Statistical Manifolds and Stochastic Dynamics: Bridging Theoretical Constructs with High-Dimensional Applications
Statistical Manifolds and Stochastic Dynamics: Bridging Theoretical Constructs with High-Dimensional Applications
Information Geometry and Measure Theoretic Approaches to High-Dimensional Statistical Analysis
About the Book
This book explores the rich intersection of statistical manifolds, information geometry, and stochastic dynamics with applications to high-dimensional data analysis. Bridging abstract mathematical theory with concrete computational approaches, it provides both rigorous foundations and practical implementations for modern statistical challenges.
Key features include:
- Measure-theoretic treatments of probability and statistical inference
- Geometric perspectives on statistical models and their properties
- Advanced computational methods for complex statistical problems
- Applications across machine learning, biostatistics, econometrics and other domains
Written for researchers and practitioners in statistics, applied mathematics, and data science, the book progresses from fundamental principles to frontier research questions. Each chapter combines theoretical depth with real-world applications, making advanced statistical theory accessible and relevant for solving today's complex data challenges.
Table of Contents
- The Statistical Method: Theory Meets Practice
- Probability Theory for Modern Research
- Frequentist Inference: Theory and Practice
- Bayesian Paradigms and Computation
- Regression Theory and Extensions
- High-Dimensional Statistical Theory
- Causal Inference Frameworks
- Statistical Learning Theory
- Nonparametric and Functional Methods
- Stochastic Processes in Practice
- Robust and Distribution-Free Methods
- Multiple Testing and Reproducibility
- Missing Data and Selection Bias
- Network and Graph-Structured Data
- Statistical Decision Theory
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