function c = tapas_hgf_jget_config
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Contains the configuration for the Hierarchical Gaussian Filter (HGF) model for the jumping
% Gaussian estimation task (JGET).
%
% The HGF is the model introduced in
%
% Mathys C, Daunizeau J, Friston, KJ, and Stephan KE. (2011). A Bayesian foundation
% for individual learning under uncertainty. Frontiers in Human Neuroscience, 5:39.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% The HGF configuration consists of the priors of parameters and initial values. All priors are
% Gaussian in the space where the quantity they refer to is estimated. They are specified by their
% sufficient statistics: mean and variance (NOT standard deviation).
%
% Quantities are estimated in their native space if they are unbounded (e.g., the omegas). They are
% estimated in log-space if they have a natural lower bound at zero (e.g., the sigmas).
%
% Parameters can be fixed (i.e., set to a fixed value) by setting the variance of their prior to
% zero. Aside from being useful for model comparison, the need for this arises whenever the scale
% and origin at the j-th level are arbitrary. This is the case if the observation model does not
% contain the representations mu_j and sigma_j. A choice of scale and origin is then implied by
% fixing the initial value mu_j_0 of mu_j and either kappa_j-1 or omega_j-1.
%
% Fitted trajectories can be plotted by using the command
%
% >> tapas_hgf_jget_plotTraj(est)
%
% where est is the stucture returned by fitModel. This structure contains the estimated
% perceptual parameters in est.p_prc and the estimated trajectories of the agent's
% representations (cf. Mathys et al., 2011). Their meanings are:
%
% est.p_prc.mux_0 row vector of initial values of mu_x (in ascending order of levels)
% est.p_prc.sax_0 row vector of initial values of sigma_x (in ascending order of levels)
% est.p_prc.mua_0 row vector of initial values of mu_alpha (in ascending order of levels)
% est.p_prc.saa_0 row vector of initial values of sigma_alpha (in ascending order of levels)
% est.p_prc.kau kappa_u
% est.p_prc.omu omega_u
% est.p_prc.kax row vector of kappa_x (in ascending order of levels)
% est.p_prc.omx row vector of omega_x (in ascending order of levels)
% est.p_prc.kaa row vector of kappa_alpha (in ascending order of levels)
% est.p_prc.oma row vector of omega_alpha (in ascending order of levels)
%
% est.traj.mux mux (rows: trials, columns: levels)
% est.traj.sax sigma_x (rows: trials, columns: levels)
% est.traj.muxhat prediction of mu_x (rows: trials, columns: levels)
% est.traj.saxhat precisions of predictions of x (rows: trials, columns: levels)
% est.traj.wx weighting factors for x (rows: trials, columns: levels)
% est.traj.dax volatility prediction errors in x (rows: trials, columns: levels)
% est.traj.mua mu_alpha (rows: trials, columns: levels)
% est.traj.saa sigma_alpha (rows: trials, columns: levels)
% est.traj.muahat prediction of mu_alpha (rows: trials, columns: levels)
% est.traj.saahat precisions of predictions of alpha (rows: trials, columns: levels)
% est.traj.wa weighting factors for alpha (rows: trials, columns: levels)
% est.traj.daa volatility prediction errors in alpha (rows: trials, columns: levels)
% est.traj.dau input prediction error
%
%
%
% Tips:
% - If you get an error saying that the prior means are in a region where model assumptions are
% violated, lower the prior means of the omegas, starting with the highest level and proceeding
% downwards.
%
% - Alternatives are lowering the prior means of the kappas, if they are not fixed, or adjusting
% the values of the kappas or omegas, if any of them are fixed.
%
% - If the log-model evidence cannot be calculated because the Hessian poses problems, look at
% est.optim.H and fix the parameters that lead to NaNs.
%
% - Your guide to all these adjustments is the log-model evidence (LME). Whenever the LME increases
% by at least 3 across datasets, the adjustment was a good idea and can be justified by just this:
% the LME increased, so you had a better model.
