N 2 for each i 1 n plug it into the likelihood

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Unformatted text preview: hod of performing inference even if relevant integrals are intractable. Algorithm 1 Use π (θ|H) to make many, N , draws of possible model parameters: {θ1 , ...θN }. 2 For each θi ∈ {θ1 , ...θN } plug it into the likelihood function (given data) fi = p (D |θi , H). 3 Given the set of {f1 , ...fN } and using an appropriate density estimation (e.g. a histogram, [1]) we will approximate π (θ|D , H) (if we normalize) increasingly well with N . We will be investigating more common methods in subsequent lectures. Nick Jones Inference, Control and Driving of Natural Systems Not covered but relevant to understanding inference 1 Improper priors: flat priors are not transformation invariant (not always a problem). 2 Jeffrey’s priors: are transformation invariant. [1] 3 The connection between The Marginal Likelihood and the Partition function in Statistical Physics. [3] 4 Bayesian Non-parametrics: Gaussian, Chinese Restaurant and Dirichlet Processes. Nick Jones Inference, Control and Driving of Natural Systems Topics covered Introduced Bayes Theorem with an emphasis on the Marginal Likelihood and an operational approach Elements of model comparison Simple evaluation of posteriors through simulation Nick Jones Inference, Control and Driving of Natural Systems Bibliography [1] L. Wasserman (2004). All of statistics: a concise course in statistical inference. Springer. [2] I. Murray and Z. Ghahramani Technical note: A note on the evidence and Bayesian Occams razor [3] D. J. C. MacKay. Information Theory, Inference, and Learning Algorithms. Cambridge University Press, 2003. [4] N. Friel and J. Wyse. Estimating the evidencea review. Statistica Neerlandica 66.3 (2012): 288-308. Nick Jones Inference, Control and Driving of Natural Systems...
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This document was uploaded on 03/01/2014 for the course EE 208 at Imperial College.

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