Bayesian settings

Shipped values, interval calibration, overrides and versioning

BayesianSettings holds every argument that changes the posterior. Symbols follow the notation page; the posterior contract gives the equations each setting enters.

Shipped values

The table shows the shipped BAYESIAN_DEFAULTS object used when no settings are supplied to BayesianPosterior. It is a compatibility configuration, not the recommended research preset. Presets lists named profiles.

Setting	Symbol	Shipped value	Meaning
`minimum_observations`	\(n_j\)	`3`	Minimum growth and error observations
`include_model`	\(x_M\)	`True`	Include the model reading
`dispersion_weighted`	\(d\)	`False`	Try analyst dispersion before historical errors
`consensus_stdev_variance_multiplier`	\(\kappa\)	`1.0`	Scale dispersion variance
`consensus_count_exponent`	\(\alpha\)	`None`	Scale dispersion precision by analyst count
`consensus_bias_lambda`	\(\lambda\)	`0.0`	Fraction of estimated consensus bias removed
`consensus_bias_process_noise`	\(Q\)	`1.0`	Kalman process variance
`consensus_bias_measurement_noise`	\(R\)	`0.5`	Kalman measurement variance
`winsorize_fraction`		`None`	Historical tail fraction to clip
`interval_width`	\(p\)	`0.9`	Nominal interval coverage
`interval_df`	\(\nu\)	`1.5`	Student-t degrees of freedom
`interval_loc`	\(\ell\)	`0.5`	Student-t location
`interval_scale`	\(\omega\)	`2.75`	Student-t scale
`preset`		`None`	Originating preset
`fitted_through`		`None`	Calibration training cutoff, if known
`version`		`bayesian-defaults`	Configuration identity

Interval calibration

The interval turns the posterior spread \(\sigma_\theta\) into growth bounds \(\theta_L=\hat\theta+\sigma_\theta q_L\) and \(\theta_U=\hat\theta+\sigma_\theta q_U\), where \(q_L\) and \(q_U\) are quantiles of a Student-t with shape \((\nu,\ell,\omega)\) at coverage \(p\).

Explicit shape: Plain BayesianSettings(version=...) is not sufficient. Supply all three shape fields \(\nu\), \(\ell\) and \(\omega\), or take settings from a preset.
Calibrated profile: Omitted shape fields can be resolved when dispersion weighting is enabled and \(\lambda\) equals the calibrated strength. The calibration depends on the variance multiplier \(\kappa\).
Other profiles: Supply explicit interval_df, interval_loc and interval_scale.
Provenance: Resolved values appear in model_dump(). A missing calibration date is not evidence that the interval was chosen without fitting.
Coverage: A shape fitted for one profile need not be calibrated for another. Nominal coverage \(p\) must be checked on the intended application data.

Calibration constants, read from the installed package:

	Constant	Value
0	CALIBRATED_BIAS_LAMBDA	0.5
1	CALIBRATED_INTERVAL_DF	1.56
2	CALIBRATED_INTERVAL_LOC_INTERCEPT	0.084
3	CALIBRATED_INTERVAL_LOC_SLOPE	0.34
4	CALIBRATED_INTERVAL_SCALE_INTERCEPT	0.254
5	CALIBRATED_INTERVAL_SCALE_SLOPE	1.512

See training provenance before using a research preset in historical evaluation.

Overriding settings

Show the code

narrow = pf.posterior_preset(
    "plain-2026-09", version="plain-narrow-v1", interval_width=0.8,
)
narrow.model_dump(include={"version", "interval_width", "interval_df", "interval_loc", "interval_scale"})

{'interval_width': 0.8,
 'interval_df': 2.84,
 'interval_loc': 0.17,
 'interval_scale': 0.835,
 'version': 'plain-narrow-v1'}

Version: Changing a posterior preset’s calculation requires a new version.
Validation: Use the constructor or model_validate to validate a payload. Unknown fields fail rather than being silently ignored.
Profile change: Changing dispersion weighting, \(\lambda\) or \(\kappa\) discards the inherited interval shape and fitted-through date. A supported calibration may replace them; otherwise an explicit shape is required.
Preparation: Rebuild subject statistics under the changed settings.
Persistence: Load JSON or TOML in the calling application, then pass the payload to BayesianSettings.model_validate. The library performs no file I/O.

Numerical guard

The variance floor \(\varepsilon\) prevents a zero variance from producing infinite precision, \(\tau_j=1/\max(\sigma_j^2,\varepsilon)\). It is an implementation guard, not a calibration option: 0.000000000001.

Renamed constants

BAYESIAN_DEFAULTS: Replaces DSL_DEFAULTS for new code.
Compatibility: The old name warns but preserves its object and version for replay.

The panel workflow reference covers its separate settings class.