Inference and posterior products

Every inference method returns the common SamplerResult interface for diagnostics, posterior component draws, and power-spectrum stacks.

Inference methods and posterior products for ML-GPR.

Each sampler explores a MultiGPRegressor and returns the same SamplerResult interface:

res = MCMCSampler(gp, n_walkers=40).run(n_steps=300)
res.plot_corner()
ps = res.get_ps_stack(ps_gen, kbins, kern_name='eor*')

Use MCMCSampler as the general-purpose default, NestedSampler for evidence or multimodal posteriors, MAPOptimizer for a fast local approximation, and NUTSSampler for gradient-based posterior sampling.

class ps_eor.ml_gpr.samplers.MCMCSamples(samples, log_prob, n_burn=50, clip_nsigma=6, discard_walkers_nsigma=10, autocorr_time=None)

Bases: object

Raw chains produced by MCMCSampler.

get() removes burn-in, poorly converged walkers, and outliers.

get()

Return filtered posterior samples and log probabilities.

save(filename)

Save the chains and filtering settings to HDF5.

static load(filename)

Load chains saved with save().

class ps_eor.ml_gpr.samplers.NestedSamples(d)

Bases: Results

Dynesty results with the common sample-container interface.

get() returns equal-weight samples by default. logz contains the Bayesian evidence.

get(resample_equal=True)

Return posterior samples and likelihoods, optionally equal-weighted.

save(filename)

Save serializable Dynesty results to HDF5.

static load(filename)

Load nested-sampling results saved with save().

class ps_eor.ml_gpr.samplers.MAPSamples(samples, log_prob)

Bases: object

MAP point followed by draws from its Laplace approximation.

Row zero is the MAP. Remaining rows approximate uncertainty and should not be interpreted as exact posterior samples.

get()

Return samples and their MAP/Laplace log probabilities.

save(filename)

Save samples to HDF5.

static load(filename)

Load samples saved with save().

class ps_eor.ml_gpr.samplers.NUTSSamples(samples, log_prob)

Bases: object

Posterior draws produced by NUTSSampler.

get()

Return posterior samples and log probabilities.

save(filename)

Save posterior samples to HDF5.

static load(filename)

Load posterior samples saved with save().

class ps_eor.ml_gpr.samplers.SamplerResult(gp, samples, diagnostics=None)

Bases: object

Posterior samples and component predictions from any sampler.

Prediction methods propagate hyperparameter uncertainty by drawing a new cube at each posterior sample. For multi-epoch results, epoch may be 'combine', 'all', or an integer index.

get_parameter_names()

Names of the free parameters, e.g. 'fg_int.variance'.

get_n_params()

Number of free parameters.

get_parameter_samples(param_name)

All samples of one parameter, in sampling space.

plot_samples()

Plot parameter traces for convergence and burn-in inspection.

plot_samples_likelihood(p_true=None)

Plot log posterior against each parameter.

plot_corner(fig=None, plot_prior=True, **kargs_corner)

Plot the posterior, optionally shading prior quantile ranges.

select_random_sample(samples=None, rng=None)

Set the kernels to one random posterior sample.

generate_data_cubes(n_pick, kern_name='eor', fill_gaps=False, epoch='combine')

Return component cubes drawn at n_pick posterior samples.

kern_name accepts component-label patterns such as 'eor*'. For a shared-fraction time kernel, append ':coherent' or ':independent' to select one latent process.

Repeated calls intentionally produce different posterior realizations. Seed NumPy and Torch before calling for reproducible draws.

get_interpolated_i_cube(epoch='combine')

The data with flagged channels filled in, at one posterior sample.

get_ps_stack(ps_gen, kbins, n_pick=100, kern_name='eor', subtract_from=None, fill_gaps=False, epoch='combine')

Return component power spectra over posterior realizations.

If subtract_from is provided, spectra of subtract_from - component are accumulated instead. Repeated calls intentionally use new posterior realizations; seed NumPy and Torch before calling for reproducible results.

class ps_eor.ml_gpr.samplers.AbstractSampler(gp)

Bases: object

Base class for inference methods operating on one regressor.

get_parameter_names()

Return free parameter names in sampler-vector order.

get_result()

SamplerResult for the run so far. Subclasses implement this; run() calls it and returns the result.

log_marginal_likelihood(p)

Evaluate the likelihood at sampling-space vector p.

prior_transform(uu)

Transform a unit-cube vector into sampling space.

class ps_eor.ml_gpr.samplers.MAPOptimizer(gp, n_restarts=4, n_laplace_samples=2000, optimizer_cls=None, debug=False, validate_feasible=False)

Bases: AbstractSampler

Find the MAP and approximate local uncertainty with Laplace draws.

