Summary
This chapter has been a culmination of the many ideas and concepts we have introduced in the previous three chapters. At the heart of this chapter is the idea that because data is random, predictive models that attempt to explain and use that data should be probabilistic. To build probabilistic models, we have had to learn about the probability distributions that describe the data and the distributions that describe the models. Specifically, we have had to learn about the following:
- Likelihood as the probability of data given a model
- How to use the likelihood to estimate model parameters via maximum likelihood
- Bayes’ theorem and about prior and posterior distributions
- How the posterior distribution quantifies the probability of the model parameters given the data or information we have received
- How we can use the posterior in Bayesian model averaging, or MAP estimation calculations
- How to perform those Bayesian model averaging and MAP estimation...
