bayespecon.models.flow.PoissonFlow¶

class bayespecon.models.flow.PoissonFlow(y, G, X, **kwargs)[source]¶

Non-spatial Bayesian OD-flow Poisson gravity model (count baseline).

Aspatial count analogue of OLSFlow: models origin-destination flow counts \(y_{ij} \in \mathbb{N}_0\) with a log-linear gravity mean and no spatial-lag terms,

\[y_{ij} \sim \operatorname{Poisson}(\lambda_{ij}), \qquad \log \boldsymbol{\lambda} = X\beta.\]

Provided as the count-data baseline analogue of OLSFlow, matching the role PoissonSARFlow plays relative to SARFlow. No spatial filter is applied (A = I_N), so there is no log-determinant precomputation, no rho_* parameters, and no sigma (the Poisson variance equals the mean).

Parameters:¶

y : array-like, shape (n, n) or (N,)¶

Observed non-negative integer flow counts. Float arrays whose values are close to integers are silently rounded.

G : libpysal.graph.Graph¶

Graph on n units. Required for API symmetry but the spatial weights are not used in estimation.

X : np.ndarray or pandas.DataFrame, shape (N, p)¶

Full origin-destination design matrix.

col_names : list[str], optional

Column labels for X. Defaults to ["x0", "x1", ...] when not provided and X is not a DataFrame.

k : int, optional

Number of regional attribute columns. Inferred from column names when they follow the dest_*/orig_* convention.

priors : dict, optional

Override default priors. Supported keys:

• beta_mu : float, default 0.0 — Normal prior mean for beta.

• beta_sigma : float, default 10.0 — Normal prior std for beta.

Spatial keys (rho_*) and sigma_sigma are ignored.

symmetric_xo_xd : bool, optional

If None (default), origin/destination design symmetry is auto-detected. Set explicitly to override.

Notes

No spatial filter is applied (A = I_N); the closed-form Thomas-Agnan & LeSage (2014, Table 83.1) effects from OLSFlow are reused unchanged on the (log-mean) linear-predictor scale.

__init__(y, G, X, **kwargs)[source]¶

Methods

__init__(y, G, X, **kwargs)
fit([draws, tune, chains, target_accept, ...])	Draw samples from the posterior.
fit_approx([draws, n, method, random_seed, ...])	Fit a variational approximation and return posterior draws.
posterior_predictive([n_draws, random_seed, ...])	Draw posterior-predictive flow counts for the Poisson gravity model.
spatial_diagnostics()	Run Bayesian LM specification tests for flow models.
spatial_diagnostics_decision([alpha, ...])	Return a model-selection decision from Bayesian LM test results.
spatial_effects([draws, ...])	Summarise posterior origin/destination/intra/network/total effects.
summary([var_names])	Return posterior summary table via ArviZ.

Attributes

approximation	Return the most recent PyMC variational approximation, if any.
inference_data	Return ArviZ InferenceData from the most recent fit, or None.
pymc_model	Return the PyMC model used for the most recent fit, or None.

property approximation[source]¶

Return the most recent PyMC variational approximation, if any.

fit(draws=2000, tune=1000, chains=4, target_accept=0.9, random_seed=None, store_lambda=False, idata_kwargs=None, **sample_kwargs)[source]¶

Draw samples from the posterior.

Parameters:¶

draws : int, default 2000¶

Number of posterior samples per chain (after tuning).

tune : int, default 1000¶

Number of tuning (warm-up) steps per chain.

chains : int, default 4¶

Number of parallel chains.

target_accept : float, default 0.9¶

Target acceptance rate for NUTS.

random_seed : int, optional¶

Seed for reproducibility.

store_lambda : bool, default False¶

If True, include the high-dimensional fitted mean lambda in the stored posterior. Leaving this False reduces memory and conversion overhead for Poisson flow models.

idata_kwargs : dict, optional¶

Forwarded to pm.sample. Defaults to {"log_likelihood": True} so that az.loo / az.waic / az.compare work out of the box; for SAR flow variants the captured Gaussian log-likelihood is post-processed to add the Jacobian contribution from log|I_N - rho_d W_d - rho_o W_o - rho_w W_w|.

**sample_kwargs¶

Additional keyword arguments forwarded to pm.sample.

