Inference
1
Inference
2
Deriving Point Estimates
2.1
Bayesian Inference
2.1.1
Mechanics
2.1.2
Example: Poisson Distribution
2.1.3
Remarks
2.1.4
Exercises
2.2
Method of Moments
2.2.1
Mechanics
2.2.2
Example: Gamma Distribution
2.2.3
Example: Toothpaste Cap Problem
2.2.4
Example: Population Average
2.2.5
Example: Population Average and SD
2.2.6
Example: German Tank Problem
2.2.7
Remarks
2.2.8
Exercises
2.3
Maximum Likelihood
2.3.1
Mechanics
2.3.2
Example: Toothpaste Cap Problem
2.3.3
Example: German Tank Problem
2.3.4
Example: Poisson Distribution
2.3.5
Remarks
2.3.6
Exercises
3
Evaluating Point Estimates
3.1
Bias
3.1.1
Example: Sample Average
3.1.2
Example: Poisson Distribution
3.2
Consistency
3.3
MVUE or BUE
3.4
Exercises
4
Deriving Hypothesis Test
4.1
The Null (and Alternative) Hypothesis
4.1.1
The Most Common Null Hypotheses
4.1.2
Errors
4.2
Test Statistics
4.2.1
Power Function
4.2.2
The Likelihood Ratio Test
4.2.3
Wald Test
4.3
Evaluating Tests
4.4
Size of the LRT
4.4.1
p
-Values
4.4.2
Size of the Wald Test
4.4.3
Size of the
5
Ways to Find a Confidence Interval
5.0.1
Bayesian Tests
6
Appendix: Code for Beta Prior
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Inference in Six Lessons
4.3
Evaluating Tests