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Priors

Priors in BayesBiont are explicit, optional, and biology-grounded by default. The package ships with curated priors for canonical models and falls back to empirical priors derived from Kinbiont.NLModel.guess(...) for anything else.

Default behaviour

Pass a BayesianModelSpec without priors= and BayesBiont picks:

  1. Curated entry from DEFAULT_PRIORS if your model name is registered (e.g. "NL_Gompertz", "NL_logistic", "aHPM").
  2. Empirical fallback — LogNormal(log(guess_i), 1.0) per parameter, where guess_i comes from model.guess(data_matrix). A 95 % CI of roughly ×7 either way.

You can inspect the curated registry:

using BayesBiont
BayesBiont.DEFAULT_PRIORS["NL_Gompertz"]
# (
#     N_max       = LogNormal(log(1.0), 0.7),   # ~0.25 .. 4 OD
#     growth_rate = LogNormal(log(0.5), 0.8),   # ~0.10 .. 2.4 hr⁻¹
#     lag         = LogNormal(log(5.0), 1.0),   # ~0.7  .. 35 hr
# )

The curated priors are calibrated for plate-reader OD data on typical bacteria. If your scale is different (cell counts, slow-growing organisms, dense cultures) supply explicit priors.

Supplying your own priors

custom_priors = (
    N_max       = LogNormal(log(2.0), 0.4),     # tighter; expecting ~2 OD plateau
    growth_rate = LogNormal(log(0.8), 0.5),
    lag         = LogNormal(log(3.0), 0.4),
)
spec = BayesianModelSpec(
    [MODEL_REGISTRY["NL_Gompertz"]];
    priors = [custom_priors],
    sigma_prior = Exponential(0.05),            # 5 % expected noise
)

The priors field is a vector — one prior NamedTuple per model in the spec (currently only the first model is fit; future versions will support multi-model spec for compare()).

What the priors do internally

For positive parameters with LogNormal priors, BayesBiont samples in log-space internally (Normal on log(p), deterministic transform to p). For hierarchical fits, this becomes a non-centered reparameterisation across replicates, which sidesteps Neal's funnel and dramatically improves NUTS efficiency. Users always see native-scale samples in the output Chains — the log-space trick is invisible.

Tightness as a diagnostic

If you see the posterior staying very close to your prior centre regardless of data, the data isn't informative about that parameter. This is a signal worth heeding:

  • For identifiability problems on lag-like parameters with short experiments, the lag prior dominates — narrow your prior using biological knowledge.
  • For poorly-constrained parameters in ODE models (e.g. exit_lag_rate in aHPM), expect wide posteriors unless your data sampling captures the relevant phase.
  • The Pareto-k diagnostic in Diagnostics is the formal version of this check.

Public API