Return type:¶

arviz.InferenceData

fit_approx(draws=2000, n=10000, method='advi', random_seed=None, store_lambda=False, compute_log_likelihood=True, **fit_kwargs)[source]¶

Fit a variational approximation and return posterior draws.

Parameters:¶

draws : int, default 2000¶

Number of samples to draw from the fitted approximation.

n : int, default 10000¶

Number of optimisation iterations for pm.fit.

method : {"advi", "fullrank_advi"}, default "advi"¶

Variational inference family to fit.

random_seed : int, optional¶

Seed for optimisation and posterior sampling.

store_lambda : bool, default False¶

If True, keep the high-dimensional fitted mean lambda in the posterior draws.

compute_log_likelihood : bool, default True¶

If True, compute pointwise log-likelihood after sampling and attach to the InferenceData (with Jacobian correction for SAR flow variants), enabling az.loo / az.waic.

**fit_kwargs¶

Additional keyword arguments forwarded to pm.fit.

property inference_data : arviz.data.inference_data.InferenceData | None[source]¶

Return ArviZ InferenceData from the most recent fit, or None.

posterior_predictive(n_draws=None, random_seed=None, parallel=-1)[source]¶

Draw posterior-predictive flow counts for the Poisson gravity model.

property pymc_model : pymc.model.core.Model | None[source]¶

Return the PyMC model used for the most recent fit, or None.

spatial_diagnostics()[source]¶

Run Bayesian LM specification tests for flow models.

Iterates over the class-level _spatial_diagnostics_tests registry and returns a tidy DataFrame with one row per test. See bayespecon.models.base.SpatialModel.spatial_diagnostics() for the column schema.

Raises:¶

RuntimeError – If the model has not been fit yet.

spatial_diagnostics_decision(alpha=0.05, format='graphviz', theme='default')[source]¶

Return a model-selection decision from Bayesian LM test results.

Walks the flow decision tree using Bayesian p-values from spatial_diagnostics() and recommends either OLSFlow (no spatial dependence detected) or SARFlow (at least one direction is significant).

Parameters:¶

alpha : float, default 0.05¶

Significance level for the Bayesian p-values.

format : {"graphviz", "ascii", "model"}, default "graphviz"¶

Output format. "model" returns the recommended model name string. "ascii" returns an indented box-drawing tree. "graphviz" returns a graphviz.Digraph (with ASCII fallback if graphviz is not installed).

Return type:¶

str or graphviz.Digraph

spatial_effects(draws=None, return_posterior_samples=False, ci=0.95, mode='auto', parallel=-1)[source]¶

Summarise posterior origin/destination/intra/network/total effects.

Wraps _compute_spatial_effects_posterior() to produce a tidy DataFrame indexed by predictor with posterior means, credible-interval bounds, and Bayesian p-values for each effect type (origin, destination, intra, network, total). Following Thomas-Agnan & LeSage (2014, §83.5.2), when destination and origin design blocks differ the decomposition is reported separately for shocks applied to each side.

Parameters:¶

draws : int, optional¶

Maximum number of posterior draws to use. Defaults to all.

return_posterior_samples : bool, default False¶

If True, also return the underlying posterior-draw arrays.

ci : float, default 0.95¶

Credible-interval coverage.

mode : {"auto", "combined", "separate"}, default "auto"¶

Controls whether destination- and origin-side effects are summed or reported separately. "auto" collapses to combined when the destination and origin design blocks are identical (self._symmetric_xo_xd) and reports both sides otherwise. "combined" always sums; "separate" always reports both.

parallel : int or None, default -1¶

Number of worker threads for the per-draw effects loop. -1 uses os.cpu_count(); None/0/1 forces sequential execution. Ignored by closed-form (OLSFlow, SEMFlow) variants.

Returns:¶

Long-format summary indexed by (predictor, side, effect) where side is one of "combined", "dest", "orig".

Return type:¶

pandas.DataFrame, or (DataFrame, dict)

summary(var_names=None, **kwargs)[source]¶

Return posterior summary table via ArviZ.

Parameters:¶

var_names : list, optional¶

Variable names to include. Defaults to all parameters.

**kwargs¶

Additional keyword arguments forwarded to az.summary.

Return type:¶

pandas.DataFrame