L1-inferencebasics

Introduction to bayesian inference bayesian inference

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Unformatted text preview: rst unit on inference. Introduction to Bayesian Inference Bayesian inference with chemistry Bayesian inference with neurons Sampling approaches to Bayesian inference. Nick Jones Inference, Control and Driving of Natural Systems What we’ll cover in this lecture A basic introduction that makes sure we’re on the same page. Bayes Theorem Evaluating Integrals Bayes Factors Examples of the above (applied lecture) Nick Jones Inference, Control and Driving of Natural Systems Components for Bayes Theorem Data, D . Hypothesized model structure, H. Model parameters, θ. Model p (D |θ, H) Nick Jones Inference, Control and Driving of Natural Systems Components for Bayes Theorem Data, D . Hypothesized model structure, H. Model parameters, θ. Model p (D |θ, H) Prior π (θ|H) Nick Jones Inference, Control and Driving of Natural Systems Components for Bayes Theorem Data, D . Hypothesized model structure, H. Model parameters, θ. Model p (D |θ, H) Prior π (θ|H) Posterior π (θ|D , H) Nick Jones Inference, Control and Driving of Natural Systems Components for Bayes Theorem Data, D . Hypothesized model structure, H. Model parameters, θ. Model p (D |θ, H) Prior π (θ|H) Posterior π (θ|D , H) Evidence or The Marginal Likelihood p (D |H) Nick Jones Inference, Control and Driving of Natural Systems Theorem Bayes Theorem π (θ|D , H) = p (D |θ, H)π (θ|H) p (D |H) Theorem Posterior over parameters = Data likelihood given parameters × Prior over parameters/Chance of data given model Nick Jones Inference, Control and Driving of Natural Systems Example elements of Bayes...
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