243 lines
6.4 KiB
Matlab
243 lines
6.4 KiB
Matlab
function m = compute_prior_mode(hyperparameters,shape)
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% This function computes the mode of the prior distribution given the (two, three or four) hyperparameters
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% of the prior distribution.
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%
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% INPUTS
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% hyperparameters [double] 1*n vector of hyper parameters.
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% shape [integer] scalar specifying the prior shape:
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% shape=1 => Beta distribution,
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% shape=2 => Gamma distribution,
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% shape=3 => Gaussian distribution,
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% shape=4 => Inverse Gamma (type 1) distribution,
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% shape=5 => Uniform distribution,
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% shape=6 => Inverse Gamma (type 2) distribution,
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% shape=8 => Weibull distribution.
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%
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% OUTPUTS
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% m [double] scalar or 2*1 vector, the prior mode.
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%
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% REMARKS
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% [1] The size of the vector of hyperparameters is 3 when the Gamma or Inverse Gamma is shifted and 4 when
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% the support of the Beta distribution is not [0,1].
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% [2] The hyperparameters of the uniform distribution are the lower and upper bounds.
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% [3] The uniform distribution has an infinity of modes. In this case the function returns the prior mean.
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% [4] For the beta distribution we can have 1, 2 or an infinity of modes.
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% Copyright © 2009-2023 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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m = NaN ;
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switch shape
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case 1
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if (hyperparameters(1)>1 && hyperparameters(2)>1)
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m = (hyperparameters(1)-1)/(hyperparameters(1)+hyperparameters(2)-2) ;
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elseif (hyperparameters(1)<1 && hyperparameters(2)<1)
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m = [ 0 ; 1 ] ;
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elseif ( hyperparameters(1)<1 && hyperparameters(2)>1-eps ) || ( abs(hyperparameters(1)-1)<2*eps && hyperparameters(2)>1 )
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m = 0;
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elseif ( hyperparameters(1)>1 && hyperparameters(2)<1+eps ) || ( abs(hyperparameters(1)-1)<2*eps && hyperparameters(2)<1 )
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m = 1;
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elseif ( abs(hyperparameters(1)-1)<2*eps && abs(hyperparameters(2)-1)<2*eps )% Uniform distribution!
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m = .5 ;
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end
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if length(hyperparameters)==4
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m = m*(hyperparameters(4)-hyperparameters(3)) + hyperparameters(3) ;
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end
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case 2
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% a = hyperparameters(1) [shape parameter]
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% b = hyperparameters(2) [scale parameter]
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if hyperparameters(1)<1
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m = 0;
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else
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m = (hyperparameters(1)-1)*hyperparameters(2);
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end
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if length(hyperparameters)>2
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m = m + hyperparameters(3);
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end
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case 3
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m = hyperparameters(1);
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case 4
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% s = hyperparameters(1)
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% nu = hyperparameters(2)
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m = 1/sqrt((hyperparameters(2)+1)/hyperparameters(1));
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if length(hyperparameters)>2
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m = m + hyperparameters(3);
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end
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case 5
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m = hyperparameters(1);
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case 6
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% s = hyperparameters(1)
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% nu = hyperparameters(2)
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m = hyperparameters(1)/(hyperparameters(2)+2) ;
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if length(hyperparameters)>2
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m = m + hyperparameters(3) ;
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end
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case 8
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% k = hyperparameters(1) [shape parameter]
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% s = hyperparameters(2) [scale parameter]
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if hyperparameters(1)<=1
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m = 0;
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else
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m = hyperparameters(2)*((hyperparameters(1)-1)/hyperparameters(1))^(1/hyperparameters(1));
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end
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if length(hyperparameters)>2
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% Add location parameter
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m = m + hyperparameters(3) ;
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end
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otherwise
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error('Unknown prior shape!')
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end
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return % --*-- Unit tests --*--
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%@test:1
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% Beta density
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try
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m1 = compute_prior_mode([2 1],1);
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m2 = compute_prior_mode([2 5 1 4],1); % Wolfram Alpha: BetaDistribution[2,5]
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,1,1e-6);
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t(3) = dassert(m2,1/5*3+1,1e-6);
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end
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T = all(t);
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%@eof:1
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%@test:2
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% Gamma density
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try
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m1 = compute_prior_mode([1 2],2);
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m2 = compute_prior_mode([9 0.5 1],2); % Wolfram Alpha: GammaDistribution[9,0.5]
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,0,1e-6);
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t(3) = dassert(m2,4+1,1e-6);
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end
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T = all(t);
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%@eof:2
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%@test:3
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% Normal density
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try
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m1 = compute_prior_mode([1 1],3);
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m2 = compute_prior_mode([2 5],3);
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,1,1e-6);
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t(3) = dassert(m2,2,1e-6);
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end
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T = all(t);
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%@eof:3
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%@test:4
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% Inverse Gamma I density
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try
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m1 = compute_prior_mode([8 2],4);
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m2 = compute_prior_mode([8 2 1],4);
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,1.632993161855452,1e-6);
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t(3) = dassert(m2,1.632993161855452+1,1e-6);
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end
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T = all(t);
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%@eof:4
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%@test:5
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% Uniform density
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try
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m1 = compute_prior_mode([0.5 1/sqrt(12)],5);
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m2 = compute_prior_mode([2 5 1 2],5);
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,0.5,1e-6);
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t(3) = dassert(m2,2,1e-6);
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end
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T = all(t);
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%@eof:5
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%@test:6
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% Inverse Gamma II density, parameterized with s and nu where s=2*beta and nu=2*alpha
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try
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m1 = compute_prior_mode([8 2],6); % Wolfram Alpha, parameterized with alpha beta: InversegammaDistribution[1,4]
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m2 = compute_prior_mode([8 4 1],6); % Wolfram Alpha, parameterized with alpha beta: InversegammaDistribution[2,4]
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,2,1e-6);
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t(3) = dassert(m2,1+4/3,1e-6);
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end
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T = all(t);
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%@eof:6
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%@test:7
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% Weibull density
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try
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m1 = compute_prior_mode([1 1],8);
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m2 = compute_prior_mode([2 1 1],8); % Wolfram Alpha: WeibullDistribution[2,1]
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t(1) = true;
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catch
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t(1) = false;
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end
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% Check the results
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if t(1)
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t(2) = dassert(m1,0,1e-6);
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t(3) = dassert(m2,1+1/sqrt(2),1e-6);
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end
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T = all(t);
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%@eof:7
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%@test:8
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% Unknown density
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try
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m1 = compute_prior_mode([1 1],7);
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t(1) = false;
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catch
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t(1) = true;
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end
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T = all(t);
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%@eof:8 |