# Don't worry, be Happy

Sampling a smiley face likelihood function.

## Contents

- Smiley face equation
- Draw samples from the distribution using GWMCMC
- Important links

## 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