An Introduction to Bayesian Inference Michael Betancourt April 8, 2009 8.882.
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Transcript of An Introduction to Bayesian Inference Michael Betancourt April 8, 2009 8.882.
An Introduction to Bayesian Inference
Michael BetancourtApril 8, 2009
8.882
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Introduction to Bayesian Inference
An Example
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Introduction to Bayesian Inference
The General Problem
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Introduction to Bayesian Inference
Estimators
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Introduction to Bayesian Inference
Estimators: An Example
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Introduction to Bayesian Inference
Estimators: The Danger
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Introduction to Bayesian Inference
Estimators: The Limitation
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Introduction to Bayesian Inference
Maximum Likelihood
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Introduction to Bayesian Inference
Maximum Log Likelihood
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Introduction to Bayesian Inference
Minimization
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Introduction to Bayesian Inference
Maximum Likelihood: An Example
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Introduction to Bayesian Inference
Maximum Likelihood Biases
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Introduction to Bayesian Inference
Maximum Likelihood Subtleties
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Introduction to Bayesian Inference
Bimodal Distributions
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Introduction to Bayesian Inference
Back to the Drawing Board
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Introduction to Bayesian Inference
Bayes Theorem
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Introduction to Bayesian Inference
A New Approach?
The are not random variables!
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Introduction to Bayesian Inference
Frequentist Statistics
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Introduction to Bayesian Inference
Uncertainty of Belief
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Introduction to Bayesian Inference
‣ Axiom One
‣ Axiom Two
The Cox Axioms
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Introduction to Bayesian Inference
A New Approach!
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Introduction to Bayesian Inference
Selecting Priors
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Introduction to Bayesian Inference
Selecting Priors
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Introduction to Bayesian Inference
An Example
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Introduction to Bayesian Inference
An Example
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Introduction to Bayesian Inference
An Example Revisted
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Introduction to Bayesian Inference
Marginalization
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Introduction to Bayesian Inference
Marginalization: An Example
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Introduction to Bayesian Inference
Marginalization: An Example
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Introduction to Bayesian Inference
Frequentist vs. Bayesian
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Introduction to Bayesian Inference
Bayesian Inference in Practice
Frequentist ➲ Bayesian
Optimization ➲ Expectation
(Differentiation) ➲ (Integration)
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Introduction to Bayesian Inference
The Opposition
‣“Priors are Subjective, Science Isn’t”
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Introduction to Bayesian Inference
Application: Model Selection
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Introduction to Bayesian Inference
Application: Model Selection
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Introduction to Bayesian Inference
Application: Model Selection
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Introduction to Bayesian Inference
The Bayesian Razor
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Introduction to Bayesian Inference
Application: Systematics
Energy Scale 5%
Background Subtraction 1%
Trigger Bias 2%
Luminosity 4%
... n%
Total 7%
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Introduction to Bayesian Inference
Application: Systematics
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Introduction to Bayesian Inference
Application: Nonparametric Estimation
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Introduction to Bayesian Inference
Further Reading
‣ Information Theory, Inference, and Learning Algorithms,
‣MacKay, http://www.inference.phy.cam.ac.uk/mackay/itila/
‣Data Analysis,
‣ Sivia with Skilling, Oxford 2006
‣ Lectures on Probability, Entropy, and Statistical Physics,
‣ Caticha, http://arxiv.org/abs/0808.0012v1