Likelihood Methods in Biology and Ecology: A Modern Approach to Statistics

ISBN-13: 9781584887881 / Angielski / Twarda / 2019 / 202 str.

Brimacombe Michael

Opis

Using an integrated and comparative approach, this book provides a guide to the development, application, and interpretation of Bayesian statistical methods to real-world scientific problems in ecology and biology. It presents an overview of likelihood-bas

Recenzje

"The book under review is targeted at applied scientists with a focus on explaining the applications of different statistical methods based on the likelihood... This book provides particular emphasis on the interpretability aspects of statistics for its use by an applied scientist for the analysis of their research data without a
background in statistics or mathematics. To me, the book mostly succeeds to fulfil this objective. Although it is surely difficult to provide a comprehensive overview of all modelling issues and the corresponding statistical methods under one book of around 200 pages, the author has done a pretty good job of covering the most important issues related to likelihood based inference... In this book, the author has avoided the question of superiority of inferiority of any particular statistical paradigm and discussed the applications of both frequentist and Bayesian methods simultaneously to answer a scientific question by combining both results... All of the case studies are nicely present to provide ideas of different issues in a data analysis process and their solutions based on likelihood based statistical procedures... Overall, this is a great effort in the difficult task of writing a book on statistical inferences for applied scientists from different disciplines and I want to thank the author for such a great job."
- Abhik Ghosh, ISCB December 2019

Spis treści

          I Introduction

1. Statistical Models in Scientific Research

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

2. Data Analysis and Patterns

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

3. Some Basic Concepts in the Design of Experiments

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

4. Prior Beliefs and Basic Statistical Models

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

5. Introduction to Frequentist Likelihood Based Statistical Theory

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

6. Introduction to Bayesian Statistical Methods

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

7. Case Studies: Bayesian and Frequentist Perspectives

Preface

Some Particulars

Case Studies

8. Biodiversity: Modeling Species Abundance

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

9. Soil Erosion in Relation to Season and Land Usage Patterns

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

10. Immunity and Dose Response in Relation to Aquaculture

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

11. Patterns of Genetic Expression in Mouse Liver Cancer

Science

Data

Specific Aims, Hypotheses and Models

Analysis:

Data Analysis

Likelihood Function

Likelihood Frequentist Analysis

Likelihood Bayesian Analysis

Analysis/Integration/Comparisons

Suggested Exercises

12. 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

 

O autorze

Michael Brimacombe