Statistical Manifolds and Stochastic Dynamics: Bridging Theoretical Constructs with High-Dimensional Applications
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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.

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    • Data Science
    • Mathematics
    • Data Structures
    • Physics
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About the Author

Kalyan Chakravarthy Kodela
Kalyan Chakravarthy Kodela

Kalyan is a software engineer and interdisciplinary researcher bridging advanced mathematics, physics, and computer science to solve complex real-world challenges. His work integrates machine learning, scientific computing, quantum machine learning, computational physics, dynamical systems, artificial intelligence, and data science, transforming theoretical concepts into practical solutions across multiple domains.

Table of Contents

  1. The Statistical Method: Theory Meets Practice
  2. Probability Theory for Modern Research
  3. Frequentist Inference: Theory and Practice
  4. Bayesian Paradigms and Computation
  5. Regression Theory and Extensions
  6. High-Dimensional Statistical Theory
  7. Causal Inference Frameworks
  8. Statistical Learning Theory
  9. Nonparametric and Functional Methods
  10. Stochastic Processes in Practice
  11. Robust and Distribution-Free Methods
  12. Multiple Testing and Reproducibility
  13. Missing Data and Selection Bias
  14. Network and Graph-Structured Data
  15. Statistical Decision Theory

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