Democratizing Data Analysis Tools
Inverse (i.e., inference) methods used in inferring stochastic processes from data are a critical part of a modern, data-driven, modeling frameworks. In order to teach state-of-the-art inference tools relevant to stochastic processes, we recently wrote a tutorial article and two extensive reviews. In describing these tools, for lack of space, we made pedagogic concessions and assumed working knowledge of topics such as Gibbs sampling (as we do here). Yet, admittedly, this is not always reasonable. That is, Physical Scientists working with stochastic models, across condensed matter, are not always aware of the tools of Computational Statistics and Data Science needed to infer such models from their data.
For this reason, I have begun writing a textbook with a focus on Data Analysis for Physical Scientists. There are already many excellent texts, e.g., C. Bishop’s classic text on “Machine Learning and Pattern Recognition.” However, this textbook is meant for Computer Scientists not the Physical Sciences and are free of applications to stochastic processes as we see them here.
We are therefore currently writing a book (under contract with Cambridge Univ. Press) that introduces mathematical topics such as Bayesian inference; computational statistics (e.g. MCMC, Gibbs sampling, Viterbi, EM); time-independent models (e.g. latent feature and mixture models, Gaussian processes); hidden Markov models (including forward filter/backward sample, iHMM, Dirichlet processes); and continuous state space models (e.g. Kalman filters).
These mathematical tools are discussed in the context of physical concepts and equations used in modeling such as master equations, chemical master equations, mass action laws, Gillespie simulations, Fokker-Planck equations, Langevin and GLEs.
I have hosted hands-on activities with the Phoenix Zoo and its affiliated South Mountain Environmental Education Center (SMEEC). These involved a typical number of children running from 15 to 30. The activity display (including a microscope through which children can monitor desert bacteria we culture in our own lab) allows us to introduce children to simple physical concepts relevant to thinking about living, active, matter quantitatively with Arizona-appropriate themes.