Bayesian Inference. Ekaterina Lomakina TNU seminar: Bayesian inference 1 March 2013. Outline. Probability distributions Maximum likelihood estimation Maximum a posteriori estimation Conjugate priors Conceptualizing models as collection of priors Noninformative priors Empirical Bayes.
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TNU seminar: Bayesian inference
1 March 2013
Bean machine by Sir Francis Galton
– data are i.i.d
– monotonic transformation
– simple average
Posterior distribution is given by
– weighted average
Binomial – Beta
Multinomial – Dirichlet
Gaussian – Gaussian (for mean)
Gaussian – Gamma (for precision)
Exponential – Gamma
is given by
where l = N – m, simply the number of “tails”.
Where yn is some function of xn
Compute p(θ|X,λ) given fixed λ*