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    Metadata details:
    filename: DEM_MDP_decision.m
    path of file: ./repos/spm/toolbox/DEM
    
    the code of the file until where you have to start completion: function MDP = DEM_MDP_decision
% Demo of active inference for visual salience
%__________________________________________________________________________
%
% This routine illustrates the treatment of signal detection paradigms in
% the context of active inference and Markov decision processes. This is
% probably one of the simplest paradigms to model; in which there are just
% too  hidden states generating ambiguous stimuli - and the agent move from
% an undecided (hidden) state to a definitive choice. The A tensor in this
% instanceen codes ambiguity (perceptual noise), while the B matrix encodes
% the behaviour-dependent transitions among decision states. Finally,
% the C matrix  encodes  prior costs or preferences. In this instance, the
% agent does not want to be wrong - and prefers to be right.

    
function MDP = DEM_MDP_decision
% Demo of active inference for visual salience
%__________________________________________________________________________
%
% This routine illustrates the treatment of signal detection paradigms in
% the context of active inference and Markov decision processes. This is
% probably one of the simplest paradigms to model; in which there are just
% too  hidden states generating ambiguous stimuli - and the agent move from
% an undecided (hidden) state to a definitive choice. The A tensor in this
% instanceen codes ambiguity (perceptual noise), while the B matrix encodes
% the behaviour-dependent transitions among decision states. Finally,
% the C matrix  encodes  prior costs or preferences. In this instance, the
% agent does not want to be wrong - and prefers to be right.
%
% in what follows, we simulate a single trial to illustrate the underlying
% Bayesian belief updating and associated behavioural and physiological
% responses. We then consider multiple trials under different levels of
% ambiguity and cost. The dependent measures in this instance include the
% behavioural accuracy, reaction times (assuming 250 ms time bins) and the
% uncertainty about the cause of sensory cues and control - as measured by
% the entropy of posterior beliefs prior to making a choice.
%
% see also: DEM_demo_MDP_rule.m and spm_MPD_VB_X.m
%__________________________________________________________________________

% Karl Friston
% Copyright (C) 2008-2022 Wellcome Centre for Human Neuroimaging

% set up and preliminaries
%==========================================================================

% [D]efault prior beliefs about initial states (in terms of counts): D
%--------------------------------------------------------------------------
D{1} = [1 1]';        % rule:   {'left','right'}
D{2} = [0 0 1]';      % report: {'left','right','undecided'}

% [A]mbiguous mapping from hidden states to outcomes: A
%--------------------------------------------------------------------------
Nf    = numel(D);
Ns    = zeros(1,Nf);
for f = 1:Nf
    Ns(f) = numel(D{f});
end