Amit Kumar Tyagi is an Assistant Professor at the National Forensic Sciences University, Gandhinagar, India. He previously held academic and research positions, including at Vellore Institute of Technology (2019–2022), and earned his PhD from Pondicherry Central University in 2018. He has supervised doctoral and master’s students and contributed to research projects on privacy and security in vehicular applications and medical cyber-physical systems. He has published over 200 peer-reviewed papers and holds more than 25 patents in areas such as deep learning, the Internet of Things, cyber-physical systems, and computer vision.He has edited over 25 books and authored four books in related fields, and has received multiple research awards. His interests include machine-based communications, blockchain, and secure, privacy-preserving computing. He is a member of ACM and IEEE.

• Part I: Foundations of Probability1. Introduction to Probabilistic Modeling2. Basic Probability Concepts3. Random Variables and Probability Distributions4. Common Probability DistributionsPart II: Probabilistic Thinking in Science and Engineering5. Joint, Marginal, and Conditional Probabilities6. Bayesian Thinking for Scientists and Engineers7. Markov Chains and Stochastic Processes8. Monte Carlo Methods and Simulation9. Parameter Estimation and Maximum LikelihoodPart III: Practical Applications of Probabilistic Models10. Uncertainty Quantification in Engineering11. Reliability Engineering and Failure Probabilities12. Bayesian Inference in Science and Engineering13. Time Series and Probabilistic ForecastingPart IV: Advanced Topics and Case Studies14. Probabilistic Graphical Models15. Hidden Markov Models (HMMs) and Applications16. Optimization Under UncertaintyPart V: Advanced Probability and Statistical Inference17. Measure Theory and Probability Foundations18. Information Theory and Entropy19. Bayesian Inference and Hierarchical Models19.1. Bayesian conjugate priors20. Stochastic Differential Equations (SDEs)21. Extreme Value Theory and Rare Event ModelingPart VI: Probabilistic Machine Learning and AI22. Gaussian Processes for Regression and Classification23. Variational Inference and Approximate Bayesian Computation (ABC)24. Deep Probabilistic Models and Bayesian Neural Networks25. Probabilistic Graphical Models (PGMs)26. Reinforcement Learning with Probabilistic ModelsPart VII: Advanced Engineering and Scientific Applications27. Reliability Theory and Probabilistic Risk Assessment (PRA)28. Probabilistic Optimization and Decision Theory29. Uncertainty Quantification in Scientific ComputingPart VIII: Cutting-Edge Topics and Future Directions30. Random Graphs and Network Science31. Nonparametric Bayesian Methods32. Probabilistic Programming and Automated Inference34. Case Studies in Science and Engineering35. Conclusion and Future of Probabilistic Modeling in Science and Engineering

Amit Kumar Tyagi is an Assistant Professor at the National Forensic Sciences University, Gandhinagar, India. He previously held academic and research positions, including at Vellore Institute of Technology (2019–2022), and earned his PhD from Pondicherry Central University in 2018. He has supervised doctoral and master’s students and contributed to research projects on privacy and security in vehicular applications and medical cyber-physical systems. He has published over 200 peer-reviewed papers and holds more than 25 patents in areas such as deep learning, the Internet of Things, cyber-physical systems, and computer vision.He has edited over 25 books and authored four books in related fields, and has received multiple research awards. His interests include machine-based communications, blockchain, and secure, privacy-preserving computing. He is a member of ACM and IEEE.

