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Genere:Libro

Lingua: Inglese

Editore: **Chapman and Hall/CRC**

Pubblicazione: 12/2017

Edizione: 1° edizione

**Big Data in Omics and Imaging: Association Analysis** addresses the recent development of association analysis and machine learning for both population and family genomic data in sequencing era. It is unique in that it presents both hypothesis testing and a data mining approach to holistically dissecting the genetic structure of complex traits and to designing efficient strategies for precision medicine. The general frameworks for association analysis and machine learning, developed in the text, can be applied to genomic, epigenomic and imaging data.

**FEATURES**

Bridges the gap between the traditional statistical methods and computational tools for small genetic and epigenetic data analysis and the modern advanced statistical methods for big data

Provides tools for high dimensional data reduction

Discusses searching algorithms for model and variable selection including randomization algorithms, Proximal methods and matrix subset selection

Provides real-world examples and case studies

Will have an accompanying website with R code

The book is designed for graduate students and researchers in genomics, bioinformatics, and data science. It represents the paradigm shift of genetic studies of complex diseases– from shallow to deep genomic analysis, from low-dimensional to high dimensional, multivariate to functional data analysis with next-generation sequencing (NGS) data, and from homogeneous populations to heterogeneous population and pedigree data analysis. Topics covered are: advanced matrix theory, convex optimization algorithms, generalized low rank models, functional data analysis techniques, deep learning principle and machine learning methods for modern association, interaction, pathway and network analysis of rare and common variants, biomarker identification, disease risk and drug response prediction.

**Mathematical Foundation**

**Sparsity-Inducing Norms, Dual Norms and Fenchel Conjugate**

**Subdifferential**

Definition of Subgradient

Subgradients of differentiable functions

Calculus of subgradients

**Proximal Methods**

Introduction

Basics of Proximate Methods

Properties of the Proximal Operator

Proximal Algorithms

Computing the Proximal Operator

**Matrix Calculus**

Derivative of a Function with Respect to a Vector

Derivative of a Function with Respect to a Matrix

Derivative of a Matrix with Respect to a Scalar

Derivative of a Matrix with Respect to a Matrix or a Vector

Derivative of a Vector Function of a Vector

Chain Rules

Widely Used Formulae

**Functional Principal Component Analysis (FPCA)**

Principal Component Analysis (PCA)

Basic Mathematical Tools for Functional Principal Component Analysis

Unsmoothed Functional Principal Component Analysis

Smoothed Principal Component Analysis

Computations for the Principal Component Function and the Principal Component Score

**Canonical Correlation Analysis**

**Exercises**

**Appendix**

**Linkage Disequilibrium**

**Concepts of Linkage Disequilibrium**

**Measures of Two-locus Linkage Disequilibrium**

Linkage Disequilibrium Coefficient D

Normalized Measure of Linkage Disequilibrium

Correlation Coefficient r

Composite Measure of Linkage Disequilibrium

The Relationship Between the Measure of LD and Physical Distance

**Haplotype Reconstruction**

Clark’s Algorithm

EM algorithm

Bayesian and Coalescence-based Methods

**Multi-locus Measures of Linkage Disequilibrium**

Mutual Information Measure of LD

Multi-Information and Multi-locus Measure of LD

Joint Mutual Information and a Measure of LD between a Marker and a Haplotype Block or Between Two Haplotype Blocks

Interaction Information

Conditional Interaction Information

Normalized Multi-Information

Distribution of Estimated Mutual Information, Multi-information and Interaction Information

