ex_behappy.m

%% Don't worry, be Happy
%
% Sampling a smiley face likelihood function.
% 

%% Smiley face equation
% Formulate a likelihood function inspired by an equation of a smiley face.
%  
% Source Michael Borcherds: https://twitter.com/mike_geogebra/status/135391208703930369

logHappiness=@(m)1-exp(1e-4*((m(1)^4+2*m(1)^2*m(2)^2-0.3*m(1)^2*m(2)-40.75*m(1)^2+m(2)^4-m(2)^3-40.75*m(2)^2+25*m(2)+393.75)*((m(1)+3)^2+(m(2)-7)^2-1)*((m(1)-3)^2+(m(2)-7)^2-1)*(m(1)^2+(m(2)-2)^2-64)));


%% Draw samples from the distribution using GWMCMC
%
% Now we apply the MCMC hammer to draw samples from the logHappiness distribution.
%

[models,logP]=gwmcmc(randn(2,100),logHappiness,100000,'ThinChain',2);
models(:,:,1:end*.2)=[];
models=models(:,:)';


plot(models(:,1),models(:,2),'yo','markerfacecolor',[1 1 0]*.8);

axis equal off 


title('GWMCMC says: "Don''t Worry, Be Happy!"');


%% Important links
% Bobby McFerrin on youtube: https://www.youtube.com/watch?v=d-diB65scQU