• Part I: Foundations of Probability1. Introduction to Probabilistic Modeling2. Basic Probability Concepts3. Random Variables and Probability Distributions4. Common Probability DistributionsPart II: Probabilistic Thinking in Science and Engineering5. Joint, Marginal, and Conditional Probabilities6. Bayesian Thinking for Scientists and Engineers7. Markov Chains and Stochastic Processes8. Monte Carlo Methods and Simulation9. Parameter Estimation and Maximum LikelihoodPart III: Practical Applications of Probabilistic Models10. Uncertainty Quantification in Engineering11. Reliability Engineering and Failure Probabilities12. Bayesian Inference in Science and Engineering13. Time Series and Probabilistic ForecastingPart IV: Advanced Topics and Case Studies14. Probabilistic Graphical Models15. Hidden Markov Models (HMMs) and Applications16. Optimization Under UncertaintyPart V: Advanced Probability and Statistical Inference17. Measure Theory and Probability Foundations18. Information Theory and Entropy19. Bayesian Inference and Hierarchical Models19.1. Bayesian conjugate priors20. Stochastic Differential Equations (SDEs)21. Extreme Value Theory and Rare Event ModelingPart VI: Probabilistic Machine Learning and AI22. Gaussian Processes for Regression and Classification23. Variational Inference and Approximate Bayesian Computation (ABC)24. Deep Probabilistic Models and Bayesian Neural Networks25. Probabilistic Graphical Models (PGMs)26. Reinforcement Learning with Probabilistic ModelsPart VII: Advanced Engineering and Scientific Applications27. Reliability Theory and Probabilistic Risk Assessment (PRA)28. Probabilistic Optimization and Decision Theory29. Uncertainty Quantification in Scientific ComputingPart VIII: Cutting-Edge Topics and Future Directions30. Random Graphs and Network Science31. Nonparametric Bayesian Methods32. Probabilistic Programming and Automated Inference34. Case Studies in Science and Engineering35. Conclusion and Future of Probabilistic Modeling in Science and Engineering

Amit Kumar Tyagi is an Assistant Professor at the National Forensic Sciences University, Gandhinagar, India. He previously held academic and research positions, including at Vellore Institute of Technology (2019–2022), and earned his PhD from Pondicherry Central University in 2018. He has supervised doctoral and master’s students and contributed to research projects on privacy and security in vehicular applications and medical cyber-physical systems. He has published over 200 peer-reviewed papers and holds more than 25 patents in areas such as deep learning, the Internet of Things, cyber-physical systems, and computer vision.He has edited over 25 books and authored four books in related fields, and has received multiple research awards. His interests include machine-based communications, blockchain, and secure, privacy-preserving computing. He is a member of ACM and IEEE.

• Part I: Foundations of Probability1. Introduction to Probabilistic Modeling2. Basic Probability Concepts3. Random Variables and Probability Distributions4. Common Probability DistributionsPart II: Probabilistic Thinking in Science and Engineering5. Joint, Marginal, and Conditional Probabilities6. Bayesian Thinking for Scientists and Engineers7. Markov Chains and Stochastic Processes8. Monte Carlo Methods and Simulation9. Parameter Estimation and Maximum LikelihoodPart III: Practical Applications of Probabilistic Models10. Uncertainty Quantification in Engineering11. Reliability Engineering and Failure Probabilities12. Bayesian Inference in Science and Engineering13. Time Series and Probabilistic ForecastingPart IV: Advanced Topics and Case Studies14. Probabilistic Graphical Models15. Hidden Markov Models (HMMs) and Applications16. Optimization Under UncertaintyPart V: Advanced Probability and Statistical Inference17. Measure Theory and Probability Foundations18. Information Theory and Entropy19. Bayesian Inference and Hierarchical Models19.1. Bayesian conjugate priors20. Stochastic Differential Equations (SDEs)21. Extreme Value Theory and Rare Event ModelingPart VI: Probabilistic Machine Learning and AI22. Gaussian Processes for Regression and Classification23. Variational Inference and Approximate Bayesian Computation (ABC)24. Deep Probabilistic Models and Bayesian Neural Networks25. Probabilistic Graphical Models (PGMs)26. Reinforcement Learning with Probabilistic ModelsPart VII: Advanced Engineering and Scientific Applications27. Reliability Theory and Probabilistic Risk Assessment (PRA)28. Probabilistic Optimization and Decision Theory29. Uncertainty Quantification in Scientific ComputingPart VIII: Cutting-Edge Topics and Future Directions30. Random Graphs and Network Science31. Nonparametric Bayesian Methods32. Probabilistic Programming and Automated Inference34. Case Studies in Science and Engineering35. Conclusion and Future of Probabilistic Modeling in Science and Engineering