Probabilistic Modelling for Advanced Data Analysis
- 1st Edition - January 1, 2027
- Latest edition
- Authors: Amit Kumar Tyagi, Soumya Mazumdar
- Language: English
Probabilistic Modelling for Advanced Data Analysis provides a practical and rigorous guide for data practitioners to effectively implement probabilistic models in real-world scenar… Read more
Description
Description
Probabilistic Modelling for Advanced Data Analysis provides a practical and rigorous guide for data practitioners to effectively implement probabilistic models in real-world scenarios. The book strikes a balance between high-level intuition and technical derivations, offering step-by-step explanations, real-world case studies, and Python implementation examples. The authors offer specific solutions that include modeling and quantifying uncertainty in data-driven decision-making, applying Bayesian inference to real-world problems and implementing scalable probabilistic models for large-scale datasets, all of which contribute to explainable and trustworthy AI.
This book presents readers with theoretical foundations and practical applications of probabilistic modeling, providing a structured approach for researchers, data scientists, and industry professionals. It meets the increasing demand for uncertainty-aware AI models, Bayesian inference, and probabilistic graphical models across various fields of research.
This book presents readers with theoretical foundations and practical applications of probabilistic modeling, providing a structured approach for researchers, data scientists, and industry professionals. It meets the increasing demand for uncertainty-aware AI models, Bayesian inference, and probabilistic graphical models across various fields of research.
Key features
Key features
- Includes real-world case studies from various industries and step-by-step Python implementations of probabilistic models
- Presents visual explanations, graphical representations, easy-to-follow analogies, and a focus on Bayesian methods, uncertainty quantification, and probabilistic inference
- Features approximate inference techniques, probabilistic deep learning approaches for AI applications, and strategies for handling high-dimensional data with probabilistic models
Readership
Readership
Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers, engineers, and scientists in a wide range of modelling applications for engineering and scientific research. The primary audience also includes researchers and professionals in the fields of mathematics, IT, physics, engineering, biomedicine, AI, ML, biology, healthcare, and economics
