function [error, freq_predV, freq_predA, simVA, sV_hat]=PeerJModelSample(paras,Ntrials,data,selection)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%A sample modeling file for Odegaard, Wozny, & Shams (2017).
%Can be combined with fminsearch or fminsearchbnd to optimize parameters
%for a given subject.  This represents one way of implementing the causal
%inference model.  Other versions use analytic solutions, which run MUCH
%faster and usually contain fewer parameters.  This code is based on previous
%model versions used by the lab, but includes more comments and does things 
%in a way that makes the comptuations more explicit for people hoping
%to learn from this (equations are from the manuscript). This also makes it
%slower to optimize the parameters.  MUCH slower.  
%Should be run on something that has a lot of computing power.
%Note that the lab will be releasing a modeling toolbox in 2017 that includes 
%full documentation + files with the analytic solution that can be fit to new
%experimental data, as well as a GUI interface to visualize parameters.

%Inputs:
%paras: Put in values for the eight parameters.  These can be randomly
%initialized in a fitting procedure.
%Ntrials: 10000 should work fine.
%data: An individual subject's data file.
%Selection: choose the strategy:
% -1 = Probability matching
% 0 = Model Averaging
% 1 = Model selection

%initialize random number generator for optimization
%otherwise optimization becomes very difficult as simulated data changes
s1 = rand('state');
s2 = randn('state');
rand('state',13);
randn('state',13);

warning off MATLAB:divideByZero
warning off MATLAB:logofZero

%%%%%%%%%%%%%%%%%%

%N=max(max(conditions))+1;
N=6;

range=-50:50;
p_cutoff = 0.5;

freq_dataV=zeros(N,N,length(range));
freq_dataA=zeros(N,N,length(range));
freq_predV=zeros(N,N,length(range));
freq_predA=zeros(N,N,length(range));

%Free Parameters
p_common = paras(1); %a.k.a. the "binding tendency"
sigV = paras(2); %Visual likelihood
sigA = paras(3);  %Auditory likelihood
deltaV = paras(4); %Visual likelihood mean delta
deltaA = paras(5); %Auditory likelihood mean delta
deltasigV = paras(6); %Visual likelihood variance delta
xPu = paras(7); %Spatial prior mean
sigPu = paras(8);  %Spatial prior variance

%Variances of the Visual and Auditory Likelihoods
varV = sigV^2;
varA = sigA^2;
varPu = sigPu^2;

%Load the degrees, speakers used, the different stim locations, and another
%speaker vector to be used for the shifts in likelihood means
degs=(unique(data(find(~isnan(data(:,4))),4)));
speakers=(unique(data(find(~isnan(data(:,1))),1)));
sourcevec=[NaN; degs];
speakervec=[NaN; speakers];

%Create the matrix that will hold simulated data
simVA=[]; 
%Create the error functions that will sum the error
splineV=0;
splineA=0;


%Modeling the bimodal trials
for sVind = 1:N
    for sAind = 1:N
        %This section grabs trials from all 25 AV conditions
        if sVind > 1 & sAind > 1

            condIdx=find(data(:,1)==sVind-4 & data(:,9)==sAind-4);
            respV = data(condIdx,7);
            respA = data(condIdx,15);
            
            %Create histograms of V and A responses, 
            %and normalize them by dividing by the sum
            h=hist(respV, range);
            freq_dataV(sVind, sAind, :) = h/sum(h);
            h=hist(respA, range);
            freq_dataA(sVind, sAind, :) = h/sum(h);

            %Grab the locations of the stimuli in both degrees and integer
            sV = sourcevec(sVind);    
            sA = sourcevec(sAind);
            speakerV = speakervec(sVind);
            speakerA = speakervec(sAind);
                        
            % Generation of simulated data 
            xVall = sV + (speakerV*deltaV) + (abs(speakerV*deltasigV) + sigV) * randn(1, Ntrials);
            xAall = sA + (speakerA*deltaA) + sigA * randn(1, Ntrials);
            
            x=range;
            
            for i=1:Ntrials
                % This part of the file grabs likelihood means one at a time,
                % builds distributions around the mean, and then completes the
                % other steps necessary for causal inference
                xV=xVall(1,i);
                xA=xAall(1,i);
            
