## STA215: Statistical Inference

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

TA: | Merrill Liechty | |
*merrill**@stat.duke.edu* (222 Old Chem, 684-8088) |

Class: | Tue & Thu 2:15-3:30pm |
| Old Chemistry
025 |

OH: | Mon 3:45-5:00pm Fri 2:15-3:15pm |
| 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) |

| George Casella & Roger Berger, |
| Statistical Inference |

| 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 |

| Tom Leonard & John Hsu, |
| Bayesian Methods |

| Anthony O'Hagan, |
| Kendall's Advanced Theory of Statistics,
v2B: Bayesian Inference |

Comp: | Phil Spector, |
| An Introduction to S and S-Plus |

### 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; traditional properties of estimators
(bias, consistency, efficiency, sufficiency, etc.) and tests (size,
power, probability) are considered in detail.
Students are assumed to be familiar with random variables and their
distributions from a calculus-based or 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), as well as the optional text
by Spector listed above) or Matlab (a primer and intro are available), both
easier to use than compiled languages like f77, c, or c++.

Not all homework sets will be graded, but they should be turned in for
comment; Tuesday 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