Module model 

The taste model as a fugue program, and its MCMC posterior.

θ_k  ~ Normal(0, σ_θ)      per style k, per feature      addr theta<k>#i
τ_s  ~ Normal(0, 1)        per session s (keep/kill bar) addr tau#s
cuts : c_1 = −2 + 1.5·raw₀;  c_j = c_{j−1} + exp(−0.5 + 0.7·raw_j)
                                                         addr cut#j
u(x) = max_k θ_k · φ(x)

Mixture semantics (K > 1): taste is a max of linear experts — a candidate is as good as its best style thinks it is. This is what lets one user’s taste span several islands (dark drones and bright plucks): each island gets its own linear lens, and every judgment — including a duel across islands — compares candidates on the shared scale u(x) = max_k u_k(x). (A per-observation latent-lens mixture cannot do this: it forces both duel items through the same lens, so cross-island comparisons are unrepresentable. The max-utility form was adopted after a synthetic bimodal user exposed exactly that failure.) There are no discrete latent sites, and at K = 1 the model reduces exactly to the plain linear taste.

One factor carries the total log-likelihood: Bradley–Terry for duels, σ(u − τ_s) for keep/kill, cumulative-logit ordinal for stars. Inference is fugue’s adaptive single-site MH — every site is F64, so the generic chain applies unchanged.

Default σ_θ = 1/(√d · s_K), making the prior utility of a standardized candidate roughly unit-variance — likelihood scales stay sane at any feature count and at any K. The s_K factor is the correction the max-of-experts form forces on us: with ‖φ‖² ≈ d each u_k is marginally N(0,1) under the prior, so u = max_k u_k is the max of K iid standard normals, whose SD falls with K (1.000, 0.826, 0.748, 0.701, 0.669). The mean shift cancels in duels and is absorbed by τ/cuts elsewhere; the variance shrinkage does not. Left uncorrected, Var(u_a − u_b) drops from 2.0 at K=1 to 0.90 at K=5, so growing K mid-session would quietly make the model less able to express a strong preference — the opposite of what adding capacity is supposed to do.

Mixture posteriors are permutation-symmetric in the style labels (label switching); call TastePosterior::aligned before per-style summaries.

Posterior draws carry importance weights. A full MCMC fit costs seconds, which is far too slow to run after every vote, so between fits the session layer folds each new observation in by sequential importance sampling (TastePosterior::reweighted): w_s ← w_s · p(y | θ_s). That is exact — the weighted draws target the updated posterior — and it costs O(S). It degrades gracefully rather than silently: effective sample size (TastePosterior::ess) falls as the weights concentrate, and that is the signal to pay for a real refit.

Structs

SiteAddrs

The MCMC site addresses of one taste program, built once.

TasteConfig

Model configuration.

TasteModel

The taste model: prior over latents + observation-log likelihood.

TastePosterior

A fitted posterior: thinned MCMC draws, their importance weights, and summaries. Weights are uniform straight out of a fit and concentrate as TastePosterior::reweighted folds in observations between fits.

TasteSample

One posterior draw of every latent.

Constants

KEEP

Posterior draws retained from a fit, after thinning.

MAX_NORMAL_SD

SD of the maximum of K iid standard normals, K = 1..=5. See the module doc.