stepsFtoH.m

function output = stepsFtoH(x,confidence,binLimits, coherence, sigma)%sivaHack: Sigma passed in
    
    guessMu = x(1);
    guessSigma = x(2);
    guessK = x(3);

    % ==============================================
    % Step F: 

    %Preallocate matrix to hold lower limit (col 1) and upper limit (col 2) on
    %the decision variable (Xj lower and Xj upper)
    decisionVariableLimits = nan(length(confidence),2);

    %Use a loop to calculate the lower limt and upper limit of decision
    %variables
    for i = 1:length(confidence)

        % Make sure that all values are > 0 and < 1. If they are out of the range, pull
        % them back in
        binLimits(binLimits < 0) = 0.0000000000000001;
        binLimits(binLimits > 1) = 0.9999999999999999;
        
        
        %[askBrian] Is the below guessMu, or just set to 0? (Set to 0 in
        %cookbook, but maybe that's just for the first round. Because we
        %need it to vary when calculating maximum log likelihood, it makes
        %sense to make it vary. But even so, is it varied here or in Step G
        %below? (Makes sense to not do it there since it is for the "fitted
        %psychometric function"))
        % Lower limits
       decisionVariableLimits(i,1) = inverseCumulativeGaussian([0, guessK*sigma],binLimits(i,1)); %sivaHack: Sigma passed in, used to be guessSigma
       % Upper limits
       decisionVariableLimits(i,2) = inverseCumulativeGaussian([0, guessK*sigma],binLimits(i,2));%sivaHack: Sigma passed in, used to be guessSigma

       %[askBrian] Do we need this bound? (Probably not)
       %Values that are < -1 or > 1 are meaningless (i.e. coherence cannot be
       %less than -1 or more than 1)
       %If they are outside that range, then make them -1 or 1
       %decisionVariableLimits(decisionVariableLimits < -1) = -1;
       %decisionVariableLimits(decisionVariableLimits > 1) = 1;
    end


    % ==============================================
    % Step G: 


    %Calculate the probability of the specific confidence probability judgment
    %(Pj)
    %(Sj is the stimulus intensity/coherence at trial j)

    %Preallocate matrix to hold the confidence probability judgments for each
    %trial
    likelihood = nan(length(confidence),1);


    %Make a loop to go through each trial and calculate the
    %confidenceProbabilityJudgment (Pj)
    for i = 1:length(confidence)

        %Sj is the stimulus intensity/coherence at the current trial
        Sj = coherence(i);

        %Place lower and upper bounds of the confidence probability judgment
        %into variables for easy handling
        XjLower = decisionVariableLimits(i,1);
        XjUpper = decisionVariableLimits(i,2);

        %Calculate the upper and lower bound probabilities
        UpperLimitProbability = cumulativeGaussian(XjUpper,[Sj+guessMu, guessSigma]);
        LowerLimitProbability = cumulativeGaussian(XjLower,[Sj+guessMu, guessSigma]);

        %Calculate the probability for that interval and store it in the
        %likelihood array
        likelihood(i,1) = UpperLimitProbability - LowerLimitProbability;

    end
    
    logLikelihood = log(likelihood);
    
    %Since the fmincon seeks to minimize, but we want the logLikelihood 
    %to be maximized, we take the negative of the logLikelihood as the
    %output (to be minimized by fmincon)
    output = sum(-logLikelihood);

end