%
% --------------------------------------------------------------------------------------------------
% Copyright (C) 2013-2014 Christoph Mathys, TNU, UZH & ETHZ
%
% This file is part of the HGF toolbox, which is released under the terms of the GNU General Public
% Licence (GPL), version 3. You can redistribute it and/or modify it under the terms of the GPL
% (either version 3 or, at your option, any later version). For further details, see the file
% COPYING or <http://www.gnu.org/licenses/>.
% Config structure
c = struct;
% Model name
c.model = 'hgf_jget';
% Number of levels (minimum: 2)
c.n_levels = 2;
% Input intervals
% If input intervals are irregular, the last column of the input
% matrix u has to contain the interval between inputs k-1 and k
% in the k-th row, and this flag has to be set to true
c.irregular_intervals = false;
% Sufficient statistics of Gaussian parameter priors
% PLACEHOLDER VALUES
% It is often convenient to set some priors to values
% derived from the inputs. This can be achieved by
% using placeholder values. The available placeholders
% are:
%
% 99991 Value of the first input
% Usually a good choice for mux_0mu(1)
% 99992 Variance of the first 20 inputs
% Usually a good choice for mux_0sa(1)
% 99993 Log-variance of the first 20 inputs
% Usually a good choice for logsax_0mu(1) and mua_0mu(1)
% 99994 Log-variance of the first 20 inputs minus two
% Usually a good choice for omxmu(1)
% Initial mus and sigmas
% Format: row vectors of length n_levels
% For all but the first level, this is usually best
% kept fixed to 1 (determines origin on x_i-scale).
c.mux_0mu = [99991, 1];
c.mux_0sa = [ 0, 0];
c.logsax_0mu = [log(3), log(0.1)];
c.logsax_0sa = [ 0, 0];
c.mua_0mu = [log(1), 1];
c.mua_0sa = [ 0.1, 0];
c.logsaa_0mu = [log(3), log(0.1)];
c.logsaa_0sa = [ 0, 0];
% Kappas
% Format: row vector of length n_levels-1 (except kappa_u: scalar)
% This should be fixed (preferably to 1) if the observation model
% does not use mu_i+1 (kappa then determines the scaling of x_i+1).
c.logkaumu = log(1);
c.logkausa = 0;
c.logkaxmu = [log(1)];
c.logkaxsa = [ 0];
c.logkaamu = [log(1)];
c.logkaasa = [ 0];
% Omegas
% Format: row vector of length n_levels (except omega_u: scalar)
c.omumu = 0;
c.omusa = 0;
c.omxmu = [ 0, -7];
c.omxsa = [5^2, 1];
c.omamu = [ 0, -7];
c.omasa = [5^2, 1];
% Gather prior settings in vectors
c.priormus = [
c.mux_0mu,...
c.logsax_0mu,...
c.mua_0mu,...
c.logsaa_0mu,...
c.logkaumu,...
c.logkaxmu,...
c.logkaamu,...
c.omumu,...
c.omxmu,...
c.omamu,...
];
c.priorsas = [
c.mux_0sa,...
c.logsax_0sa,...
c.mua_0sa,...
c.logsaa_0sa,...
c.logkausa,...
c.logkaxsa,...
c.logkaasa,...
c.omusa,...
c.omxsa,...
c.omasa,...
];
% Check whether we have the right number of priors
expectedLength = 8*c.n_levels;
if length([c.priormus, c.priorsas]) ~= 2*expectedLength;
error('tapas:hgf:PriorDefNotMatchingLevels', 'Prior definition does not match number of levels.')
end
% Model function handle
c.prc_fun = @tapas_hgf_jget;
% Handle to function that transforms perceptual parameters to their native space
% from the space they are estimated in
c.transp_prc_fun = @tapas_hgf_jget_transp;
return;