Fields

Which name does your field give to binference’s model, and which tools does it use? Several fields arrived at the same model on their own. Each gave it its own names and wrote its own software. Each page in this section takes one field. It states the problem in that field’s terms and maps it onto binference. It lists the field’s methods and software, and the mistakes the field has documented.

The census behind these pages recorded the facts about other packages on 22 October 2026. Releases of binference do not update them. Statements about binference describe the current code.

One model under many names

Every field below has \(N\) objects, \(K\) bins or classes, and for each object \(i\) a bin-averaged likelihood \(L_{ik}\). The population fractions \(\rho\) lie on the simplex, and the likelihood of the whole catalogue is

\[ p(D\mid\rho)=\prod_{i=1}^{N}\sum_{k=1}^{K}L_{ik}\,\rho_k . \]

The model page derives this model and its extensions. The two tables below collect each field’s names for binference’s terms in one place. A dash means the field has no common name for the term. Each field page uses its own names only on that page.

Vocabulary

field	object	bin	fractions \(\rho\)	likelihood \(L_{ik}\)	interim prior	response	selection	hierarchical posterior
astronomy	galaxy, star, planet	redshift bin, colour–magnitude cell, Hess-diagram cell	redshift distribution \(n(z)\) (a density), occurrence rate, luminosity function	binned photo-\(z\) likelihood; a star’s likelihood in a kernel	prior of the photo-\(z\) code; implicit training-set prior	—	completeness	posterior shrunk by the population
gravitational waves	event	bin of masses, spins and redshift	population model; rates in bins	per-event weights: samples divided by the PE prior	PE prior	—	detection probability; \(VT\)	population-informed (reweighted) event posterior
particle-physics unfolding	event	true bin	true spectrum	row of the response matrix	simulation prior	response matrix; migration matrix with efficiency	efficiency and acceptance	—
empirical Bayes	unit	support point	prior \(g\), mixing distribution	likelihood matrix	—	—	truncation	empirical-Bayes posterior
ML quantification	item	class	prevalence, class proportions	classifier posterior divided by the training prevalence	training prevalence	confusion matrix	—	corrected per-item posterior
ecology and genetics	fish, turtle, read	stock, source, transcript	mixture proportions, stock proportions	genotype likelihood under each baseline; read compatibility	—	—	—	per-fish assignment probability

Methods

field	point estimate of \(\rho\)	posterior over \(\rho\)	smoothness prior	stacking
astronomy	EM	Dirichlet Gibbs sampling; mean-field VB (RAIL)	logistic GP, GP, random walk	stacked \(p(z)\)
gravitational waves	maximum hyper-likelihood	NUTS over binned log-rates	ICAR, GP, P-splines	—
particle-physics unfolding	iterative Bayesian unfolding (D’Agostini, Richardson–Lucy)	Fully Bayesian Unfolding	Tikhonov, GP unfolding	—
empirical Bayes	NPMLE (Kiefer–Wolfowitz)	variational Dirichlet posterior (ashr mixVBEM)	log-spline \(g\) (Efron)	—
ML quantification	EMQ, SLD, MLLS	BayesianCC, BayesianMAPLS, BayesianKDEy	ordinal Tikhonov penalties	probabilistic classify and count (PCC)
ecology and genetics	conditional maximum likelihood (SPAM, ONCOR); EM (salmon)	BAYES, rubias, SourceTracker (Gibbs)	—	—

Each field’s point estimator is EM, or a truncation or acceleration of it (theory).

What binference adds in every field

Each field page lists only what binference adds for that field. These additions hold for all of them:

• binference samples the exact posterior of \(\rho\) with NUTS or Gibbs, and flags approximations (engines guide).

• It divides the interim prior out of posteriors and posterior samples (inputs guide).

• It models selection on the truth or on the measurement (selection guide).

• It infers a tallied response matrix jointly with the fractions (binned measurements).

• It checks a whole analysis by simulation-based calibration (checking guide).

Pages

• Photometric redshifts and astronomical populations
• Gravitational-wave populations
• Unfolding in particle physics
• Empirical Bayes deconvolution and g-modelling
• Quantification and prevalence estimation
• Mixed-stock analysis and source tracking
• Neural and simulation-based deconvolution
• Priors on the simplex and inference for mixture weights
• The software landscape

Source material

These pages condense a census of the software and literature made while binference was designed. The census keeps every citation, the code read and the numerical checks. The repository holds ten research notes in research_notes/ and a synthesis report in reports/. The design notes include the report as Reinvented everywhere, packaged nowhere: pastry’s opening. Nobody updates the notes; they describe each project as it was in October 2026.