Outline

The probability approach to forecasting

Statistical vs Bayesian Approach

Bayesian Approach: Average case over distributions

Likelihoods and Priors

Example: Bernoulli Likelihood

Priors for the Bernoulli Likelihood

Inference

Bayes Rule

Obtaining Bayes Forecast from Bayes Rule

Interpretation

Choosing a Likelihood

Choosing a Prior

Prior and Posterior Predictions

Computing the Posterior

Computing Posterior Predictive Distribution and Bayes Forecast

Example: Beta-Bernoulli Posterior

Example Continued: Beta-Bernoulli Forecast

Example 2: Normal-Normal Model

Conclusion

Bonus: Gaussian Posterior Calculation