Introduction to Statistics and Probability for Topologists

Applying topological methods for the analysis of complex data sets require two skill sets: a knowledge of topology and an understanding of the basically stochastic nature of data, which is typically sampled from some underlying random structure. Acknowledging the fact that topologists are only rarely trained in statistical methodology, the aim of this tutorial will be to acquaint topologists with the basic concepts and tools of probability and statistics, as well of some of the more advanced techniques of specific interest in topological data analysis.

Topics to be covered will include basic probability, statistical inference (both classical frequentist and Bayesian approaches), and an introduction to Gaussian and Markov stochastic processes along with Markov chain Monte Carlo as a simulation and inference tool. Among the more advanced topics to be described will be handling statistical outliers, graphical models, statistical clustering tools, and spatial dependence.