L1-inferencebasics

Hypothesized model structure h its a coin bernoulli

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Unformatted text preview: Theorem Data, D 3 Heads, 2 tails. Hypothesized model structure, H, it’s a coin (Bernoulli process). Model parameters, θ the bias of the coin (probability of a head). Model p (D |θ, H) = θ3 (1 − θ)2 Nick Jones Inference, Control and Driving of Natural Systems Example elements of Bayes Theorem Data, D 3 Heads, 2 tails. Hypothesized model structure, H, it’s a coin (Bernoulli process). Model parameters, θ the bias of the coin (probability of a head). Model p (D |θ, H) = θ3 (1 − θ)2 Prior π (θ|H) = Beta(1, 1) ∝ θ1−1 (1 − θ)1−1 (uniform on the range [0, 1]) Nick Jones Inference, Control and Driving of Natural Systems Example elements of Bayes Theorem Data, D 3 Heads, 2 tails. Hypothesized model structure, H, it’s a coin (Bernoulli process). Model parameters, θ the bias of the coin (probability of a head). Model p (D |θ, H) = θ3 (1 − θ)2 Prior π (θ|H) = Beta(1, 1) ∝ θ1−1 (1 − θ)1−1 (uniform on the range [0, 1]) Posterior π (θ|D , H) = Beta(1 + 3, 1 + 2) ∝ θ4−1 (1 − θ)3−1 Nick Jones Inference, Control and Driving of Natural Systems The Marginal Likelihood While the ﬁrst three expressions listed above are always presented and discussed, less is...
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