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Lecture 3: Bayesian parameter estimates I.

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Page 1: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Lecture 3: Bayesian parameter estimates I.

Page 2: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

how to calculate Bayesian probabilities:

Page 3: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

how to calculate Bayesian probabilities:

Page 4: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

how to calculate Bayesian probabilities:

Page 5: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 6: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 7: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 8: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 9: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 10: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 11: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 12: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

%%syms nn nb xnum = x^nb*(1-x)^(nn-nb);denom = gamma(nn-nb+1)*gamma(nb+1)/gamma(nn+2);p = num/denom;p=x^nb*(1-x)^(nn-nb)/gamma(nn- nb+1)/gamma(nb+1)*gamma(nn+2);figure(30)ezplot(subs(p,[nn,nb],[35,15]),[0,1]);

%%

Matlab code:

Bayesian parameter estimates:

Page 13: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bayesian parameter estimates:

Page 14: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bernoulli distribution:

Page 15: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

Bernoulli distribution:

Page 16: Lecture 3: Bayesian parameter estimates I. · Bayes says posterior oc evidence x prior . Our next topic is Bayesian Estimation of Parameters. We'll ease into it with an example that

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