Stochastic Processes, 2nd Edition, now with Python Code

The book covers supervised classification, including fractal classification, as well as unsupervised clustering, using an innovative approach. Datasets are first mapped onto an image, then processed using image filtering techniques. I discuss the analogy with neural networks, comparing very deep but sparse neural networks, with standard networks.

Topics Covered

The book covers many aspects of geospatial statistics including coverage problems and nearest neighbor graphs. Applications range from cellular networks (optimum distribution of cell towers), sensor data and IoT (optimum location of sensor devices), to crystallography or chemistry with lattice structures. Simulated (synthetic) data is based on various distributions, including a new type of generalized logistic, and Poisson-binomial distributions.

Highly clustered Brownian motion (left), automated detection of number of clusters (right)

You will learn how to generate synthetic data and build interpretable machine learning models. The approach, though similar to Bayesian mixtures and generative models, is simpler and more intuitive, using the concept of overlapping stochastic processes. It constitutes a first solid introduction to the topic, accessible to beginners. I avoid using measure theory and more obscure mathematical concepts. Yet I cover some advanced topics such as minimum contrast estimation, new tests of true independence to detect weak dependencies, unusually clustered Brownian motions, the shape of confidence regions, elements of graph theory, and more.


The format is easy to navigate, with many links, and back-links from the index, glossary and bibliography. Numerous exercises with solution, over 20 pages of Python code, 80 references, 20+ figures, highlighted index terms, and professional Excel spreadsheets complete the package. Datasets, spreadsheets and Python code are also available on the accompanying GitHub repository.

Get your copy, here. For the table of contents, follow this link.

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