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Priors, Normal Models, Computing Posteriors

Priors, Normal Models, Computing Posteriors. st5219 : Bayesian hierarchical modelling lecture 2.2. The normal distribution. Stupid name. The normal distribution. Although data are normally not normal, the normal distribution is a popular model for data Assume normal distributions in:

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Priors, Normal Models, Computing Posteriors

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  1. Priors, Normal Models, Computing Posteriors st5219: Bayesian hierarchical modelling lecture 2.2

  2. The normal distribution Stupid name

  3. The normal distribution • Although data are normally not normal, the normal distribution is a popular model for data • Assume normal distributions in: • paired t tests • two sample t tests • ANOVAs • regression • multiple regression ++? • and use it as a limiting distribution for other models • We’ll look at how to deal with a single sample now • Next week: multiple normal data sets

  4. A normal model Board work

  5. Conjugate priors for a normal model • The normal-scaled inverse χ²(NSIχ²) distribution is conjugate for the normal distribution • If (μ,σ²)~NSIχ²(μ0, κ0, ν0, σ0²)and xi~N(μ,σ²) then(μ,σ²)|x ~ NSIχ²(μn, κn, νn, σn²) • Use geoR’sdinvchisq, rinvchisq for the inverse χ² bit • To sample NSIχ², • first draw σ² from Iχ²(μk, κk, νk, σk²) and • then μ |σ² from N(μk, σ²/κk) • See Gelman et al (2003) Bayesian Data Analysis Chapman & Hall

  6. In practice See computing posteriors (next section)

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