*Canonical Correlation Analysis Measure for LD between Two Genomic Regions*

Association Measure between Two Genomic Regions Based on CCA

Relationship between Canonical Correlation and Joint Information

**Software Package**

**Bibliographical Notes**

**Appendices**

**Exercises**

**Association Studies for Qualitative Traits**

*Population-based Association Analysis for Common Variants*

Introduction

The Hardy-Weinberg Equilibrium

Genetic Models

Odds Ratio

Single Marker Association Analysis

Multi-marker Association Analysis

**Population-based Multivariate Association Analysis for Next-generation Sequencing**

Multivariate Group Tests

Score Tests and Logistic Regression

Application of Score Tests for Association of Rare Variants

Variance-component Score Statistics and Logistic Mixed Effects Models

**Population-based Functional Association Analysis for Next-generation Sequencing**

Introduction

Functional Principal Component Analysis for Association Test

Smoothed Functional Principal Component Analysis for Association Test

**Software Package**

**Appendices**

**Exercises**

**Association Studies for Quantitative Traits****Fixed Effect Model for a Single Trait**

Introduction

Genetic Effects

Linear Regression for a Quantitative Trait

Multiple Linear Regression for a Quantitative Trait

**Gene-based Quantitative Trait Analysis**

Functional Linear Model for a Quantitative Trait

Canonical Correlation Analysis for Gene-based Quantitative Trait Analysis

**Kernel Approach to Gene-based Quantitative Trait Analysis**

Kernel and RKHS

Covariance Operator and Dependence Measure

**Simulations and Real Data Analysis**

Power Evaluation

Application to Real Data Examples

**Software Package**

**Appendices**

**Exercises**

**Multiple Phenotype Association Studies****Pleiotropic Additive and Dominance Effects**

**Multivariate Marginal Regression**

Models

Estimation of Genetic Effects

Test Statistics

**Linear Models for Multiple Phenotypes and Multiple Markers**

Multivariate Multiple Linear Regression Models

Multivariate Functional Linear Models for Gene-based Genetic Analysis of Multiple Phenotypes

**Canonical Correlation Analysis for Gene-based Genetic Pleiotropic Analysis**

Multivariate Canonical Correlation Analysis (CCA)

Kernel CCA

Functional CCA

Quadratically Regularized Functional CCA

**Dependence Measure and Association Tests of Multiple Traits**

**Principal Component for Phenotype Dimension Reduction**

Principal Component Analysis

Kernel Principal Component Analysis

Quadratically Regularized PCA or Kernel PCA

**Other Statistics for Pleiotropic Genetics Analysis**

Sum of Squared Score Test

Unified Score-based Association Test (USAT)

Combining Marginal Tests

FPCA-based Kernel Measure Test of Independence

**Connection between Statistics**

**Simulations and Real Data Analysis**

Type Error Rate and Power Evaluation

Application to Real Data Example

**Software Package**

**Appendices **

**Exercises**

**Family-based Association Analysis**

**Genetic Similarity and Kinship Coefficients**

Kinship Coefficients

Identity Coefficients

Relation between identity coefficients and kinship coefficient

Estimation of Genetic Relations from the Data

**Genetic Covariance between Relatives**

Assumptions and Genetic Models

Analysis for Genetic Covariance between Relatives

**Mixed Linear Model for a Single Trait**

Genetic Random Effect

Mixed Linear Model for Quantitative Trait Association Analysis

Estimating Variance Components

Hypothesis Test in Mixed Linear Models

Mixed Linear Models for Quantitative Trait Analysis with Sequencing Data

**Mixed Functional Linear Models for Sequence-based Quantitative Trait Analysis**

Mixed Functional Linear Models (Type )

Mixed Functional Linear Models (Type : Functional Variance Component Models)

**Multivariate Mixed Linear Model for Multiple Traits**

Multivariate Mixed Linear Model

Maximum Likelihood Estimate of Variance Components

REML Estimate of Variance Components

**Heritability**

Heritability Estimation for a Single Trait

Heritability Estimation for Multiple Traits

**Momiao Xiong**, is a professor in the Department of Biostatistics, University of Texas School of Public Health, and a regular member in the Genetics & Epigenetics (G&E) Graduate Program at The University of Texas MD Anderson Cancer Center, UTHealth Graduate School of Biomedical Science.

ISBN: **9781498725781**

Condizione: Nuovo

Collana: Chapman & Hall/CRC Mathematical and Computational Biology

Dimensioni: 10 x 7 in Ø 3.70 lb

Formato: Copertina rigida

Illustration Notes:3 b/w images, 60 color images and 26 tables

Pagine Arabe: 668

Pagine Romane: xxxii

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Capitale sociale in euro: deliberato 4.000.000,00; sottoscritto: 4.000.000,00; versato: 4.000.000,00.

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