Introduction to Probability Theory and Statistics
Basic probability theory and statistical models and procedures for the analysis of genetic studies are covered in Chap. 1. This chapter starts with an introduction to basic distribution theory and common distributions that are used in the book, including the uniform, multinomial, normal, t-, F-, Beta, Gamma, chi-squared and hypergeometric distributions. The basic distributions for order statistics are also given. Several types of stochastic convergence used in the book are summarized. Maximum likelihood estimation and its large sample properties are discussed. Various tests, including the efficient Score test, likelihood ratio test and Wald test, are studied with or without nuisance parameters. Multiple testing issues related to testing association with multiple genetic markers and related to hypothesis testing with an unknown genetic model are briefly reviewed. This chapter also covers the Delta method, the EM algorithm, basic concepts of sample size and power calculations, and asymptotic relative efficiency.
KeywordsCovariance Black Ball
- 73.Elston, R.C., Johnson, W.D.: Basic Biostatistics for Genetists and Epidemiologists. Wiley, West Sussex (2008) Google Scholar
- 333.Zheng, G., Freidlin, B., Gastwirth, J.L.: Robust TDT-type candidate-gene association tests. Ann. Hum. Hered. 66, 145–155 (2002) Google Scholar
- 334.Zheng, G., Freidlin, B., Gastwirth, J.L.: Comparison of robust tests for genetic association using case-control studies. In: Rojo, J. (ed.) Optimality: The Second Erich L. Lehmann Symposium. Lecture Notes–Monograph Series, vol. 49, pp. 320–336. Institute of Mathematical Statistics, Beachwood (2006) Google Scholar