Table of contents
Table of contents
Part I: Foundations of Probability
1. Introduction to Probabilistic Modeling
1.1. Why probability matters in science and engineering
1.2. Real-world examples of probabilistic models
1.3. Overview of the book
2. Basic Probability Concepts
2.1. Definitions: Sample space, events, probability axioms
2.2. Classical vs. frequentist vs. Bayesian probability
2.3. Common pitfalls and misconceptions
2.4. Expectation, Variance, and Moments
2.4.1. Mean, variance, standard deviation
2.4.2. Moments and moment generating functions
2.4.3. Interpretation in scientific and engineering contexts
3. Random Variables and Probability Distributions
3.1. Discrete vs. continuous random variables
3.2. Probability mass functions (PMFs) and probability density functions (PDFs)
3.3. Cumulative distribution functions (CDFs)
4. Common Probability Distributions
4.1. Bernoulli, Binomial, Poisson (discrete)
4.2. Uniform, Normal, Exponential (continuous)
4.3. When and how to use them
Part II: Probabilistic Thinking in Science and Engineering
5. Joint, Marginal, and Conditional Probabilities
5.1. Independence and dependence of events
5.2. Law of total probability and Bayes’ theorem
5.3. Applications in engineering and science
6. Bayesian Thinking for Scientists and Engineers
6.1. Introduction to Bayes’ theorem
6.2. Prior, likelihood, posterior distributions
6.3. Simple Bayesian inference problems
7. Markov Chains and Stochastic Processes
7.1. Introduction to Markov processes
7.2. Transition matrices and steady-state probabilities
7.3. Real-world applications (e.g., reliability, genetics, queueing systems)
8. Monte Carlo Methods and Simulation
8.1. What is Monte Carlo simulation?
8.2. Generating random variables
8.3. Applications in physics, finance, and engineering
8.4. Monte Carlo Methods for High-Dimensional Problems
8.4.1. Importance sampling and rejection sampling
8.4.2. Markov Chain Monte Carlo (MCMC) methods
8.4.3. Applications in Bayesian inference and physics simulations
9. Parameter Estimation and Maximum Likelihood
9.1. Estimating probabilities from data
9.2. Maximum Likelihood Estimation (MLE)
9.3. Applications in machine learning and signal processing
Part III: Practical Applications of Probabilistic Models
10. Uncertainty Quantification in Engineering
10.1. Why uncertainty matters in design and decision-making
10.2. Sensitivity analysis
10.3. Real-world examples
11. Reliability Engineering and Failure Probabilities
11.1. Modeling system failures probabilistically
11.2. Mean Time to Failure (MTTF) and Mean Time Between Failures (MTBF)
11.3. Reliability block diagrams and fault trees
12. Bayesian Inference in Science and Engineering
12.1. Simple Bayesian models for inference
12.2. Bayesian updating with real-world data
12.3. Case studies
13. Time Series and Probabilistic Forecasting
13.1. Basics of time series data
13.2. AR, MA, ARMA, and ARIMA models
13.3. Probabilistic forecasting methods
Part IV: Advanced Topics and Case Studies
14. Probabilistic Graphical Models
14.1. Introduction to graphical models
14.2. Bayesian networks and Markov random fields
14.3. Applications in AI and system modeling
15. Hidden Markov Models (HMMs) and Applications
15.1. Understanding state transitions in hidden systems
15.2. HMMs in speech recognition, bioinformatics, and finance
15.3. Continuous-time vs. discrete-time Markov chains
15.4. Hidden Markov models (HMMs) for speech recognition and bioinformatics
15.5. Inference and learning in HMMs
16. Optimization Under Uncertainty
16.1. Probabilistic optimization methods
16.2. Decision-making with uncertainty
16.3. Risk analysis in engineering design
Part V: Advanced Probability and Statistical Inference
17. Measure Theory and Probability Foundations
17.1. Sigma-algebras and probability spaces
17.2. Lebesgue integration and expectation
17.3. Convergence of random variables (almost sure, in probability, in distribution)
18. Information Theory and Entropy
18.1. Shannon entropy and mutual information
18.2. Kullback-Leibler (KL) divergence
18.3. Applications in data compression and machine learning
19. Bayesian Inference and Hierarchical Models
19.1. Bayesian conjugate priors
19.2. Hierarchical Bayesian modeling
19.3. MCMC sampling methods (Gibbs, Metropolis-Hastings)
20. Stochastic Differential Equations (SDEs)
20.1. Brownian motion and Wiener processes
20.2. Langevin equations and applications in physics
20.3. Numerical solutions of SDEs
21. Extreme Value Theory and Rare Event Modeling
21.1. Extreme value distributions (Gumbel, Fréchet, Weibull)
21.2. Statistical methods for rare events
21.3. Applications in climate science, finance, and engineering failures
Part VI: Probabilistic Machine Learning and AI
22. Gaussian Processes for Regression and Classification
22.1. Probabilistic Machine Learning Foundations
22.1.1. How probability powers machine learning
22.1.2. Naïve Bayes classifier
22.1.3. Gaussian Mixture Models (GMMs)
22.2. Kernel functions and covariance matrices
22.3. Bayesian nonparametric modeling
22.4. Applications in function approximation and time-series forecasting
23. Variational Inference and Approximate Bayesian Computation (ABC)
23.1. Variational Bayes (VB)
23.2. Expectation-Maximization (EM) algorithm
23.3. ABC methods for inference in complex models
24. Deep Probabilistic Models and Bayesian Neural Networks
24.1. Probabilistic deep learning architectures
24.2. Dropout as Bayesian approximation