                %Create ways to keep all of the distributions separate:
                expvisnum = ((x-xV).^2);
                expaudnum = ((x-xA).^2);
                expcprinum = ((x-xPu).^2);

                %The equations for the two distributions, to be either combined
                %for the C=1 scenario, or kept separate for the C=2
                %scenario:
                vlike=(exp(-expvisnum/(2*(varV)))/(sqrt(2*pi*varV)));
                alike=(exp(-expaudnum/(2*(varA)))/(sqrt(2*pi*varA)));
                cprior=(exp(-expcprinum/(2*(varPu)))/(sqrt(2*pi*varPu)));
                
                %Multiply distributions together, normalize, and take the max to find
                %the optimal solutions for the C=1 and C=2 scenarios 
                CommonSolution=vlike.*alike.*cprior/sum(vlike.*alike.*cprior);
                VisualSolution=vlike.*cprior/sum(vlike.*cprior);
                AuditorySolution=alike.*cprior/sum(alike.*cprior);
                [CommonMAP I] = max(CommonSolution);
                [VisualMAP J] = max(VisualSolution);
                [AuditoryMAP K] = max(AuditorySolution);
            
                s_hat_common(1,i)=x(I);
                sV_hat_indep(1,i)=x(J);
                sA_hat_indep(1,i)=x(K);
                
                %Thus, we now have the optimal estimates for each causal
                %structure, but the causal structure isn't known, and must
                %be inferred.  
                likelihood_common(1,i) = sum(vlike.*alike.*cprior);
                likelihoodV_indep(1,i) = sum(vlike.*cprior);
                likelihoodA_indep(1,i) = sum(alike.*cprior);
                likelihood_indep(1,i)=likelihoodV_indep(1,i).*likelihoodA_indep(1,i);
                
            end
                
                %Now that we have integrated over the likelihoods to get a single 
                %value, you can multiply that by p_common to compute the posterior
                %probability of a common cause or independent causes.  Down below, 
                %this posterior probability of a common cause will be combined
                %with the optimal estimates in various ways to implement
                %the 3 strategies
                post_common = likelihood_common * p_common;
                post_indep = likelihood_indep * (1-p_common);
                pC = post_common./(post_common + post_indep);
           
                %Implementing probability matching . . . 
                match=1-rand(1,Ntrials);
                        
                %The three potential perceptual strategies
                if selection>0 %model selection
                    sV_hat=(pC>p_cutoff).*s_hat_common + (pC<=p_cutoff).*sV_hat_indep;
                    sA_hat=(pC>p_cutoff).*s_hat_common + (pC<=p_cutoff).*sA_hat_indep;
                elseif selection<0 %matching
                    sV_hat=(pC>match).*s_hat_common + (pC<=match).*sV_hat_indep;
                    sA_hat=(pC>match).*s_hat_common + (pC<=match).*sA_hat_indep;
                else  %model averaging
                    sV_hat = pC .* s_hat_common + (1-pC) .* sV_hat_indep;
                    sA_hat = pC .* s_hat_common + (1-pC) .* sA_hat_indep;
                end
            
                %Load the 25 bimodal conditions, and then load the
                %simulated data in a matrix
                sim(1:Ntrials,1)=sVind-4;
                sim(1:Ntrials,2)=sAind-4;
                sim(1:Ntrials,3)=sV_hat;
                sim(1:Ntrials,4)=sA_hat;
                simVA=[simVA; sim];
            
                %Normalize the simulated responsesin the same way we did 
                %for the actual responses in the earlier part of the file
                h=hist(sV_hat, range);
                freq_predV(sVind, sAind, :) = h/sum(h);
                h=hist(sA_hat, range);
                freq_predA(sVind, sAind, :) = h/sum(h);
            
                %Compute the error (may want to look at alternative ways
                %of computing this . . . it ain't the only way)
                splineV = splineV + sum( log(max(spline(range,freq_predV(sVind, sAind, :),respV),0.00001)) );
                splineA = splineA + sum( log(max(spline(range,freq_predA(sVind, sAind, :),respA),0.00001)) );
                
        %Now do the modeling work for the unimodal visual trials        
        elseif sVind > 1 & sAind == 1
            
            condIdx=find(data(:,1)==sVind-4 & isnan(data(:,9)));
            respV = data(condIdx,7);
            
