Priors in the d2d framework

Prior knowledge about parameters can be considered as well. If knowledge is available, it is used as a penalisation term for individual parameters by setting

#!matlab

ar.type(jp)=1;

for a quadratic penalty which corresponds to a normal distributed prior.

#!matlab

ar.type(jp)=2;

can be used to switch from hard lower and upper boundaries to quadratic penalization if p exceeds the lower bounds ar.lb or the upper bounds ar.ub. The default weight of such a penalty is 0.1. Within the bounds, there is no penalty.

The third possibility is

#!matlab

ar.type(jp)=3;

for a L1 penalisation term. L1-penalization is frequently applied for model discrimination, i.e. for finding sparse models with a reduced number of parameters.

For type 1 and 3, one needs to further specify the mean and the standard deviation of the required distribution. These parameters can be set at

#!matlab

ar.mean(jp)

and

#!matlab

ar.std(jp)

Utilizing priors as described enables Bayesian parameter estimation by maximizing the posterior.

For information on how priors enter the objective function of the parameter estimation process, consider the wiki-section about Objective function, likelihood and chi-square.