24.3. Generative models (VAEs, normalizing flows)
25. Probabilistic Graphical Models (PGMs)
25.1. Directed vs. undirected graphical models
25.2. Inference methods: Belief propagation, variational methods
25.3. Applications in robotics, genomics, and AI
26. Reinforcement Learning with Probabilistic Models
26.1. Markov Decision Processes (MDPs)
26.2. Bayesian reinforcement learning
26.3. Monte Carlo Tree Search (MCTS)
Part VII: Advanced Engineering and Scientific Applications
27. Reliability Theory and Probabilistic Risk Assessment (PRA)
27.1. Fault tree and event tree analysis
27.2. Bayesian reliability models
27.3. Uncertainty quantification in engineering design
28. Probabilistic Optimization and Decision Theory
28.1. Bayesian decision theory
28.2. Stochastic optimization algorithms (Simulated Annealing, Evolutionary Strategies)
28.3. Multi-armed bandits and Thompson sampling
29. Uncertainty Quantification in Scientific Computing
29.1. Stochastic finite element methods
29.2. Polynomial chaos expansions
29.3. Bayesian calibration of computational models
Part VIII: Cutting-Edge Topics and Future Directions
30. Random Graphs and Network Science
30.1. Erdős–Rényi and scale-free networks
30.2. Probabilistic models for social and biological networks
30.3. Stochastic block models
31. Nonparametric Bayesian Methods
31.1. Dirichlet Process (DP) and Chinese Restaurant Process (CRP)
31.2. Infinite mixture models
31.3. Pitman-Yor process and applications
32. Probabilistic Programming and Automated Inference
32.1. Languages for probabilistic modeling (Stan, PyMC, TensorFlow Probability)
32.2. Automatic differentiation and probabilistic computation
32.3. Real-world case studies
33. Physics-Inspired Probabilistic Models
33.1. Statistical mechanics and probability
33.2. Maximum entropy methods
33.3. Applications in quantum mechanics and thermodynamics
34. Case Studies in Science and Engineering
34.1. Real-world examples of probabilistic modeling
34.2. Applications in physics, civil engineering, and robotics
35. Conclusion and Future of Probabilistic Modeling in Science and Engineering
1. Introduction to Probabilistic Modeling
1.1. Why probability matters in science and engineering
1.2. Real-world examples of probabilistic models
1.3. Overview of the book
2. Basic Probability Concepts
2.1. Definitions: Sample space, events, probability axioms
2.2. Classical vs. frequentist vs. Bayesian probability
2.3. Common pitfalls and misconceptions
2.4. Expectation, Variance, and Moments
2.4.1. Mean, variance, standard deviation
2.4.2. Moments and moment generating functions
2.4.3. Interpretation in scientific and engineering contexts
3. Random Variables and Probability Distributions
3.1. Discrete vs. continuous random variables
3.2. Probability mass functions (PMFs) and probability density functions (PDFs)
3.3. Cumulative distribution functions (CDFs)
4. Common Probability Distributions
4.1. Bernoulli, Binomial, Poisson (discrete)
4.2. Uniform, Normal, Exponential (continuous)
4.3. When and how to use them
Part II: Probabilistic Thinking in Science and Engineering
5. Joint, Marginal, and Conditional Probabilities
5.1. Independence and dependence of events
5.2. Law of total probability and Bayes’ theorem
5.3. Applications in engineering and science
6. Bayesian Thinking for Scientists and Engineers
6.1. Introduction to Bayes’ theorem
6.2. Prior, likelihood, posterior distributions
6.3. Simple Bayesian inference problems
7. Markov Chains and Stochastic Processes
7.1. Introduction to Markov processes
7.2. Transition matrices and steady-state probabilities
7.3. Real-world applications (e.g., reliability, genetics, queueing systems)
8. Monte Carlo Methods and Simulation
8.1. What is Monte Carlo simulation?
8.2. Generating random variables
8.3. Applications in physics, finance, and engineering
8.4. Monte Carlo Methods for High-Dimensional Problems
8.4.1. Importance sampling and rejection sampling
8.4.2. Markov Chain Monte Carlo (MCMC) methods
8.4.3. Applications in Bayesian inference and physics simulations
9. Parameter Estimation and Maximum Likelihood
9.1. Estimating probabilities from data
9.2. Maximum Likelihood Estimation (MLE)
9.3. Applications in machine learning and signal processing
Part III: Practical Applications of Probabilistic Models
10. Uncertainty Quantification in Engineering
10.1. Why uncertainty matters in design and decision-making
10.2. Sensitivity analysis
10.3. Real-world examples
11. Reliability Engineering and Failure Probabilities
11.1. Modeling system failures probabilistically
11.2. Mean Time to Failure (MTTF) and Mean Time Between Failures (MTBF)
11.3. Reliability block diagrams and fault trees
12. Bayesian Inference in Science and Engineering
12.1. Simple Bayesian models for inference
12.2. Bayesian updating with real-world data
12.3. Case studies
13. Time Series and Probabilistic Forecasting
13.1. Basics of time series data
13.2. AR, MA, ARMA, and ARIMA models
13.3. Probabilistic forecasting methods
Part IV: Advanced Topics and Case Studies
14. Probabilistic Graphical Models
14.1. Introduction to graphical models
14.2. Bayesian networks and Markov random fields
14.3. Applications in AI and system modeling
15. Hidden Markov Models (HMMs) and Applications
15.1. Understanding state transitions in hidden systems
15.2. HMMs in speech recognition, bioinformatics, and finance
15.3. Continuous-time vs. discrete-time Markov chains
