I. Bayesian econometrics

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model
• Some general issues in Bayesian inference
• 1. Statistical decision theory

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• Question once weve calculated the posterior
  distribution, what do we do with it?
• Answer Use it to make optimal decisions under
  uncertainty
• Example portfolio allocation problem

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• In general, Bayesian does not separate problem of
  how to estimate parameters from how to use the
  estimates-- goal is to calculate distribution,
  not point estimate.
• To give a parameter estimate rather than a
  distribution, Bayesian needs a loss function

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model
• Some general issues in Bayesian inference
• 1. Statistical decision theory
• 2. Large-sample properties of posterior
  distribution

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• Goal of this section
• A Bayesian is doing something with the data.
  How would a classical econometrician describe
  what that is?
• Example i.i.d. discrete data

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• Conclusion Bayesian posterior distribution
  collapses to a point mass around true value as
  sample size grows

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I. Bayesian econometrics

• C. Some general issues in Bayesian inference
• 1. Statistical decision theory
• 2. Large-sample properties of posterior
  distribution
• 3. Bayesian posterior distribution as
  approximation to asymptotic distribution of MLE

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I. Bayesian econometrics

• C. Some general issues in Bayesian inference
• 1. Statistical decision theory
• 2. Large-sample properties of posterior
  distribution
• 3. Bayesian posterior distribution as
  approximation to asymptotic distribution of MLE
• 4. Diffuse priors

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• Recommendation
• Use improper prior of Jeffreys prior only for
  guidance or checking
• Use mildly informative prior to avoid all
  problems