gwkokab.inference.flowMC_analytical_gwalk_poisson_likelihood¶

FlowMC log-posterior over per-event Gaussian summaries.

The counterpart of flowMC_discrete_poisson_likelihood for the analytical GWalk data representation, where each event is a mean and covariance rather than a cloud of posterior samples.

Functions¶

flowMC_analytical_gwalk_poisson_likelihood(...)

Build the flowMC log-posterior for the analytical GWalk data representation.

Module Contents¶

gwkokab.inference.flowMC_analytical_gwalk_poisson_likelihood.flowMC_analytical_gwalk_poisson_likelihood(dist_fn: Callable[..., numpyro.distributions.Distribution], priors: gwkokab.models.utils.JointDistribution, variables: Dict[str, numpyro.distributions.Distribution], constant_params: Dict[str, Any], variables_index: Dict[str, int], poisson_mean_estimator: Callable[[gwkokab.models.utils.ScaledMixture], tuple[jaxtyping.Array, jaxtyping.Array]], variance_cut_threshold: float | None) → Callable[[jaxtyping.Array, Dict[str, Any]], jaxtyping.Array][source]¶

Build the flowMC log-posterior for the analytical GWalk data representation.

The likelihood is that of the inhomogeneous Poisson process,

\[\log\mathcal{L}(\Lambda) \propto -\mu(\Lambda) + \sum_{n=1}^N \log \int \ell_n(\lambda)\,\rho(\lambda\mid\Lambda) \,\mathrm{d}\lambda\]

where \(\rho(\lambda\mid\Lambda) = \mathrm{d}N/\mathrm{d}V\,\mathrm{d}t\,\mathrm{d}\lambda\) is the merger rate density of a population parameterised by \(\Lambda\), \(\mu(\Lambda)\) is the expected number of detections for that population, and \(\ell_n(\lambda)\) is the likelihood for the \(n\)-th observed event’s parameters.

with the per-event integral evaluated over points resampled from each event’s Gaussian summary.

Parameters:

  • dist_fn (Callable[..., Distribution]) – Builds the population model from the sampled variables and the constants.

  • priors (JointDistribution) – Joint prior over the sampled variables, ordered as variables_index says.

  • variables (Dict[str, Distribution]) – Unused here; flowMC takes its priors from priors as a joint distribution rather than site by site.

  • constant_params (Dict[str, Any]) – Hyper-parameters frozen by the prior configuration rather than sampled.

  • variables_index (Dict[str, int]) – Maps each variable name to its position in the flat parameter vector. This is the ordering recorded as variables_index in the output HDF5.

  • poisson_mean_estimator (Callable) – Estimator of \(\mu(\Lambda)\), returning (mean, variance). See gwkokab.poisson_mean.

  • variance_cut_threshold (float | None) – Threshold above which the Monte Carlo variance of the estimate is penalised by variance_tapering_fn(). None disables the penalty.

Returns:

A log_posterior(x, data) callable. Non-finite values are mapped to \(-\infty\), so the sampler rejects such points rather than propagating NaN.

Return type:

Callable[[Array, Dict[str, Any]], Array]