This is fast, but its uncertainty assumes a locally Gaussian posterior. Check result.diagnostics['laplace_valid'] before using the error bars.

Parameters:

• n_restarts – independent optimizations from different starting points; the best is kept. Guards against local optima.

• n_laplace_samples – draws from the Gaussian around the MAP, which become the “samples” downstream code uses for uncertainty.

• optimizer_cls – torch optimizer, LBFGS by default.

• validate_feasible – Check that every Laplace draw produces a valid covariance. This is slower and normally unnecessary.

run(n_steps, lr=1.0, verbose=False)

Optimize to the MAP and return a SamplerResult.

Parameters:

• n_steps – optimizer steps per restart.

• lr – learning rate.

• verbose – report the loss of each restart.

Leaves the kernels at the best-fit hyperparameters.

get_result()

SamplerResult holding the MAP point plus its Laplace approximation.

Computes the Hessian and draws within the priors’ hard bounds.

class ps_eor.ml_gpr.samplers.MCMCSampler(gp, n_walkers, emcee_moves='stretch', debug=False)

Bases: AbstractSampler

Ensemble MCMC via emcee – the dependable default.

Gradient-free and robust. Walkers start from prior draws, so n_walkers should comfortably exceed the number of free parameters. run(n_steps) discards a burn-in before returning; check SamplerResult.plot_samples() to confirm the chains have converged before trusting the result.

run(n_steps, verbose=False, live_update=False, n_burn=50, clip_nsigma=6, discard_walkers_nsigma=10)

Run n_steps of ensemble MCMC and return the result.

Walkers start from prior draws. n_steps counts steps per walker, so the total number of likelihood evaluations is n_steps * n_walkers. n_burn and the clipping controls determine which chain samples are retained in the returned result. live_update displays traces in a notebook.

get_result(n_burn=50, clip_nsigma=6, discard_walkers_nsigma=10)

SamplerResult for the chains sampled so far.

Parameters:

• n_burn – initial steps to discard. Set it from the trace plot rather than trusting the default.

• clip_nsigma – drop samples this far from the median of a parameter.

• discard_walkers_nsigma – drop whole walkers stuck at a much worse likelihood than the rest, i.e. never converged.

class ps_eor.ml_gpr.samplers.NestedSampler(gp, nlive=500, bound='multi', sample='auto', **kargs_dynesty)

Bases: AbstractSampler

Nested sampling via dynesty.

Handles multimodal posteriors and provides Bayesian evidence for model comparison.

run(live_update=False, **kargs_dynesty)

Run to convergence and return a SamplerResult.

Extra keyword arguments go to dynesty’s own run_nested, e.g. dlogz. Interrupting the run keeps whatever has been sampled.

get_result()

SamplerResult for the run so far. The underlying samples also carry the Bayesian evidence, for model comparison.

class ps_eor.ml_gpr.samplers.UltraNestNestedSampler(gp, nlive=500, bound='multi', **kargs_ultranest)

Bases: AbstractSampler

Nested sampling through the optional UltraNest dependency.

run(live_update=False, **kargs_ultranest)

Run to convergence and return a SamplerResult.

Extra keyword arguments go to ultranest’s own run. Interrupting the run keeps whatever has been sampled.

get_result()

SamplerResult for the run so far.

class ps_eor.ml_gpr.samplers.NUTSSampler(gp, warmup_steps=500, num_chains=1, max_tree_depth=8, target_accept_prob=0.8, full_mass=False, warm_start_map=False, debug=False)

Bases: AbstractSampler

No-U-Turn sampling through Pyro.

NUTS can sample strongly correlated posteriors more efficiently than gradient-free MCMC. Always inspect divergences, effective sample sizes, and r_hat before using the result.

Parameters:

• warmup_steps – Adaptation steps; several hundred are usually needed.

• max_tree_depth – Maximum trajectory depth and primary runtime control.

• target_accept_prob – Increase to reduce step size when chains diverge.

• full_mass – Adapt a dense mass matrix for correlated parameters.

• warm_start_map – Initialize at the MAP instead of a prior draw.

run(n_steps, verbose=False, seed=None)

Run NUTS and return samples with convergence diagnostics.

n_steps is the number of retained posterior draws per chain; warmup_steps additional adaptation steps are discarded. Multiple chains run sequentially because the stateless likelihood is not process-pickleable. The result records divergences, effective sample sizes, and split r_hat. Use at least four chains for a robust convergence assessment.

summary()

Print per-parameter between-chain ESS and r_hat from the last run.