New Book: Stochastic Processes and Simulations


This scratch course on stochastic processes covers significantly more material than usually found in traditional books or classes. The approach is original: I introduce a new yet intuitive type of random structure called perturbed lattice or Poisson-binomial process, as the gateway to all the stochastic processes. Such models have started to gain considerable momentum recently, especially in sensor data, cellular networks, chemistry, physics and engineering applications. I present state-of-the-art material in simple words, in a compact style, including new research developments and open problems. I focus on the methodology and principles, providing the reader with solid foundations and numerous resources: theory, applications, illustrations, statistical inference, references, glossary, educational spreadsheet, source code, stochastic simulations, original exercises, videos and more.

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Below is a short selection highlighting some of the topics featured in the textbook. Some are research results published here for the first time.

  • GPU clustering: Fractal supervised clustering in GPU (graphics processing unit) using image filtering techniques akin to neural networks, automated black-box detection of the number of clusters, unsupervised clustering in GPU using density (gray levels) equalizer.
  • GPU clustering: Fractal supervised clustering in GPU (graphics processing unit) using image filtering techniques akin to neural networks, automated black-box detection of the number of clusters, unsupervised clustering in GPU using density (gray levels) equalizer.
  • Inference: New test of independence, spatial processes, model fitting, dual confidence regions, minimum contrast estimation, oscillating estimators, mixture and surperimposed models, radial cluster processes, exponential-binomial distribution with infinitely many parameters, generalized logistic distribution.
  • Nearest neighbors: Statistical distribution of distances and Rayleigh test, Weibull distribution, properties of nearest neighbor graphs, size distribution of connected components, geometric features, hexagonal lattices, coverage problems, simulations, model-free inference.
  • Cool stuff: Random functions, random graphs, random permutations, chaotic convergence, perturbed Riemann Hypothesis (experimental number theory), attractor distributions in extreme value theory, central limit theorem for stochastic processes, numerical stability, optimum color palettes, cluster processes on the sphere.
  • Resources: 28 exercises with solution expanding the theory and methods presented in the textbook, well documented source code and formulas to generate various deviates and simulations, simple recipes (with source code) to design your own data animations as MP4 videos – see ours on YouTube, here.

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Volume 1

This first volume deals with point processes in one and two dimensions, including spatial processes and clustering. The next volume in this series will cover other types of stochastic processes, such as Brownian-related and random, chaotic dynamical systems. The point process which is at the core of this textbook is called the Poisson-binomial process (not to be confused with a binomial nor a Poisson process) for reasons that will soon become apparent to the reader. Two extreme cases are the standard Poisson process, and fixed (non-random) points on a lattice. Everything in between is the most exciting part.

View the table of contents on our GitHub repository.

Target Audience

College-educated professionals with an analytical background (physics, economics, finance, machine learning, statistics, computer science, quant, mathematics, operations research, engineering, business intelligence), students enrolled in a quantitative curriculum, decision makers or managers working with data scientists, graduate students, researchers and college professors, will benefit the most from this textbook. The textbook is also intended to professionals interested in automated machine learning and artificial intelligence.

It includes many original exercises requiring out-of-the-box thinking, and offered with solution. Both students and college professors will find them very valuable. Most of these exercises are an extension of the core material. Also, a large number of internal and external references are immediately accessible with one click, throughout the textbook: they are highlighted respectively in red and blue in the text. The material is organized to facilitate the reading in random order as much as possible and to make navigation easy. It is written for busy readers.

The textbook includes full source code, in particular for simulations, image processing, and video generation. You don’t need to be a programmer to understand the code. It is well documented and easy to read, even for people with little or no programming experience. Emphasis is on good coding practices. The goal is to help you quickly develop and implement your own machine learning applications from scratch, or use the ones offered in the textbook.

The material also features professional-looking spreadsheets allowing you to perform interactive statistical tests and simulations in Excel alone, without statistical tables or any coding. The code, data sets, videos and spreadsheets are available here on our GitHub repository.

The content in this textbook is frequently of graduate or post-graduate level and thus of interest to researchers. Yet the unusual style of the presentation makes it accessible to a large audience, including students and professionals with a modest analytic background (a standard course in statistics). It is my hope that it will entice beginners and practitioners faced with data challenges, to explore and discover the beautiful and useful aspects of the theory, traditionally inaccessible to them due to jargon.

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About the Author

Vincent Granville is a pioneering data scientist and machine learning expert, co-founder of Data Science Central (acquired by TechTarget in 2020), former VC-funded executive, author and patent owner. Vincent’s past corporate experience includes Visa, Wells Fargo, eBay, NBC, Microsoft, CNET, InfoSpace. Vincent is also a former post-doc at Cambridge University, and the National Institute of Statistical Sciences (NISS).

Vincent published in Journal of Number Theory, Journal of the Royal Statistical Society (Series B), and IEEE Transactions on Pattern Analysis and Machine Intelligence. He is also the author of multiple books, available here. He lives in Washington state, and enjoy doing research on stochastic processes, dynamical systems, experimental math and probabilistic number theory.

How to Obtain the Book?

You can buy the book on our e-Store, here.

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