Statistical mechanics in biology and biocomputation
When we want to estimate parameters from data (e.g., from binding, kinetics, or electrophysiology experiments), there are two tasks: (i) estimate the most likely values, and (ii) equally importantly, estimate the uncertainty in those values. After all, if the uncertainty is huge, it’s hard to say we really know the parameters. We also need to choose the model in the first place, which is an extremely important task, but that is beyond the scope of this discussion.
Continue reading
I realized that I owe you something. In a prior post, I invoked some Bayesian ideas to contrast with boostrapping analysis of high-variance data. (More precisely, it was high log-variance data for which there was a problem, as described in our preprint.) But the Bayesian discussion in my earlier post was pretty quick. Although there are a number of good, brief introductions to Bayesian statistics, many get quite technical.
Here, I’d like to introduce Bayesian thinking in absolutely the simplest way possible. We want to understand the point of it, and get a better grip on those mysterious priors.
I want to talk again today about the essential topic of analyzing statistical uncertainty – i.e., making error bars – but I want to frame the discussion in terms of a larger theme: our community’s often insufficiently critical adoption of elegant and sophisticated ideas. I discussed this issue a bit previously in the context of PMF calculations. To save you the trouble of reading on, the technical problem to be addressed is statistical uncertainty for high-variance data with small(ish) sample sizes.