Walkthroughs
Four applied problems, each starting from what is measured and what is to be estimated. A badge says whether the page fits a reusable rule or labels a fixed sample; the chips name the library parts it uses.
Phase Estimation in a Michelson Interferometer
Which detector positions should 6 counters collect from, so the fringe phase survives while its frequency floats?
A fringe pattern is read out by a detector with a fixed number of counters, and the fringe phase is to be estimated while the fringe frequency floats beside it. The page asks which detector positions each of 6 counters should collect from, and shows why equal segments can lose the phase entirely.
Data An idealised photon-arrival model with a closed-form score, integrated by deterministic quadrature. No recorded instrument data.
From a classifier to Fisher-preserving bins
Can a calibrated classifier stand in for the likelihood, and is the retention it reports about the data or about the classifier?
A two-component mixture whose signal fraction is to be estimated, with the component densities standing in for a likelihood nobody has. A classifier's calibrated posteriors, divided by its training proportions, estimate the density ratio the score depends on. The page fits 4 bins on that estimate and asks whether the retention the library reports is about the data or about the classifier.
Data A synthetic mixture of two normal densities, generated so that the exact score is also known and the estimate can be checked against it.
A Higgs search with a floating energy scale
Fit a 6-category rule on half the simulated collisions, apply it to the other half, and measure the signal strength while the tau energy scale floats.
Simulated collision events, a signal strength to estimate, and a tau energy scale that floats in the fit as a nuisance. Only 6 counts are kept. The page fits a reusable rule for the profiled information about the signal strength, applies it to events it never saw, and shows in the fitted uncertainty why slices of the classifier output fall apart once the energy scale floats.
Data Simulated events from the FAIR Universe HiggsML public dataset, each with a Monte Carlo weight and shifted-energy-scale copies. A simulation study, not an analysis.
Bone-marrow cell populations
Fit 8 categories on reference patients, apply them to held-out patients, and measure what the reduction costs.
Each cell carries marker intensities and an expert label; the quantity to estimate is a patient's population fractions. The page fits 8 categories on reference patients from classifier-estimated scores, freezes them, applies them to held-out patients, fits the fractions from the counts, and measures the error the reduction costs.
Data Real cells from the FlowCyt classification benchmark, with whole patients held out before anything was fitted.