Probability & Statistics
Treating reconstruction as inferring a clean structure from noisy observations needs the language of probability. This base covers Bayesian inference, maximum-likelihood and MAP estimation, the EM algorithm, and entropy and KL divergence — the statistical foundations for the variational inference, energy models, and our own methods that follow.
wide posterior — uncertain, a family
Bayesian inference writes recovering a clean structure from a noisy observation as one update: the prior p(x) (amber, the energy prior — what structures are plausible) times the likelihood (blue, what this observation says) gives the posterior (purple, the updated belief). The MAP (amber tick) is the posterior's peak — all CryoGEN-I reports; the whole purple curve, peak plus width, is what CryoWGEN reports. The missing wedge weakens the observation in this direction and flattens the likelihood, so the posterior widens: the same gap admits a family of plausible answers. Drag toward ample data and the posterior tightens onto the MAP.
Articles in this base 3 articles
Bayesian inference
Describing unknowns with probability and updating a prior into a posterior from observed data via Bayes' rule.
MAP, MLE & the EM algorithm
Two routes to point estimates—maximum likelihood and maximum a posteriori—and expectation–maximization for latent-variable models.
Entropy & KL divergence
Measuring uncertainty and the discrepancy between distributions through Shannon entropy, cross-entropy, and KL divergence, with the link to maximum likelihood.