InferenceData schema specification

The InferenceData schema scheme defines a data structure compatible with NetCDF having 3 goals in mind: usefulness in the analysis of Bayesian inference results, reproducibility of Bayesian inference analysis and interoperability between different inference backends and programming languages.

Currently there are 2 beta implementations of this design:

Current design

InferenceData stores all quantities relevant to fulfilling its goals in different groups. Each group, described below, stores a conceptually different quantity. In general, each quantity will be represented by several multidimensional labeled variables.

Each group should have one entry per variable and each variable should be named. When relevant, the first two dimensions of each variable should be the sample identifier (chain, draw). For groups like observed_data or constant_data these two initial dimensions are omitted. Dimensions must be named and specify their index values, called coordinates. Coordinates can have repeated identifiers and may not be numerical. Variables must not share names with dimensions.

Moreover, each group contains the following attributes:

  • created_at: the date of creation of the group.

  • inference_library: the library used to run the inference.

  • inference_library_version: version of the inference library used.

InferenceData data objects contain any combination the groups described below. There are some relations (detailed below) between the variables and dimensions of different groups. Hence, whenever related groups are present they should comply with this relations.

posterior

Samples from the posterior distribution p(theta|y).

sample_stats

Information and diagnostics for each posterior sample, provided by the inference backend. It may vary depending on the algorithm used by the backend (i.e. an affine invariant sampler has no energy associated). The name convention used for sample_stats variables is the following:

  • lp: (unnormalized) log probability for sample

  • step_size

  • step_size_bar

  • tune: boolean variable indicating if the sampler is tuning or sampling

  • depth:

  • tree_size:

  • mean_tree_accept:

  • diverging: HMC-NUTS only, boolean variable indicating divergent transitions

  • energy: HMC-NUTS only

  • energy_error

  • max_energy_error

posterior_predictive

Posterior predictive samples p(y|y) corresponding to the posterior predictive distribution evaluated at the observed_data. Samples should match with posterior ones and each variable should have a counterpart in observed_data. The observed_data counterpart variable may have a different name.

observed_data

Observed data on which the posterior is conditional. It should only contain data which is modeled as a random variable. Each variable should have a counterpart in posterior_predictive, however, the posterior_predictive counterpart variable may have a different name.

constant_data

Model constants, data included in the model which is not modeled as a random variable. It should be the data used to generate the posterior and posterior_predictive samples.

prior

Samples from the prior distribution p(theta). Samples need not match posterior samples. However, this group will still follow the convention on chain and draw as first dimensions. Each variable should have a counterpart in posterior.

sample_stats_prior

Information and diagnostics for each prior sample, provided by the inference backend. It may vary depending on the algorithm used by the backend. Variable names follow the same convention defined in ``sample_stats` <#sample_stats>`_.

prior_predictive

Samples from the prior predictive distribution. Samples should match prior samples and each variable should have a counterpart in posterior_predictive/observed_data.

Planned features

The InferenceData structure is still evolving, with some feature being currently developed. This section aims to describe the roadmap of the specification.

Sampler parameters

Parameters of the sampling algorithm and sampling backend to be used for analysis reproducibility.

Out of sample posterior_predictive samples

predictions

Out of sample posterior predictive samples p(y’|y). Sample should match posterior samples. Its variables should have a counterpart in posterior_predictive. However, variables in predictions and their counterpart in posterior_predictive may not share coordinates.

predictions_constant_data

Model constants used to get the predictions samples. Its variables should have a counterpart in constant_data. However, variables in predictions_constant_data and their counterpart in constant_data may not share coordinates.

Examples

In order to clarify the definitions above, an example of InferenceData generation for a 1D linear regression is available in several programming languages and probabilistic programming frameworks. This particular inference task has been chosen because it is widely well known while still being useful and it also allows to populate all the fields in the InferenceData object.