Likelihood Methods in Biology and Ecology: A Modern Approach to Statistics, 1st Edition (Hardback) book cover

Likelihood Methods in Biology and Ecology

A Modern Approach to Statistics, 1st Edition

By Michael Brimacombe

Chapman and Hall/CRC

202 pages | 50 B/W Illus.

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Description

Likelihood Methods in Biology and Ecology: A Modern Approach to Statistics emphasizes the importance of the likelihood function in statistical theory and applications and discusses it in the context of biology and ecology. Bayesian and frequentist methods both use the likelihood function and provide differing but related insights. This is examined here both through review of basic methodology and also the integrated use of these approaches in case studies.

Features:

  • Discusses the likelihood function in both Bayesian and frequentist contexts.
  • Reviews and discusses standard methods of data analysis, model selection and statistical analysis, and how to apply and interpret them in real world situations.
  • Examines the application of statistical methods to observed data in the context of case studies drawn from biology and ecology.
  • Uniquely discusses frequentist and Bayesian approaches to statistics as complementary allowing many standard approaches to be presented in a single book.
  • Poses questions to ask when planning the design and analysis of a study or experiment.

This book is written for applied researchers, scientists, consultants, statisticians and applied scientists. Although it uses examples drawn from biology, the methods here can be applied to a wide variety of research areas and provides an accessible handbook of available statistical methods for scientific settings where there is an assumed theoretical model that can be represented using a likelihood function.

Table of Contents

I Introduction

  1. Statistical Models in Scientific Research
  2. Statistics in Science

    Guidelines to Statistical Model Building

    Questions & Answers

    Basic Statistical Models

    Likelihood Function

    Frequentist Interpretation

    Bayesian Statistical Analysis and Interpretation

    A Comparative and Practically Integrated Approach

    Computing

    Bibliography

    Suggested Readings

    II Basic Tools for Data Analysis, Study Design and Model Development

  3. Data Analysis and Patterns
  4. Data Analysis, Beliefs and Statistical Models

    Basic Graphical and Visualization Tools

    Data in One-Dimension

    Example

    Example

    Data Patterns in Higher Dimensions: Correlations and Associations

    Example

    Principal Components Analysis

  5. Some Basic Concepts in the Design of Experiments
  6. Design of Experiments and Data Collection

    Simpsons Paradox

    Example

    Example

    Path Analysis

    Replication in The Design and Analysis of Experiments

    Replication and Modeling

    Fully Replicated Design in Single Overall Model

    Significance Issues

    Pseudo-Replication in Observational Studies

    Replication and Meta-Analysis

    Incorporating Expectations and Beliefs

  7. Prior Beliefs and Basic Statistical Models
  8. Selecting Prior Densities

    Subjective Priors

    Previous Likelihoods: A Source of Prior Information

    Jeffrey’s Prior

    Non-Informative and Improper priors

    Conjugate Priors

    Reference priors

    Elicitation

    Model Nonlinearity & Prior Selection

    Example : BOD Example

    Example : Whale Population Dynamics Example

    Selecting Parametric Models and Likelihoods

    Bibliography

    Questions

    Suggested Readings

    III Likelihood Based Statistical Theory and Methods:Frequentist and Bayesian

  9. Introduction to Frequentist Likelihood Based Statistical Theory
  10. Statistical Theory Related to Likelihoods

    Example: Normal Distribution

    Basic Statistical Models

    T-test

    ANOVA

    More on Linear Models

    Centering and Interaction Effects in Linear Models

    Example: Penrose Bodyfat

    High-Dimensional Linear Models

    Ridge Regression

    Generalized Linear Models

    Random Effects

    Nonlinear Models

    Model Mis-specification: Nonlinearity

    Introduction to Basic Survival Analysis

    Survival Analysis Modeling

    Linear Models in Survival Analysis

    Random Effects in Survival Settings

    Comparisons to Standard Methods:

    Estimation and Testing

    Assessing Significance

    Generic Bootstrap Procedure

  11. Introduction to Bayesian Statistical Methods
  12. Bayesian Approach to Statistical Modeling and Inference

    Priors & Posteriors

    Modeling Strategy

    Some Standard Prior Choices

    Example: Normal Sample

    Example: Linear Model

    Information Sensitive Priors

    Example

    Bayesian Estimation: Marginal Posteriors

    Normal Approximation

    Laplace Approximation

    Monte Carlo Probability Based Estimation

    Testing: Measures of Evidence

    Posterior Odds Ratios

    Bayes Factors

    Example: Linear Model

    Model Selection Criteria

    Model Averaging

    Predictive Probability

    Hierarchical Structures and Modeling Approaches

    Empirical Bayesian Approach

    Example: Two-Stage Normal Model

    High Dimensional Models and Related Statistical Models

    Summary

    Applying the Theory

    Bibliography

    Questions

    Suggested Readings

    IV Applications Using Bayesian and Frequentist Likelihood Methods in Biology and Ecology

  13. Case Studies: Bayesian and Frequentist Perspectives
  14. Preface

    Some Particulars

    Case Studies

  15. Biodiversity: Modeling Species Abundance
  16. Case Studies in Ecology

    Biodiversity: Modeling Species Abundance

    Science

    Data

    Specific Aims, Hypotheses and Models

    Analysis and Interpretation

    Data Analysis

    Likelihood Function

    Likelihood Frequentist Analysis

    Likelihood Bayesian Analysis

    Analysis/Integration/Comparisons

    Suggested Exercises

    Bibliography

  17. Soil Erosion in Relation to Season and Land Usage Patterns
  18. Science

    Data

    Specific Aims, Hypotheses and Models

    Analysis and Interpretation

    Data Analysis

    Likelihood Function

    Likelihood Frequentist Analysis

    Likelihood Bayesian Analysis

    Analysis/Integration/Comparisons

    Suggested Exercises

    Bibliography

  19. Immunity and Dose Response in Relation to Aquaculture
  20. Case Studies in Biology

    Science

    Data

    Specific Aims, Hypotheses, Models

    Analysis

    Data Analysis

    Likelihood function

    Likelihood Frequentist Analysis

    Likelihood Bayesian Analysis

    Analysis/Integration/Comparisons

    Suggested Exercises

  21. Patterns of Genetic Expression in Mouse Liver Cancer
  22. Science

    Data

    Specific Aims, Hypotheses and Models

    Analysis:

    Data Analysis

    Likelihood Function

    Likelihood Frequentist Analysis

    Likelihood Bayesian Analysis

    Analysis/Integration/Comparisons

    Suggested Exercises

  23. Antibiotic Resistance in Relation to Genetic Patterns in Tuberculosis

Science

Data

Specific Aims, Hypotheses, Models

Analysis

Data Analysis

Likelihood function

Likelihood Frequentist Analysis

Likelihood Bayesian Analysis

Analysis/Integration/Comparisons

Suggested Exercises

Bibliography

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
NAT010000
NATURE / Ecology