Posterior mean of conjugate Bayesian models
14 hours ago
- Bayesian data models provide an objective framework for updating prior beliefs with new data.
- The posterior mean is a weighted average of the prior mean and the data mean, with weights determined by precision.
- In the normal-normal model, precision is the reciprocal of variance; in the beta-binomial model, precision is sample size; in the gamma-Poisson model, precision is time.
- All three examples are conjugate models from the exponential family of probability distributions.