# Stochastic point processes and their practical value

## Data scientists learn and utilize stochastic point processes for myriad pragmatic uses. Data scientist Vincent Granville explains this in his new book.

Poisson-binomial point processes are gaining considerable momentum, as their applications in the real world are numerous.

Point processes map a collection of data points, sometimes called events, that occur over a length of time. When collections of random variables model events that show the evolution of a given system over time, they are known as stochastic point processes.

Author Vincent Granville, a data scientist and machine learning expert who cofounded Data Science Central (acquired by TechTarget in 2020), wrote Stochastic Processes and Simulations to serve as a scratch course on stochastic processes. It covers more ground than traditional college courses or textbooks typically would. His approach is to introduce a new yet intuitive type of random structure for modeling mathematical points called a Poisson-binomial process.

Looking at the distinction between binomial and Poisson process examples will allow readers to better understand Poisson-binomial, which he uses as a gateway to understanding all stochastic point processes. A binomial distribution is used to model, for example, the probability of the number of successes we can expect from a given number of independent and identical success/failure trials (known as Bernoulli trials). A Poisson distribution in this context is attached to the number of points found in any domain -- say, a square -- under the assumption of independence among non-overlapping domains.

In Poisson-binomial processes, however, the point counts are location-dependent and thus not identically distributed nor independent. So, they are different from binomial and Poisson despite the other similarities discussed in this book. The name Poisson-binomial has historical connotations and generalizes the classic Poisson process: The point count distribution, rather than being Poisson, is Poisson-binomial.