            %Create and normalize the response historgrams for the V-only
            %conditions
            h=hist(respV, range);
            freq_dataV(sVind, sAind, :) = h/sum(h);

            %Grab the location of the stimuli in both degrees and integer
            sV = sourcevec(sVind);
            speakerV = speakervec(sVind);
            
            % Generation of simulated data
            xVall = sV + (speakerV*deltaV) + (abs(speakerV*deltasigV) + sigV) * randn(1, Ntrials);
              
            x=range;
            
            for i=1:Ntrials
                % This part of the file grabs likelihood means one at a time,
                % builds distributions around the mean, and then completes the
                % other steps necessary for causal inference
                xV=xVall(1,i);

                %Create ways to keep all of the distributions separate:
                expvisnum = ((x-xV).^2);
                expcprinum = ((x-xPu).^2);

                %The equations for the visual estimate:
                vlike=(exp(-expvisnum/(2*(varV)))/(sqrt(2*pi*varV)));
                cprior=(exp(-expcprinum/(2*(varPu)))/(sqrt(2*pi*varPu)));

                %Multiply the visual likelihood and spatial prior, and
                %normalize.
                VisualSolution=vlike.*cprior/sum(vlike.*cprior);

                %Take the max of the posterior
                [VisualMAP J] = max(VisualSolution);
                sV_hat(1,i)=x(J);

             end

                %Load the vis-only conditions, and simulated vis-only
                %responses into the simulated data matrix
                sim(1:Ntrials,1)=sVind-4;
                sim(1:Ntrials,2)=NaN;
                sim(1:Ntrials,3)=sV_hat;
                sim(1:Ntrials,4)=NaN;
                simVA=[simVA; sim];

                %Create a histogram of the simulated data and normalize
                h=hist(sV_hat, range);
                freq_predV(sVind, sAind, :) = h/sum(h);
            
                %Compute the error for the vis-only conditions
                splineV = splineV + sum( log(max(spline(range,freq_predV(sVind, sAind, :),respV),0.00001)) );
         
         %Now do the modeling work for the unimodal auditory trials
         elseif sVind == 1 & sAind > 1
            
            condIdx=find(isnan(data(:,1)) & data(:,9)==sAind-4);
            respA = data(condIdx,15);
            
            %Create and normalize the response historgrams for the A-only
            %conditions
            h=hist(respA, range);
            freq_dataA(sVind, sAind, :) = h/sum(h);

            %Grab the location of the stimuli in both degrees and integer
            sA = sourcevec(sAind);
            speakerA = speakervec(sAind);
            
            % Generation of simulated data . . .
            xAall = sA + (speakerA*deltaA) + sigA * randn(1, Ntrials);
            
            x=range;
            
            for i=1:Ntrials
                % This part of the file grabs likelihood means one at a time,
                % builds distributions around the mean, and then completes the
                % other steps necessary for causal inference
                xA=xAall(1,i);

                %Create ways to keep all of the distributions separate:
                expaudnum = ((x-xA).^2);
                expcprinum = ((x-xPu).^2);

                %The equations for the auditory estimate:
                alike=(exp(-expaudnum/(2*(varA)))/(sqrt(2*pi*varA)));
                cprior=(exp(-expcprinum/(2*(varPu)))/(sqrt(2*pi*varPu)));

                %Multiply the auditory likelihood and spatial prior
                %together, and normalize
                AuditorySolution=alike.*cprior/sum(alike.*cprior);

                %Take the max of the posterior
                [AuditoryMAP K] = max(AuditorySolution);
                sA_hat(1,i)=x(K);
            
            end
            
                %Load the aud-only conditions, and simulated aud-only
                %responses into the simulated data matrix
                sim(1:Ntrials,1)=NaN;
                sim(1:Ntrials,2)=sAind-4;
                sim(1:Ntrials,3)=NaN;
                sim(1:Ntrials,4)=sA_hat;
                simVA=[simVA; sim];
            
                %Create a histogram of the simulated data and normalize
                h=hist(sA_hat, range);
                freq_predA(sVind, sAind, :) = h/sum(h);
            
                %Compute the error for the aud-only conditions
                splineA = splineA + sum( log(max(spline(range,freq_predA(sVind, sAind, :),respA),0.00001)) );

        end
    end
end
        
error = -(splineV+splineA);

%go back to old initialization
rand('state',s1);
randn('state',s2);