MATH 3465 Statistical Inference
This is a second course in Statistical Theory. The course may be thought of as a direct continuation of the introductory second year course Statistics I. This course is necessary to expose students to both classical and Bayesian inference which they would not have encountered in Statistics I. While Statistics I gives a relatively broad nontheoretical approach to statistics, this course completes the undergraduate statistical theory so that students can understand the underlying concepts in a more concise mathematical setting.
The course consists of three fairly distinct modules–frequentist inference, Bayesian inference and non-parametric methods. We continue the discussion of classical inference begun in Math 2275 Likelihood techniques are applied to a wide range of models. There is a fairly detailed discussion of unbiasedness and sufficiency. UMP and likelihood ratio tests are discussed. For Bayesian Inference, we introduce the ideas of subjective probability, prior and posterior distributions and the basics of Bayesian estimation and testing. In the short section on non-parametric methods we introduce the empirical distribution function and tests based on it. There is a brief introduction to inference on censored data and an introduction to the bootstrap.