(2)<1+eps ) || ( abs(hyperparameters(1)-1)<2*eps && hyperparameters(2)<1 )
m = 1;
elseif ( abs(hyperparameters(1)-1)<2*eps && abs(hyperparameters(2)-1)<2*eps )% Uniform distribution!
m = .5 ;
end
if length(hyperparameters)==4
m = m*(hyperparameters(4)-hyperparameters(3)) + hyperparameters(3) ;
end
case 2
% a = hyperparameters(1) [shape parameter]
% b = hyperparameters(2) [scale parameter]
if hyperparameters(1)<1
m = 0;
else
m = (hyperparameters(1)-1)*hyperparameters(2);
end
if length(hyperparameters)>2
m = m + hyperparameters(3);
end
case 3
m = hyperparameters(1);
case 4
% s = hyperparameters(1)
% nu = hyperparameters(2)
m = 1/sqrt((hyperparameters(2)+1)/hyperparameters(1));
if length(hyperparameters)>2
m = m + hyperparameters(3);
end
case 5
m = hyperparameters(1);
case 6
% s = hyperparameters(1)
% nu = hyperparameters(2)
m = hyperparameters(1)/(hyperparameters(2)+2) ;
if length(hyperparameters)>2
m = m + hyperparameters(3) ;
end
case 8
% k = hyperparameters(1) [shape parameter]
% s = hyperparameters(2) [scale parameter]
if hyperparameters(1)<=1
m = 0;
else
m = hyperparameters(2)*((hyperparameters(1)-1)/hyperparameters(1))^(1/hyperparameters(1));
end
if length(hyperparameters)>2
% Add location parameter
m = m + hyperparameters(3) ;
end
otherwise
error('Unknown prior shape!')
end
%@test:1
%$ % Beta density
%$ try
%$ m1 = compute_prior_mode([2 1],1);
%$ m2 = compute_prior_mode([2 5 1 4],1); % Wolfram Alpha: BetaDistribution[2,5]
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,1,1e-6);
%$ t(3) = dassert(m2,1/5*3+1,1e-6);
%$ end
%$ T = all(t);
%@eof:1
%@test:2
%$ % Gamma density
%$ try
%$ m1 = compute_prior_mode([1 2],2);
%$ m2 = compute_prior_mode([9 0.5 1],2); % Wolfram Alpha: GammaDistribution[9,0.5]
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,0,1e-6);
%$ t(3) = dassert(m2,4+1,1e-6);
%$ end
%$ T = all(t);
%@eof:2
%@test:3
%$ % Normal density
%$ try
%$ m1 = compute_prior_mode([1 1],3);
%$ m2 = compute_prior_mode([2 5],3);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,1,1e-6);
%$ t(3) = dassert(m2,2,1e-6);
%$ end
%$ T = all(t);
%@eof:3
%@test:4
%$ % Inverse Gamma I density
%$ try
%$ m1 = compute_prior_mode([8 2],4);
%$ m2 = compute_prior_mode([8 2 1],4);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,1.632993161855452,1e-6);
%$ t(3) = dassert(m2,1.632993161855452+1,1e-6);
%$ end
%$ T = all(t);
%@eof:4
%@test:5
%$ % Uniform density
%$ try
%$ m1 = compute_prior_mode([0.5 1/sqrt(12)],5);
%$ m2 = compute_prior_mode([2 5 1 2],5);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,0.5,1e-6);
%$ t(3) = dassert(m2,2,1e-6);
%$ end
%$ T = all(t);
%@eof:5
%@test:6
%$ % Inverse Gamma II density, parameterized with s and nu where s=2*beta and nu=2*alpha
%$ try
%$ m1 = compute_prior_mode([8 2],6); % Wolfram Alpha, parameterized with alpha beta: InversegammaDistribution[1,4]
%$ m2 = compute_prior_mode([8 4 1],6); % Wolfram Alpha, parameterized with alpha beta: InversegammaDistribution[2,4]
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,2,1e-6);
%$ t(3) = dassert(m2,1+4/3,1e-6);
%$ end
%$ T = all(t);
%@eof:6
%@test:7
%$ % Weibull density
%$ try
%$ m1 = compute_prior_mode([1 1],8);
%$ m2 = compute_prior_mode([2 1 1],8); % Wolfram Alpha: WeibullDistribution[2,1]
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ % Check the results
%$ if t(1)
%$ t(2) = dassert(m1,0,1e-6);
%$ t(3) = dassert(m2,1+1/sqrt(2),1e-6);
%$ end
%$ T = all(t);
%@eof:7
%@test:8
%$ % Unknown density
%$ try
%$ m1 = compute_prior_mode([1 1],7);
%$ t(1) = false;
%$ catch
%$ t(1) = true;
%$ end
%$
%$ T = all(t);
%@eof:8
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