Don't worry, be Happy
=======================================

Sampling a smiley face likelihood function.



Smiley face equation
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Formulate a likelihood function inspired by an equation of a smiley face.

Source Michael Borcherds: https:\#\#twitter.com\#mike_geogebra\#status\#135391208703930369

```matlab
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.

```matlab
[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!"');
```

![IMAGE](ex_behappy_01.png)


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

