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value_MCMC.m
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value_MCMC.m
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function [RJ_MCMC_THBI_state,accepted] = value_MCMC(RJMCMC_Chain_Array_Updates,Markov_Chain)
%************************************************************************
%* 4). Value Change
%************************************************************************
RJ_MCMC_THBI_state = RJMCMC_Chain_Array_Updates;
RJ_MCMC_THBI_state_old = RJMCMC_Chain_Array_Updates;
RJ_MCMC_THBI_state.Iteration = Markov_Chain.Iteration;
Log_Likelihood_Current = RJ_MCMC_THBI_state.LogLikelihood;
Uncertainty_Current = RJ_MCMC_THBI_state.Uncertainty_Current;
% Reset acceptance and rejection counts
RJ_MCMC_THBI_state.ABirth_count = [];
RJ_MCMC_THBI_state.RBirth_count = [];
RJ_MCMC_THBI_state.ADeath_count = [];
RJ_MCMC_THBI_state.RDeath_count = [];
RJ_MCMC_THBI_state.AValue_count = [];
RJ_MCMC_THBI_state.RValue_count = [];
RJ_MCMC_THBI_state.AMove_count = [];
RJ_MCMC_THBI_state.RMove_count = [];
RJ_MCMC_THBI_state.ANoise_count = [];
RJ_MCMC_THBI_state.RNoise_count = [];
RJ_MCMC_THBI_state.Rejection = [];
RJ_MCMC_THBI_state.Acceptance = [];
RJ_MCMC_THBI_state_old.ABirth_count = [];
RJ_MCMC_THBI_state_old.RBirth_count = [];
RJ_MCMC_THBI_state_old.ADeath_count = [];
RJ_MCMC_THBI_state_old.RDeath_count = [];
RJ_MCMC_THBI_state_old.AValue_count = [];
RJ_MCMC_THBI_state_old.RValue_count = [];
RJ_MCMC_THBI_state_old.AMove_count = [];
RJ_MCMC_THBI_state_old.RMove_count = [];
RJ_MCMC_THBI_state_old.ANoise_count = [];
RJ_MCMC_THBI_state_old.RNoise_count = [];
RJ_MCMC_THBI_state_old.Rejection = [];
RJ_MCMC_THBI_state_old.Acceptance = [];
%**************************************************************************
% Current distribution parameters
%**************************************************************************
Current_Layers = [RJ_MCMC_THBI_state.Current_Layers];
Current_Nlayers = length([RJ_MCMC_THBI_state.Current_Layers]) ;
Current_Viscous = [RJ_MCMC_THBI_state.Current_Viscosity];
Zmax = [RJ_MCMC_THBI_state.Zmax];
Zmin = [RJ_MCMC_THBI_state.Zmin];
Fixed_Visc_depth = RJ_MCMC_THBI_state.Fixed_Visc_depth;
Fixed_Visc_Contrast = RJ_MCMC_THBI_state.Fixed_Visc_Contrast;
NoiseType = RJ_MCMC_THBI_state.NoiseType;
Max_Visc_value = RJ_MCMC_THBI_state.Max_Visc_value;
Min_Visc_value = RJ_MCMC_THBI_state.Min_Visc_value;
Vicosity_change_std = Markov_Chain.Vicosity_change_std;
%**************************************************************************
% Choose a viscosity randomly and purturb it.
