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I'm currently working towards a major in both chemistry and mathematical statistics as a part of my science degree, and I got to wondering:

How will these two go hand in hand and help each other?

Now, I know there's the obvious applications of statistical inference to any experimentation I do, but I'm talking about less obvious relationships. Could my knowledge of solving SDEs ever help me with my experiments? What about continuous Markov processes? Will I ever even think about a discrete random variable again if I go on to get a PhD in chemistry? Also not looking for the standard "well we use statistical physics to model electrons" example, either (welp, unless you can offer some nice specifics). Surely there's other ways that these skills I've found can interact with each other?

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Most definitely yes.

I took multiple statistics classes as an undergraduate and they have helped me considerably. (I can argue fairly that it helped me get tenure.)

A few suggestions from my own work:

  • Statistical design of multivariate experiments: Many scientists think you should test one variable at a time. No. I taught a grad student (in another group) about optimization theory and proper design and three months later, a great paper came out.
  • Data mining and exploration: Many chemistry data sets are extremely complicated, with cross-correlated factors. Understanding how to draw empirical inferences, find the most important factors, etc. is enormously helpful across a wide range of chemistry.
  • Principal component analysis: An emerging area in spectroscopy and imaging is taking complicated spectra and performing PCA to help with quantifying chemical components in mixtures and following everything from cancer growth to materials design.
  • Multivariate regression and ANOVA: My group has created numerous quick statistical screens using multivariate surrogates for complex simulations or experiments.
  • Cross-validated analysis: Again, the understanding of training and test sets, bootstrapping, etc. is very useful.

Now, you also mention SDEs and Markov processes. These are crucial in chemical kinetics, including areas like reaction-diffusion systems. Monte Carlo methods are also highly used in studying dynamical processes.

The list would be enormous. Basically, I think it's a great skill to have and you'll use it throughout your career.

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  • $\begingroup$ Oh, I almost forgot optimization theory. We've been using stochastic evolutionary algorithms heavily. People use genetic algorithm optimization to find parameters for computational models (e.g., DFT), etc. As I said.. the list is enormous. $\endgroup$
    – Geoff Hutchison
    Commented Dec 19, 2014 at 17:37
  • $\begingroup$ Investigate the umbrella term 'Chemometrics'. this covers several (if not all) of the areas covered in this answer, but also other areas and techniques. A useful piece of software called MatLab is often used in chemometrics. $\endgroup$
    – LiamH
    Commented Nov 9, 2015 at 15:43
  • $\begingroup$ Analytical chemistry of complex mixtures and anything -omics (metabolomics, foodomics, petroleomics, etc...) will use chemometrics somewhere, which often involves finding latent variables (interpreting PCA and factor analysis results). Still hot topics with lots of development. Computational chem often uses statistics as does chemoinformatics and QSAR. In addition to MATLAB, the statistical package R is highly useful (what I use). $\endgroup$
    – Matthew MacLennan
    Commented Aug 12, 2017 at 16:56

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