Table of Contents
Introduction to Bayesian Statistics
Introduction
Notation - 1: Observed Quantities
Classical Statistics: Relationships Among Observed Quantities
Notation - 2: [Unknown] Population Parameters
Notation - 3: [Unknown] Population Parameters
Classical Statistics: Relationships Among Population Parameters
Classical Statistics: Using Observed Quantities to Estimate Population Parameters
Binomial Distribution - 1
Binomial Distribution - 2
Poisson Distribution - 1
Poisson Distribution, m = rt = 0.1
Poisson Distribution, m = rt = 1
Poisson Distribution, m = rt = 3
Poisson Distribution, m = rt =10
Current Decision Level (a.k.a. Critical Level)
Standard Normal Distribution, m =0, s = 1
Cumulative Standard Normal Distribution
Current Decision Level (2)
Current Decision Level: General Case
The Difference of 2 Poissons
Difference of 2 Poissons with m = rt = 3
Difference of 2 Poissons with m = rt = 3
Difference of 2 Poissons with m = rt = 3
Test of Current DL: Definitions of Terms
Test of Current DL
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Current DL Fails Test
The Reverend Thomas Bayes 1702-1761
Conditional Probability
Bayesian Approach: An Identity
Bayesian Approach: Law of Total Probability 1
Bayesian Approach: Law of Total Probability 2
Bayesian Approach: The Prior Probability 1
Bayesian Approach: The Prior Probability 2
Philosophical Statement of Bayes’s Rule
Probability Density
Bayes’s Rule: Continuous Form
Use of the Posterior Probability Density
Bayesian Approach for Background Only
Bayesian Approach for Background Only
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Bayesian Approach
References for Bayesian N+1 Result Using a Flat Prior
Quasi-Bayesian Statistics: Relationships Among Observed Quantities
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Bayesian Approach for Background and Gross Counts: Joint Likelihood 1
Example of Joint Likelihood: mb = 3, mn = 3, so mg = 6
Bayesian Approach for Background and Gross Counts: Joint Likelihood 2
Bayesian Approach: Limitations
Other Decision Rules: Altshuler & Pasternak (1963, Eq. 15), Turner (1995)
Altshuler & Pasternak (1963) Turner (1995)
Other Decision Rules: Nicholson (1963), Sumerling & Darby (1981)
Nicholson (1963) Sumerling & Darby (1981)
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Conclusions (1)
Conclusions (2)
References
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