## STA215: Statistical Inference

Prof: | Robert L. Wolpert | |
*wolpert**@stat.duke.edu* (211c Old Chem, 684-3275) |

TA: | Enrique ter Horst Gomez | |
*enrique**@stat.duke.edu* (223a Old Chem, 684-4558) |

Class: | Mon & Wed 3:55-5:10pm |
| Soc/Psych 126 |

OH: | Tue 3:00-4:00pm |
| Old Chemistry
211c |

Text:
| Peter Bickel & Kjell Doksum, |
| Mathematical Statistics: Basic Ideas and
Selected Topics (2nd edn) |

Opt'l: | James Berger & Robert Wolpert, |
| The Likelihood Principle (2nd edn) |

| Andrew Gelman, John Carlin,
Hal Stern, & Don Rubin, |
| Bayesian Data Analysis |

| John Kalbfleisch & Ross Prentice, |
| The Statistical Analysis of Failure Time
Data |

| Erich Lehmann, |
| Theory of Point Estimation and
Testing Statistical Hypotheses |

### Description

This is a course about making inference using *statistics*, or
functions of observed data: this includes the (point and interval)
estimation of uncertain parameters and the testing of statistical
hypotheses. All three contemporary paradigms of inference (Likelihood,
Classical, Bayesian) are presented and compared; traditional properties
of estimators (bias, consistency, efficiency, sufficiency, etc.) and
tests (size, power, probability) are considered in detail. The emphasis
is perhaps 60% on frequentist methods, 30% on Bayesian methods, and 10%
on likelihoodist methods.
Students are assumed to be familiar with random variables and their
distributions from a calculus-based or (better) measure-theoretic
introduction to probability theory. Some problems and projects will
require computation; students should be or become familiar with either
S-Plus (some notes and an
intro are available, also in
an older but nice form (Contents, 1-29, 30-64, 65-85, Examples))
or Matlab (a
primer and intro are available), both
easier to use than compiled languages like Fortran or C.

Not all homework sets will be graded, but they should be turned in for
comment; Monday classes will begin with a class solution of two of the
preceeding week's problems. Here is at least a tentative
schedule, containing most of the topics below.

** OUTLINE -- course topics will include:** (look
here for a tentative schedule)

- Review of Probability (e.g. dist'ns)
- Likelihood Functions (notes)
- Likelihoodist, Bayes, & Frequentist (incl. Classical) Paradigms
- Exponential Families
- Sufficiency
- Observed & Expected (Fisher) Information
- Nuisance Parameters
- The Likelihood Principal
- Point & Interval Estimation
- Consistency
- Confidence & Credible Intervals
- Coverage Probability
- Frêchet (Cramér-Rao) Lower Bound
- Efficiency & Robustness

- Testing Statistical Hypotheses
- P-Values
- Posterior Probabilities
- Size & Power
- Neyman-Pearson Lemma