Fit

Fit(
    method,
    parameters,
    parameter_names,
    log_likelihood,
    prior_log_likelihood,
    aic,
    bic,
    nobs,
    converged,
    status,
    model,
    spec,
    dataset,
    construct_json,
    covariance=None,
    standard_errors=None,
    correlation=None,
    function_evaluations=None,
    profile=None,
    profile_intervals=None,
    optimizer=None,
    draws=None,
    posterior=None,
    posterior_rows=None,
    map=None,
    posterior_mean=None,
    mean_log_likelihood=None,
    posterior_summary=None,
    acceptance_rates=None,
    warmup=None,
    credible_level=None,
    dic=None,
    waic=None,
    waic_pd=None,
    looic=None,
    looic_se=None,
    loo_pd=None,
    j_stat=None,
    j_stat_pval=None,
    gmm_iterations=None,
    converged_within_tolerance=None,
    optimizer_fallback_count=None,
    degree_of_freedom=None,
    number_of_moment_conditions=None,
)

A fitted model: parameter estimates plus whichever estimator diagnostics the target populates.

Build one with :func:fit_mle, :func:fit_map, :func:fit_bayesian, or :func:fit_gmm rather than directly. MaximumLikelihood/MaximumAPosteriori fits additionally carry the Hessian-based covariance and (optionally) profile-likelihood intervals; a BayesianAnalysis fit carries the raw chains and posterior summary; a GMM fit carries the sandwich covariance and the J-statistic overidentification test.

Attributes

Name	Type	Description
method	str	`"MaximumLikelihood"`, `"MaximumAPosteriori"`, `"BayesianAnalysis"`, or `"GMM"`.
parameters	dict	Parameter name -> fitted value. Read the Notes below before using it on a model whose parameter names repeat.
parameter_names	list of str	Every fitted parameter’s name, in the runner’s order, repeats included. This is the parameter axis order of :attr:`covariance`/:attr:`draws`/etc., and it is the full-length record :attr:`parameters` can be short of.
covariance, correlation	numpy.ndarray or None	`n x n`, aligned with :attr:`parameter_names`. `None` when not computed (MLE/MAP with `hessian=False`).
standard_errors	dict or None	Parameter name -> standard error. `None` when not computed.
log_likelihood, aic, bic	float or None	`None` for a GMM fit (method-of-moments has no likelihood surface to report them from); see :func:`_none_if_nan` for why `None` rather than `nan` was chosen.
prior_log_likelihood	float	The prior half of the log-posterior. Kept as the runner’s raw value (including its structural `nan` for GMM) – this is bookkeeping, not a primary reporting field.
nobs	int	Number of observations the fit was computed against. For a GMM fit this is the record length the estimator itself divides its sandwich covariance by.
converged	bool
status	str	`"Success"`, `"MaximumIterationsReached"`, etc.
function_evaluations	int or None	MLE/MAP only; `None` for Bayesian/GMM fits (the runner never populates it there).
model	Model	The fitted model: :attr:`parameters` applied to the construct’s spec. Simulate from it with :func:`~corehydropy.model_simulate`.
profile	dict or None	MLE/MAP only, present when the fit was built with `profile=True`: parameter name -> `profile_bins x 2` array with columns `[value, log_likelihood]`.
draws	numpy.ndarray or None	Bayesian only: the raw chains, shape `(n_iterations, n_chains, n_params)` – the same `[iteration, chain, parameter]` axis order `corehydror` returns.
posterior	numpy.ndarray or None	Bayesian only: the thinned draw matrix the analyses consume, shape `(posterior_rows, n_params)`, its columns aligned with :attr:`parameter_names` (the same convention :attr:`draws` uses for its parameter axis).
posterior_rows	int or None	Bayesian only: the number of retained posterior draws, `posterior.shape[0]`.
map, posterior_mean	dict or None	Bayesian only: the two posterior point estimates, parameter name -> value.
mean_log_likelihood	numpy.ndarray or None	Bayesian only: the chain-averaged log-likelihood trace, one value per iteration.
posterior_summary	dict or None	Bayesian only: `parameter_names` plus the arrays `mean`, `median`, `sd`, `lower`, `upper`, `rhat`, `ess`, each aligned with `parameter_names`. (Named `posterior_summary` rather than R’s `$summary` to avoid colliding with the :meth:`summary` text-report method Python’s class namespace forces onto one object.)
acceptance_rates	numpy.ndarray or None	Bayesian only, one value per chain.
warmup	int or None	Bayesian only: the warmup actually used (see :func:`fit_bayesian`’s derived default).
credible_level	float or None	Bayesian only: the credible level :attr:`posterior_summary`’s `lower`/`upper` were computed at (:func:`fit_bayesian`’s `credible_level` argument).
dic, waic, looic	float or None	Bayesian only, the usual Bayesian goodness-of-fit scalars.
looic_se	float or None	Bayesian only: the standard error of :attr:`looic`.
waic_pd, loo_pd	float or None	Bayesian only: the effective number of parameters behind :attr:`waic` and :attr:`looic`.
j_stat, j_stat_pval	float or None	GMM only. Bulletin 17C is always just-identified, so `j_stat_pval` is structurally `None` – there is no over-identified case to report a p-value for. At zero degrees of freedom `j_stat` is not interpretable either and :meth:`summary` does not print it.
gmm_iterations, converged_within_tolerance, optimizer_fallback_count		GMM only, the estimator’s own bookkeeping.
degree_of_freedom, number_of_moment_conditions	int or None	:func:`~corehydropy.fit_gmm_moments` only, matching corehydror’s `$degree_of_freedom` and `$number_of_moment_conditions`: the number of moment conditions q your function returned, and the over-identifying degrees of freedom `max(0, q - p)` that decide whether :attr:`j_stat_pval` exists at all. The :func:`~corehydropy.fit_gmm` model path does not report them (Bulletin 17C is always just-identified) and leaves both `None`.