15.4. Hidden Markov models (HMMs) for speech recognition and bioinformatics
15.5. Inference and learning in HMMs
16. Optimization Under Uncertainty
16.1. Probabilistic optimization methods
16.2. Decision-making with uncertainty
16.3. Risk analysis in engineering design
Part V: Advanced Probability and Statistical Inference
17. Measure Theory and Probability Foundations
17.1. Sigma-algebras and probability spaces
17.2. Lebesgue integration and expectation
17.3. Convergence of random variables (almost sure, in probability, in distribution)
18. Information Theory and Entropy
18.1. Shannon entropy and mutual information
18.2. Kullback-Leibler (KL) divergence
18.3. Applications in data compression and machine learning
19. Bayesian Inference and Hierarchical Models
19.1. Bayesian conjugate priors
19.2. Hierarchical Bayesian modeling
19.3. MCMC sampling methods (Gibbs, Metropolis-Hastings)
20. Stochastic Differential Equations (SDEs)
20.1. Brownian motion and Wiener processes
20.2. Langevin equations and applications in physics
20.3. Numerical solutions of SDEs
21. Extreme Value Theory and Rare Event Modeling
21.1. Extreme value distributions (Gumbel, Fréchet, Weibull)
21.2. Statistical methods for rare events
21.3. Applications in climate science, finance, and engineering failures
Part VI: Probabilistic Machine Learning and AI
22. Gaussian Processes for Regression and Classification
22.1. Probabilistic Machine Learning Foundations
22.1.1. How probability powers machine learning
22.1.2. Naïve Bayes classifier
22.1.3. Gaussian Mixture Models (GMMs)
22.2. Kernel functions and covariance matrices
22.3. Bayesian nonparametric modeling
22.4. Applications in function approximation and time-series forecasting
23. Variational Inference and Approximate Bayesian Computation (ABC)
23.1. Variational Bayes (VB)
23.2. Expectation-Maximization (EM) algorithm
23.3. ABC methods for inference in complex models
24. Deep Probabilistic Models and Bayesian Neural Networks
24.1. Probabilistic deep learning architectures
24.2. Dropout as Bayesian approximation
24.3. Generative models (VAEs, normalizing flows)
25. Probabilistic Graphical Models (PGMs)
25.1. Directed vs. undirected graphical models
25.2. Inference methods: Belief propagation, variational methods
25.3. Applications in robotics, genomics, and AI
26. Reinforcement Learning with Probabilistic Models
26.1. Markov Decision Processes (MDPs)
26.2. Bayesian reinforcement learning
26.3. Monte Carlo Tree Search (MCTS)
Part VII: Advanced Engineering and Scientific Applications
27. Reliability Theory and Probabilistic Risk Assessment (PRA)
27.1. Fault tree and event tree analysis
27.2. Bayesian reliability models
27.3. Uncertainty quantification in engineering design
28. Probabilistic Optimization and Decision Theory
28.1. Bayesian decision theory
28.2. Stochastic optimization algorithms (Simulated Annealing, Evolutionary Strategies)
28.3. Multi-armed bandits and Thompson sampling
29. Uncertainty Quantification in Scientific Computing
29.1. Stochastic finite element methods
29.2. Polynomial chaos expansions
29.3. Bayesian calibration of computational models
Part VIII: Cutting-Edge Topics and Future Directions
30. Random Graphs and Network Science
30.1. Erdős–Rényi and scale-free networks
30.2. Probabilistic models for social and biological networks
30.3. Stochastic block models
31. Nonparametric Bayesian Methods
31.1. Dirichlet Process (DP) and Chinese Restaurant Process (CRP)
31.2. Infinite mixture models
31.3. Pitman-Yor process and applications
32. Probabilistic Programming and Automated Inference
32.1. Languages for probabilistic modeling (Stan, PyMC, TensorFlow Probability)
32.2. Automatic differentiation and probabilistic computation
32.3. Real-world case studies
33. Physics-Inspired Probabilistic Models
33.1. Statistical mechanics and probability
33.2. Maximum entropy methods
33.3. Applications in quantum mechanics and thermodynamics
34. Case Studies in Science and Engineering
34.1. Real-world examples of probabilistic modeling
34.2. Applications in physics, civil engineering, and robotics
35. Conclusion and Future of Probabilistic Modeling in Science and Engineering
Product details
Product details
- Edition: 1
- Latest edition
- Published: January 1, 2027
- Language: English
About the authors
About the authors
AT
Amit Kumar Tyagi
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.
Affiliations and expertise
Assistant Professor, National Institute of Fashion Technology, New Delhi, IndiaSM
Soumya Mazumdar
Soumya Mazumdar is an independent researcher with a background in Data Science and Computational Programming from IIT Madras and competence in Computer Science Engineering and Business Systems from Maulana Abul Kalam Azad University of Technology. He is currently pursuing his B.S. in Data Science and applications from IIT Madras. His research interests include Industry 4.0, smart infrastructure, and IoT-enabled early detection systems. In order to address global challenges in technology and sustainability, his current research focuses on developing 6G technology for Society 5.0, utilizing IoT for smart infrastructure and disaster management, integrating AI and machine learning in predictive maintenance, healthcare, and industrial robotics, and investigating the potential of blockchain and big database analytics in tandem.
Affiliations and expertise
Indian Institute of Technology - Madras, India