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name: distributions-and-shapes description: "Choose Pyro distributions and debug batch, event, plate, support, and transform shapes." disable-model-invocation: true metadata: disco-role: operating license: Apache 2.0

Distributions And Shapes

Use this sub-skill when the user needs to choose a pyro.distributions distribution, reason about sample_shape, batch_shape, event_shape, or pyro.plate dimensions, add constraints/transforms, or debug log_prob, support, validation, NaN/Inf, HMM, stable, zero-inflated, mixture, matching, or CUDA shape issues.

Route First

• For distribution selection, Pyro-specific distribution families, constructor signatures, constraints/transforms, LKJ, HMM, matching, stable, mixture, and optional SciPy caveats, read references/distribution-catalog.md.
• For shape algebra, plate dimension placement, .to_event()/Independent, observation shape checks, trace shape diagnostics, and HMM/zero-inflated shape recipes, read references/shapes-and-plates.md.
• For concrete recovery steps after errors such as invalid support, argument constraint violations, invalid log_prob shape, NaNs/Infs, CUDA device mismatches, SciPy-dependent helper failures, and HMM duration/broadcast mistakes, read references/troubleshooting.md.

Best-Fit Tasks

Use this sub-skill for requests like:

• "which Pyro distribution should I use for zero-inflated counts, correlations, an HMM, a stable process, a matching, or a mixture?";
• "why does log_prob() have the wrong shape under plate?";
• "should this tensor dimension be a batch dim, event dim, or plate dim?";
• "fix ValueError: invalid log_prob shape, expected value argument..., components event_shape disagree, or an HMM duration mismatch";
• "use constraints, transform_to, biject_to, or TransformedDistribution safely";
• "make the same distribution code work on CPU and optional CUDA".

Boundaries And Reroutes

• Basic pyro.sample, pyro.param, pyro.plate introductions, parameter-store lifecycle, PyroModule, and observation basics: route to ../modeling-basics/.
• SVI, ELBO choice, autoguides, optimizers, and training-loop decisions: route to ../svi-and-autoguides/ after this sub-skill has resolved distribution and shape contracts.
• MCMC/NUTS/HMC, initialization strategies, posterior prediction, and predictive sample shapes: route to ../mcmc-and-prediction/ after this sub-skill has resolved support and transform constraints.
• Poutine handler composition, enumeration, config_enumerate, infer_discrete, TraceEnum_ELBO, and enum dimension allocation: route to ../effect-handlers-and-enumeration/.
• Domain-specific contributed workflows and optional integrations such as funsor, Horovod, Lightning, Graphviz, torchvision, pandas, scanpy, or zuko: route to ../contrib-and-domain-workflows/ and treat them as optional unless the active environment proves support.

High-Value Checks Before Answering

1. Start with the support and event type: real scalar, positive scalar, simplex, vector, matrix/correlation, integer count, category, sequence/HMM, matching, or transformed variable.
2. Inspect d.batch_shape, d.event_shape, d.shape(sample_shape), and d.log_prob(value).shape before proposing a plate or .to_event() fix.
3. Keep Pyro validation enabled while debugging; pass validate_args=True for a single suspect distribution if global validation is uncertain.
4. Every non-event batch dimension in a Pyro sample site must be declared by an enclosing pyro.plate or deliberately reinterpreted with .to_event().
5. For observed data, require obs to broadcast to fn.batch_shape + fn.event_shape; obs_mask broadcasts only to fn.batch_shape.
6. Treat CUDA, SciPy-backed helpers, and flow/domain extras as optional; do not claim they are available merely because CPU Pyro imports.