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Formula for posterior
posterior ∝ likelihood * prior
Formula for prior predictive distribution
p(ynew) = ∫(over θ) f(ynew|θ) * π(θ) dθ
Formula for posterior predictive distribution
p(ynew | yold) = ∫(over θ) f(ynew|θ, yold) * p(θ|yold) dθ