%**************************************************************************
current_visco = Current_Viscous;
idx = randperm(length(current_visco),1);
Kth_Vicosity = current_visco(idx);
Vics_proposed = Kth_Vicosity + Vicosity_change_std*randn;
if(Vics_proposed > Min_Visc_value && Vics_proposed < Max_Visc_value)
% Perturb the vicosity of a chosen layer
current_visco(idx) = Vics_proposed;
Proposed_Layers = Current_Layers;
Proposed_visco = current_visco;
% Update proposed structure
RJ_MCMC_THBI_state.Proposed_Viscosity = Proposed_visco;
RJ_MCMC_THBI_state.Proposed_Layers = Proposed_Layers;
RJ_MCMC_THBI_state.NProposed_Layers = length(Proposed_Layers);
%%
%**************************************************************************
%Compute alpha prior probability P(m) = k+1/k'+1
%**************************************************************************
Proposed_Nlayers = length(Proposed_Layers);
LogAlpha_Prior = log((Current_Nlayers+1)/(Proposed_Nlayers+1));
if Markov_Chain.Proposal_sample
%**************************************************************************
%Compute proposed geoid from birth layer and visocity
%**************************************************************************
[Proposed_Layers_,ind] = sort([Fixed_Visc_depth Proposed_Layers]);
Proposed_visco_ = [Fixed_Visc_Contrast Proposed_visco];
% For pushing top viscosity to surface
if max(Proposed_Layers_)==RJ_MCMC_THBI_state.Zmax
Proposed_visco_ = exp(Proposed_visco_(ind));
elseif max(Proposed_Layers_) < RJ_MCMC_THBI_state.Zmax
Proposed_visco_ = Proposed_visco_(ind);
Proposed_Layers_ = [Proposed_Layers_ 1];
Proposed_visco_ = exp([Proposed_visco_ Proposed_visco_(end)]);
end
%[~,state] for regional
%[state,~] for global
[~,RJ_MCMC_THBI_state.Proposed_Geoid] = geoidkernel_MCMC(RJ_MCMC_THBI_state.Maximum_Degree,RJ_MCMC_THBI_state.Noden,[Proposed_Layers_; Proposed_visco_]',RJ_MCMC_THBI_state.Region,RJ_MCMC_THBI_state.Tomography,RJ_MCMC_THBI_state.Scaling,RJ_MCMC_THBI_state.Step);
%**************************************************************************
% Compute log-likelihood, Uncertainty and Misfit
%**************************************************************************
[Log_Likehood_Proposed,Prefactor,Uncertainty_Proposed,Misfit,Residual,RMS_Error] = likelihood_MCMC(RJ_MCMC_THBI_state);
%**************************************************************************
% Calculate ratio term needed to evaluate the acceptance ratio and check
%for acceptance or rejection
%**************************************************************************
Log_Alpha_Ratio = Prefactor + Log_Likehood_Proposed - Log_Likelihood_Current + LogAlpha_Prior;
%**************************************************************************
% calculate the posterior distrobution
%**************************************************************************
RJ_MCMC_THBI_state.LogPosterior = logposterior_MCMC(Log_Likehood_Proposed,Proposed_Nlayers);
%
else
Log_Alpha_Ratio = 1;
Log_Likehood_Proposed = Log_Likelihood_Current;
Uncertainty_Proposed = Uncertainty_Current;
Misfit = [];
Residual = [];
RMS_Error = [];
end
% Metropolis Hasting method:
% ==========================
Value = log(rand);
if (isfinite(Log_Likelihood_Current) && isfinite(Log_Likehood_Proposed))
if (Log_Alpha_Ratio >0 || Log_Alpha_Ratio > Value)
accepted = 1;
RJ_MCMC_THBI_state.LogLikelihood = Log_Likehood_Proposed;
RJ_MCMC_THBI_state.Current_Viscosity = Proposed_visco;
RJ_MCMC_THBI_state.Current_Layers = Proposed_Layers;
RJ_MCMC_THBI_state.NCurrent_Layers = length(Proposed_Layers);
RJ_MCMC_THBI_state.AValue_count = 1;
RJ_MCMC_THBI_state.RValue_count = 0;
RJ_MCMC_THBI_state.Acceptance = 1;
RJ_MCMC_THBI_state.Rejection = 0;
RJ_MCMC_THBI_state.Log_Alpha_Ratio = Log_Alpha_Ratio;
RJ_MCMC_THBI_state.LogPrior = LogAlpha_Prior;
RJ_MCMC_THBI_state.Misfit = Misfit;
RJ_MCMC_THBI_state.Residual = Residual;
RJ_MCMC_THBI_state.Kernel_Geoid = RJ_MCMC_THBI_state.Proposed_Geoid;
RJ_MCMC_THBI_state.Uncertainty_Current = Uncertainty_Proposed;
RJ_MCMC_THBI_state.RMS_Error = RMS_Error;
else
accepted = 0;
RJ_MCMC_THBI_state_old.AValue_count = 0;
RJ_MCMC_THBI_state_old.RValue_count = 1;
RJ_MCMC_THBI_state_old.Acceptance = 0;
RJ_MCMC_THBI_state_old.Rejection = 1;
RJ_MCMC_THBI_state_old.Iteration = RJ_MCMC_THBI_state.Iteration;
RJ_MCMC_THBI_state = RJ_MCMC_THBI_state_old;
end
end
else
accepted = -1;
RJ_MCMC_THBI_state = RJ_MCMC_THBI_state_old;
end
end