Introduction
Bayesian statistics is a branch of statistics that uses probability to quantify the degree of belief or uncertainty about an event or a parameter. Bayesian statistics allows us to update our beliefs based on new data or evidence, using a mathematical formula called Bayesian theorem. Bayesian statistics differs from classical or frequentist statistics, which interprets probability as the long-run frequency of an event in repeated trials, it
Classical statistics relies on hypothesis testing, confidence intervals, and -values to make inferences about unknown parameters or events. Bayesian statistics relies on prior distributions, posterior distributions, and credible intervals to make inferences about unknown parameters or events.
Contents
Bayesian Framework
Fisher Information
Priors
Sampling
Monte Carlo Methods
Posterior Inference
Posterior Asymptotics
References and Useful Resources
Acknowledgement
This part is mainly based on the AMSI Summer School course “Bayesian Inference and Computations” in 2024, by Prof. Yanan Fan and Dr. Ke Sun, and ANU course COMP4670 in 2023.