An Introduction to Bayesian Inference Michael Betancourt April 8,

Text Introduction to Bayesian Inference An Example

Text Introduction to Bayesian Inference The General Problem

Text Introduction to Bayesian Inference Estimators

Text Introduction to Bayesian Inference Estimators: An Example

Text Introduction to Bayesian Inference Estimators: The Danger

Text Introduction to Bayesian Inference Estimators: The Limitation

Text Introduction to Bayesian Inference Maximum Likelihood

Text Introduction to Bayesian Inference Maximum Log Likelihood

Text Introduction to Bayesian Inference Minimization

Text Introduction to Bayesian Inference Maximum Likelihood: An Example

Text Introduction to Bayesian Inference Maximum Likelihood Biases

Text Introduction to Bayesian Inference Maximum Likelihood Subtleties

Text Introduction to Bayesian Inference Bimodal Distributions

Text Introduction to Bayesian Inference Back to the Drawing Board

Text Introduction to Bayesian Inference Bayes Theorem

Text Introduction to Bayesian Inference A New Approach? The are not random variables!

Text Introduction to Bayesian Inference Frequentist Statistics

Text Introduction to Bayesian Inference Uncertainty of Belief

Text Introduction to Bayesian Inference ‣ Axiom One ‣ Axiom Two The Cox Axioms

Text Introduction to Bayesian Inference A New Approach!

Text Introduction to Bayesian Inference Selecting Priors

Text Introduction to Bayesian Inference Selecting Priors

Text Introduction to Bayesian Inference An Example

Text Introduction to Bayesian Inference An Example

Text Introduction to Bayesian Inference An Example Revisted

Text Introduction to Bayesian Inference Marginalization

Text Introduction to Bayesian Inference Marginalization: An Example

Text Introduction to Bayesian Inference Marginalization: An Example

Text Introduction to Bayesian Inference Frequentist vs. Bayesian

Text Introduction to Bayesian Inference Bayesian Inference in Practice Frequentist ➲ Bayesian Optimization ➲ Expectation (Differentiation) ➲ (Integration)

Text Introduction to Bayesian Inference The Opposition ‣ “Priors are Subjective, Science Isn’t”

Text Introduction to Bayesian Inference Application: Model Selection

Text Introduction to Bayesian Inference Application: Model Selection

Text Introduction to Bayesian Inference Application: Model Selection

Text Introduction to Bayesian Inference The Bayesian Razor

Text Introduction to Bayesian Inference Application: Systematics Energy Scale5% Background Subtraction1% Trigger Bias2% Luminosity4%...n% Total7%

Text Introduction to Bayesian Inference Application: Systematics

Text Introduction to Bayesian Inference Application: Nonparametric Estimation

Text Introduction to Bayesian Inference Further Reading ‣ Information Theory, Inference, and Learning Algorithms, ‣ MacKay, ‣ Data Analysis, ‣ Sivia with Skilling, Oxford 2006 ‣ Lectures on Probability, Entropy, and Statistical Physics, ‣ Caticha,