1D Generalized Gaussian

A 1D generalized Gaussian prior model can be specified using the ‘gaussian’ type prior model

prior{1}.type='gaussian';

A simple 1D Gaussian distribution with mean 10, and standard deviation 2, can be specified using

ip=1;
prior{ip}.type='gaussian';
prior{ip}.m0=10;
prior{ip}.std=2;

The norm of a generalized Gaussian can be set using the ‘norm’ field. A generalized 1D Gaussian with mean 10, standard deviation of 2, and a norm of 70, can be specified using (The norm is equivalent to the beta factor referenced in Wikipedia:Generalized_normal_distribution)

ip=2;
prior{ip}.type='gaussian';
prior{ip}.m0=10;
prior{ip}.std=2;
prior{ip}.norm=70;

A 1D distribution with an arbitrary shape can be defined by setting d_target, which must contain a sample of the distribution that one would like to replicate. For example, to generate a sample from a non-symmetric bimodal distribution, one can use e.g.

% Create target distribution
N=10000;
prob_chan=0.3;
d1=randn(1,ceil(N*(1-prob_chan)))*.5+8.5;
d2=randn(1,ceil(N*(prob_chan)))*.5+11.5;
d_target=[d1(:);d2(:)];

% set the target distribution
ip=3;
prior{ip}.type='gaussian';
prior{ip}.d_target=d_target;

The following figure shows the 1D histogram of a sample, consisting of 8000 realizations, generated using

sippi_plot_prior_sample(prior,1:ip,8000);