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Applied Statistics with AI Hypothesis Testing and Inference for Modern Models

Applied Statistics with AI Hypothesis Testing and Inference for Modern Models
Anshuman Mishra

Statistics is the language of uncertainty. AI is the science of learning from data. Together, they provide a powerful foundation for modern intelligent systems.

Applied Statistics with AI: Hypothesis Testing and Inference for Modern Models is designed for learners who want to understand how statistical methods can be applied to Artificial Intelligence, Machine Learning, Data Science, and modern research.

The book begins with essential statistical foundations, including data types, sampling, preprocessing, descriptive statistics, visualization, probability, and probability distributions. It then builds toward statistical inference, covering estimation, Maximum Likelihood Estimation, Bayesian estimation, hypothesis testing, p-values, confidence intervals, Type I and Type II errors, and statistical significance.

Readers will learn how classical statistical tests such as t-tests, ANOVA, and Chi-Square tests can be used in AI-related contexts, along with non-parametric methods such as Wilcoxon, Mann-Whitney, Kruskal-Wallis, and Kolmogorov-Smirnov tests.

The book then connects statistics directly to Machine Learning through regression, model evaluation, cross-validation, resampling, feature selection, PCA, regularization, A/B testing, and statistical power.

Advanced chapters explore Bayesian inference, MCMC, causal inference, uncertainty quantification in deep learning, and confidence estimation in AI predictions. Real-world case studies demonstrate how statistical inference can support applications in healthcare, finance, Natural Language Processing, and Computer Vision.

The book also addresses an increasingly important dimension of AI: responsible statistical practice. Readers will explore bias detection, fairness, ethical hypothesis testing, and the responsible interpretation of AI research results.

Finally, the book looks ahead to automated statistical inference, AI-driven hypothesis generation, and emerging research challenges.

Whether you are a student learning statistics for AI, a researcher evaluating machine learning experiments, a data scientist analyzing evidence, or an AI practitioner seeking stronger statistical foundations, this book provides a structured path from fundamental concepts to modern applications.

Understand the data. Test the hypothesis. Quantify uncertainty. Make better AI decisions.

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About the Book

Applied Statistics with AI: Hypothesis Testing and Inference for Modern Models is a practical and conceptually focused guide to understanding how statistical thinking, probability, hypothesis testing, and statistical inference can be applied to modern Artificial Intelligence and Machine Learning systems.

Statistics provides the foundation for making reliable decisions from data, while AI and Machine Learning increasingly depend on statistical methods to evaluate models, quantify uncertainty, compare experiments, select features, and interpret results. This book brings these two areas together in a structured learning journey.

The book begins with the foundations of applied statistics, including data types, sampling, preprocessing, descriptive statistics, and visualization. It then introduces probability theory, conditional probability, Bayes' theorem, random variables, probability distributions, sampling distributions, and the Central Limit Theorem.

The statistical inference section covers estimation, Maximum Likelihood Estimation, Bayesian estimation, hypothesis testing, p-values, significance levels, Type I and Type II errors, parametric tests, and non-parametric methods.

The later chapters connect statistical inference directly to AI and Machine Learning. Topics include regression, model evaluation, cross-validation, confidence intervals, feature selection, PCA, regularization, A/B testing, statistical power, Bayesian Machine Learning, causal inference, uncertainty estimation in deep learning, and applied case studies.

The book concludes with statistical ethics, AI fairness, automated statistical inference, AI-driven hypothesis generation, and future research directions.

Designed for students, researchers, data scientists, AI practitioners, and professionals, this book aims to bridge the gap between traditional statistical theory and modern AI applications while encouraging rigorous, evidence-based interpretation of machine learning results.

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About the Author

Anshuman Mishra

Anshuman Kumar Mishra, M.Tech (Computer Science) Assistant Professor, Doranda College, Ranchi University

Prolific Author of 50+ Books on AI, Machine Learning & Computer Science | 20+ Years Experience

Anshuman Kumar Mishra is a dedicated educator, researcher, and highly prolific author with over 20 years of experience in Computer Science and Information Technology. Holding an M.Tech in Computer Science from BIT Mesra, he brings a rare combination of academic depth and practical teaching expertise.

Currently serving as Assistant Professor at Doranda College under Ranchi University, he has mentored thousands of students, helping them build strong foundations in programming, data science, and artificial intelligence. His student-centric teaching style emphasizes conceptual clarity, hands-on practice, and real-world application.

Anshuman is a prolific author with more than 50 books published across a wide spectrum of computer science and emerging technology domains. From foundational programming languages to advanced topics in Artificial Intelligence, Machine Learning, Reinforcement Learning, Decision Theory, and Computer Vision — his books are widely appreciated by students, educators, and professionals for their clear explanations, strong theoretical foundation, and practical approach.

His extensive body of work reflects his deep commitment to making complex subjects accessible and meaningful for learners at all levels. He is particularly recognized for creating well-structured learning paths that help readers progress from beginner to advanced levels with confidence.

Driven by the mission to democratize quality technical education, Anshuman continues to write and update books that bridge the gap between academic theory and industry practice.

