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A dog, who fell into the ocean of statistics, tries to write down his ideas and notes to save himself.

The Normal Model

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Tags: Bayesian Inference

The normal model

Inference for the mean, conditional on the variance

Joint inference for the mean and variance

posterior inference

and joint distribution can be

inverse-gamma distribution:

precision = $1/\sigma^2$

variance = $\sigma^2$

posterior inference

Bias, variance and mean squared error

Prior specification based on expectations

  • $t(y)=(y,y^2)$
  • $\phi = (\theta/\sigma^2,-(2\sigma^2)^{-1})$
  • $c(\phi)=\vert \phi_2\vert^{1/2}exp(\phi_1^2/(2\phi_2))$

a conjugate prior distribution

where $t_0=(E(Y), E(Y^2))$.

The normal model for non-normal data

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