*Shuo Jiao*

- Published in print:
- 2016
- Published Online:
- May 2017
- ISBN:
- 9780262034685
- eISBN:
- 9780262335522
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262034685.003.0004
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter presents set-based approaches that focus on identifying G X E interactions rather than set-based approaches that are based primarily on detecting G main effects (e.g., via marginal ...
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This chapter presents set-based approaches that focus on identifying G X E interactions rather than set-based approaches that are based primarily on detecting G main effects (e.g., via marginal effects). The author reviews both his own research and the development of his Set Based Gene EnviRonment InterAction test (SBERIA), as well as another set-based G X E approach referred to as GESAT. GESAT extends the variance component test of the SNP-set Kernel Association Test (SKAT) to evaluate G x E effects while incorporating the main SNP effects as covariates. While both of these approaches (SBERIA and GESAT) have outperformed other benchmark methods (e.g., likelihood ratio test) and have been demonstrated to retain the appropriate Type 1 error rate, in this chapter the author conducts simulation studies to compare findings for SBERIA and GESAT approaches, and identifies associated strengths and limitations of the respective methods.Less

This chapter presents set-based approaches that focus on identifying G X E interactions rather than set-based approaches that are based primarily on detecting G main effects (e.g., via marginal effects). The author reviews both his own research and the development of his Set Based Gene EnviRonment InterAction test (SBERIA), as well as another set-based G X E approach referred to as GESAT. GESAT extends the variance component test of the SNP-set Kernel Association Test (SKAT) to evaluate G x E effects while incorporating the main SNP effects as covariates. While both of these approaches (SBERIA and GESAT) have outperformed other benchmark methods (e.g., likelihood ratio test) and have been demonstrated to retain the appropriate Type 1 error rate, in this chapter the author conducts simulation studies to compare findings for SBERIA and GESAT approaches, and identifies associated strengths and limitations of the respective methods.

*Ziheng Yang*

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199602605
- eISBN:
- 9780191782251
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199602605.003.0012
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This chapter introduces computer simulation and in particular simulation of the molecular evolutionary process. It covers the generation of random numbers as well as other discrete and continuous ...
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This chapter introduces computer simulation and in particular simulation of the molecular evolutionary process. It covers the generation of random numbers as well as other discrete and continuous random variables. The chapter then discusses the simulation of the Poisson process, the variable-rate Poisson process, and discrete-time and continuous-time Markov chains. Different strategies for simulating sequence alignments through molecular evolution are then discussed.Less

This chapter introduces computer simulation and in particular simulation of the molecular evolutionary process. It covers the generation of random numbers as well as other discrete and continuous random variables. The chapter then discusses the simulation of the Poisson process, the variable-rate Poisson process, and discrete-time and continuous-time Markov chains. Different strategies for simulating sequence alignments through molecular evolution are then discussed.

*M. D. Edge*

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198827627
- eISBN:
- 9780191866463
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827627.003.0001
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

There are two traditional ways to learn statistics. One way is to pass over the mathematical underpinnings and focus on developing relatively shallow knowledge about a wide variety of statistical ...
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There are two traditional ways to learn statistics. One way is to pass over the mathematical underpinnings and focus on developing relatively shallow knowledge about a wide variety of statistical procedures. Another is to spend years learning the mathematics necessary for traditional mathematical approaches to statistics. For many people who need to analyze data, neither of these paths is sufficient. The shallow-but-wide approach fails to provide students with the foundation that allows for confidence and creativity in analyzing modern datasets, and many researchers—though possibly motivated to learn math—do not have the background to start immediately on a traditional mathematical approach. This book exists to help researchers jump between tracks, providing motivated students whose knowledge of mathematics may be incomplete or rusty with a serious introduction to statistics that allows further study from more mathematical sources. This is done by focusing on a single statistical technique that is fundamental to statistical practice—simple linear regression—and supplementing the exposition with ample simulations conducted in the statistical programming language R. The first half of the book focuses on preliminaries, including the use of R and probability theory, whereas the second half covers statistical estimation and inference from semiparametric, parametric, and Bayesian perspectives.Less

There are two traditional ways to learn statistics. One way is to pass over the mathematical underpinnings and focus on developing relatively shallow knowledge about a wide variety of statistical procedures. Another is to spend years learning the mathematics necessary for traditional mathematical approaches to statistics. For many people who need to analyze data, neither of these paths is sufficient. The shallow-but-wide approach fails to provide students with the foundation that allows for confidence and creativity in analyzing modern datasets, and many researchers—though possibly motivated to learn math—do not have the background to start immediately on a traditional mathematical approach. This book exists to help researchers jump between tracks, providing motivated students whose knowledge of mathematics may be incomplete or rusty with a serious introduction to statistics that allows further study from more mathematical sources. This is done by focusing on a single statistical technique that is fundamental to statistical practice—simple linear regression—and supplementing the exposition with ample simulations conducted in the statistical programming language R. The first half of the book focuses on preliminaries, including the use of R and probability theory, whereas the second half covers statistical estimation and inference from semiparametric, parametric, and Bayesian perspectives.