When not teaching or writing, he actively follows and explores new developments in AI, Quantum Machine Learning, and Ethical Intelligence systems.

Contents

Table of Contents

"Applied Statistics with AI: Hypothesis Testing and Inference for Modern Models" Table of Contents Part I: Foundations of Applied Statistics Chapter 1: Introduction to Applied Statistics and AI 1-27 1.1 Importance of Statistics in AI and Data Science 1.2 Classical vs. Modern Approaches 1.3 Role of Statistical Inference in Model Development Chapter 2: Data Types, Sampling, and Preprocessing 28-53 2.1 Types of Data: Numerical, Categorical, Ordinal, Time-Series 2.2 Random Sampling, Stratified Sampling, Bootstrapping 2.3 Data Cleaning, Normalization, and Feature Scaling Chapter 3: Descriptive Statistics and Visualization 54-73 3.1 Measures of Central Tendency (Mean, Median, Mode) 3.2 Measures of Spread (Variance, Standard Deviation, IQR) 3.3 Visualization: Histograms, Boxplots, Scatter Plots 3.4 Exploratory Data Analysis for AI Datasets ________________________________________ Part II: Probability and Distributions Chapter 4: Probability Theory in AI 74-99 4.1 Basic Probability Rules 4.2 Conditional Probability and Bayes’ Theorem 4.3 Applications in Bayesian Learning Chapter 5: Random Variables and Probability Distributions 100-124 5.1 Discrete Distributions: Bernoulli, Binomial, Poisson 5.2 Continuous Distributions: Normal, Exponential, Uniform 5.3 Applications in AI Algorithms Chapter 6: Sampling Distributions and Central Limit Theorem 125-140 6.1 Law of Large Numbers 6.2 Central Limit Theorem and Its Role in Hypothesis Testing 6.3 Simulation-Based Understanding ________________________________________ Part III: Statistical Inference Chapter 7: Estimation Methods 141-158 7.1 Point Estimation and Interval Estimation 7.2 Maximum Likelihood Estimation (MLE) 7.3 Bayesian Estimation Chapter 8: Hypothesis Testing Fundamentals 159-174 8.1 Null and Alternative Hypotheses 8.2 Type I and Type II Errors 8.3 p-values and Significance Levels Chapter 9: Parametric Tests in AI Context 175-193 9.1 t-tests (One-Sample, Two-Sample, Paired) 9.2 ANOVA (Analysis of Variance) 9.3 Chi-Square Tests for Categorical Data Chapter 10: Non-Parametric Tests for AI Data 194-212 10.1 Wilcoxon, Mann-Whitney, Kruskal-Wallis 10.2 Kolmogorov-Smirnov Test 10.3 Applications When Data Doesn’t Follow Assumptions ________________________________________ Part IV: Applied Statistics in AI Chapter 11: Regression Analysis for Prediction 213-230 11.1 Linear Regression and Assumptions 11.2 Logistic Regression for Classification 11.3 Residual Analysis and Goodness-of-Fit Chapter 12: Statistical Inference in Machine Learning Models 231-247 12.1 Overfitting, Underfitting, Bias-Variance Tradeoff 12.2 Cross-Validation and Resampling Techniques 12.3 Confidence Intervals for Model Predictions Chapter 13: Feature Selection and Dimensionality Reduction 248-262 13.1 Statistical Correlation and Mutual Information 13.2 Principal Component Analysis (PCA) 13.3 Regularization Techniques (Lasso, Ridge) Chapter 14: Hypothesis Testing in AI Research 263-276 14.1 A/B Testing and Experimental Design 14.2 Statistical Power in Evaluating AI Models 14.3 Applications in Reinforcement Learning and NLP ________________________________________ Part V: Advanced Topics and Case Studies Chapter 15: Bayesian Statistics for AI Models 277-292 15.1 Bayesian Inference and Posterior Estimation 15.2 Markov Chain Monte Carlo (MCMC) Methods 15.3 Applications in Probabilistic Machine Learning Chapter 16: Causal Inference in AI Systems 293-307 16.1 Correlation vs. Causation 16.2 Structural Causal Models 16.3 AI for Policy and Decision-Making Chapter 17: Statistical Inference in Deep Learning 308-321 17.1 Dropout as Bayesian Approximation 17.2 Uncertainty Quantification in Neural Networks 17.3 Confidence Estimation in Predictions Chapter 18: Applied Case Studies 322-337 18.1 Healthcare: Statistical Inference for Diagnostic AI 18.2 Finance: Hypothesis Testing for Fraud Detection 18.3 NLP & Computer Vision: Statistical Significance in Model Improvement ________________________________________ Part VI: Future Directions Chapter 19: Statistical Ethics and AI Fairness 338-344 19.1 Bias Detection and Mitigation 19.2 Ethical Use of Hypothesis Testing in AI Research Chapter 20: Next-Generation Statistical Tools for AI 345-351 20.1 Automated Statistical Inference in AutoML 20.2 AI-Driven Hypothesis Generation 20.3 Future Research Challenges

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