Courses
  /  
Descriptions
IEMS 401: Applied Mathematical Statistics

Quarter Offered

Fall : MF 9:30-10:50 ; Apley

Prerequisites

A previous course in statistics at the level of IEMS 303, plus comfort with basic linear algebra and basic probability

Description

Linear model theory with application to multiple regression and analysis of variance. Statistical inference methods, including likelihood estimation and testing, resampling, and the Bayesian approach.

LEARNING OBJECTIVES

  • Provide a sound theoretical basis for the fundamental principles for conducting general statistical inference
  • Prepare students to be able to derive appropriate methods of statistical inference when they encounter their own specialized research problems
  • Provide students with a proper context and solid background for undertaking more advanced study in statistical theory

TOPICS

  • Finding point estimators and test statistics: MLE, method of moments, likelihood ratio tests
  • Finding confidence regions and critical regions:  Inversion of hypotheses tests, asymptotic distribution of MLEs and LRTs, Monte Carlo and bootstrap methods
  • Optimality properties and limits of performance:  Cramer-Rao lower bound, efficiency, sufficient statistics, Rao-Blackwell theorem, most powerful tests
  • Prediction of random variables:  Minimum variance predictors, conditional mean predictors, linear predictors, Gauss-Markov theorem
  • Bayesian counterparts for statistical inference:  Prior and posterior distributions, Bayesian point estimators, credible regions, hypotheses tests, and predictors, loss, risk and decision theory, hierarchical Bayesian methods, conjugate priors, computational Bayesian methods

MATERIALS

Required: Hogg, R. V., Craig, A., and McKean, J. W., Introduction to Mathematical Statistics, 7/E, Pearson, 2013, ISBN-10: 0321795431; ISBN-13:  9780321795434