Notes

:attr:parameters is a dict keyed by parameter name, so a model whose parameter names repeat loses every value but the last one under each repeated name. A mixture is the case that reaches this: a two-component Normal mixture fits six parameters, two of them named D1 and two named D2, and .parameters comes back with four entries in which the surviving D1/D2 are the standard deviations carrying the means’ labels. :attr:standard_errors, keyed the same way, collapses identically.

For the full ordered vector use :attr:parameter_names together with fit.model.spec["parameter_values"], which are the same length and aligned elementwise, or read :attr:covariance/:attr:draws directly (their axes are parameter_names, never the dict). :attr:aic, :attr:bic, and every diagnostic come from the C++ estimator and count all six; only the dict is short. corehydror’s coef() returns a plain named vector, which permits duplicate names, so R is unaffected.

Methods

Name	Description
confint	Confidence or credible intervals for the fit.
diagnostics	Estimation diagnostics off this fit. See :func:`fit_diagnostics`.
quantile_variance	Delta-method variance of a fitted quantile. See :func:`quantile_variance`.
summary	A multi-line text summary, mirroring R’s `print.corehydro_fit`/`summary.corehydro_fit`.
to_json	The fitted model’s spec as the JSON the shared C++ core parses.
to_model	The fitted model (:attr:`model`), as a verb alongside :meth:`to_json`.

confint

Fit.confint(level=0.95)

Confidence or credible intervals for the fit.

MLE/MAP fits get profile-likelihood confidence intervals; a Bayesian fit gets posterior credible intervals. GMM has no interval surface (see below).

For MLE/MAP: when the fit already carries a profile block at the requested level (built with profile=True or a prior :meth:confint call), those bounds are reused; otherwise the identical fit is re-run with profiling turned on – a deterministic optimizer reproduces the identical point estimate, so the rebuild’s confidence intervals are the ones the original fit would have carried had profile=True been requested at the matching level up front.

For Bayesian: :attr:Fit.posterior_summary’s lower/upper are already the posterior credible interval at :attr:Fit.credible_level (:func:fit_bayesian’s credible_level argument, 0.9 by default). When the requested level matches, those are returned directly; otherwise the identical seeded chain is re-run with credible_interval_width set to level (the same lazy-rebuild precedent as the profile path above – re-sampling with an identical seed reproduces the same chain bit-for-bit, so only the post-hoc credible-interval quantile computation changes). Because this method’s own default is 0.95 and a fit’s default is 0.9, a bare confint() on a Bayesian fit re-runs the chain; fit_bayesian(..., credible_level=0.95) avoids that.

GMM is method-of-moments and has no likelihood or posterior to draw an interval from; calling this raises. Use :meth:quantile_variance for the delta-method variance of a fitted quantile instead.

Parameters

Name	Type	Description	Default
level	float	Confidence (MLE/MAP) or credible (Bayesian) level. Matches R’s `confint()` convention, not `BayesianAnalysis`’s own 0.9 class default.	`0.95`

Returns

Name	Type	Description
	dict	`lower` and `upper`, each a dict of parameter name -> bound.

Examples

>>> from corehydropy import fit_mle, model_univariate
>>> peaks = [12500, 15300, 8900, 22100, 18700, 14200, 9800, 28500, 17400, 11600]
>>> f = fit_mle(model_univariate("Normal", peaks))
>>> ci = f.confint(level=0.9)

diagnostics

Fit.diagnostics()

Estimation diagnostics off this fit. See :func:fit_diagnostics.

quantile_variance

Fit.quantile_variance(aep)

Delta-method variance of a fitted quantile. See :func:quantile_variance.

summary

Fit.summary()

A multi-line text summary, mirroring R’s print.corehydro_fit/summary.corehydro_fit.

Returns

Name	Type	Description
	str	Parameters, the common goodness-of-fit scalars (or the J-statistic for a GMM fit), and – for a Bayesian fit – the posterior R-hat/ESS, or – for an MLE/MAP fit – the standard errors.

to_json

Fit.to_json()

The fitted model’s spec as the JSON the shared C++ core parses.

Serializes :attr:model (parameters, family, trends, …) exactly like :meth:~corehydropy.models.Model.to_json; it does not include the covariance, draws, or any other diagnostic on this Fit.

Returns

Name	Type	Description
	str	The fitted model spec as JSON.

to_model

Fit.to_model()

The fitted model (:attr:model), as a verb alongside :meth:to_json.

Returns

Name	Type	Description
	Model	Same object as :attr:`model`.