Modes of Parametric Statistical Inference 1st Edition by Seymour Geisser, Wesley M.Johnson ISBN 0471667269 9780471667261

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ISBN 10: 0471667269 
ISBN 13: 9780471667261
Author: Seymour Geisser, Wesley M. Johnson

A fascinating investigation into the foundations of statistical inference

This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode’s strengths and weaknesses.

The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference:
* Frequentist
* Likelihood
* Fiducial
* Bayesian

The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development.

The author’s writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.

Modes of Parametric Statistical Inference 1st Table of contents:

Chapter 1: Introduction to Statistical Inference

• What is Statistical Inference?
• Types of Statistical Inference: Point Estimation, Interval Estimation, Hypothesis Testing
• The Role of Parametric Models in Inference
• Classical vs. Bayesian Approaches
• Overview of Common Parametric Models

Chapter 2: Classical Inference Methods

• Maximum Likelihood Estimation (MLE)
• Method of Moments
• Least Squares Estimation
• Unbiased Estimators and Efficiency
• Properties of Estimators: Consistency, Sufficiency, and Invariance
• Asymptotic Theory in Classical Inference

Chapter 3: Likelihood-Based Inference

• The Likelihood Function and Its Properties
• Construction of the Likelihood Function
• Estimation of Parameters using MLE
• Hypothesis Testing using the Likelihood Ratio Test
• The Role of the Fisher Information Matrix
• Confidence Intervals in MLE

Chapter 4: Bayesian Inference

• Introduction to Bayesian Statistics
• The Prior, Likelihood, and Posterior Distributions
• Bayesian Estimation: Posterior Means and Medians
• Markov Chain Monte Carlo (MCMC) Methods
• Bayes Factors and Model Comparison
• Posterior Predictive Checks and Decision Theory

Chapter 5: Parametric Hypothesis Testing

• Null and Alternative Hypotheses
• Likelihood Ratio Tests and Their Applications
• Wald Tests and Score Tests
• p-values, Power, and Type I & II Errors
• The Concept of Sufficient Statistics in Hypothesis Testing
• Confidence Intervals and their Relation to Hypothesis Testing

Chapter 6: Model Selection and Comparison

• Information Criteria: AIC, BIC, and Others
• Model Selection in the Context of Parametric Inference
• Goodness-of-Fit Tests and Residual Analysis
• Cross-Validation for Parametric Models
• Comparing Nested and Non-Nested Models
• Assessing Model Assumptions

Chapter 7: Advanced Topics in Parametric Inference

• Inference for Multivariate Data
• Parametric Inference in Time Series Models
• Generalized Linear Models (GLM) and Their Extensions
• Inference for Mixture Models and Hierarchical Models
• Nonparametric and Semiparametric Models: Hybrid Approaches

Chapter 8: Computational Methods for Parametric Inference

• Numerical Optimization for MLE
• Simulation Methods in Inference: Bootstrap and Monte Carlo
• Computational Aspects of Bayesian Inference: Gibbs Sampling, MCMC
• Tools and Software for Parametric Inference
• Handling Large Datasets and High-Dimensional Problems

Chapter 9: Applications of Parametric Statistical Inference

• Inference in Linear Regression Models
• Parametric Methods in Survival Analysis
• Inference in Experimental Design
• Model Inference in Bioinformatics and Epidemiology
• Applications to Finance and Econometrics

Chapter 10: Challenges and Future Directions

• Limitations of Parametric Models
• Dealing with Model Misspecification
• Advances in Robust Statistical Inference
• The Integration of Parametric and Machine Learning Methods
• Ethical Considerations in Statistical Inference

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Seymour Geisser,Wesley M Johnson,Parametric Statistical