posteriordb: a database of Bayesian posterior inference

What is posteriordb?

posteriordb is a set of posteriors, i.e. Bayesian statistical models and data sets, reference implementations in probabilistic programming languages, and reference posterior inferences in the form of posterior samples.

Why use posteriordb?

posteriordb is designed to test inference algorithms across a wide range of models and data sets. Applications include testing for accuracy, testing for speed, and testing for scalability. Algorithms being tested may be approximate like variational inference or asymptotically exact like Markov chain Monte Carlo. posteriordb can be used to test new algorithms being developed or deployed as part of continuous integration for ongoing regression testing of algorithms in probabilistic programming frameworks.

posteriordb also makes it easy for students and instructors to access a range of pedagogical and real-world examples with precise model definitions, well-curated data sets, and reference posteriors.

posteriordb is framework agnostic and easily accessible from R and Python.

For more details regarding the use cases of posteriordb, see doc/use_cases.md.

Content

See DATABASE_CONTENT.md for the details content of the posterior database.

Contributing

We are happy with any help in adding posteriors, data, and models to the database! See CONTRIBUTING.md for the details on how to contribute.

Quick usage of the posterior database from R

Install the package from GitHub

remotes::install_github("stan-dev/posteriordb", subdir = "rpackage")

Load the R package and load a posterior from the default posteriordb.

library(posteriordb)
pd <- pdb_default() # Posterior database connection
pn <- posterior_names(pd)
head(pn)

## [1] "arK-arK"                         "arma-arma11"                    
## [3] "bball_drive_event_0-hmm_drive_0" "bball_drive_event_1-hmm_drive_1"
## [5] "butterfly-multi_occupancy"       "diamonds-diamonds"

po <- pdb_posterior("eight_schools-eight_schools_centered", pdb = pd)
po

## Posterior (eight_schools-eight_schools_centered)
## 
## Data: eight_schools
## The 8 schools dataset of Rubin (1981)
## 
## Model: eight_schools_centered
## A centered hiearchical model for 8 schools
## Frameworks: 'stan', 'pymc3'

From the posterior, we can easily access data and models as

sc <- pdb_stan_code(x = po)
sc

## data {
##   int <lower=0> J; // number of schools
##   real y[J]; // estimated treatment
##   real<lower=0> sigma[J]; // std of estimated effect
## }
## parameters {
##   real theta[J]; // treatment effect in school j
##   real mu; // hyper-parameter of mean
##   real<lower=0> tau; // hyper-parameter of sdv
## }
## model {
##   tau ~ cauchy(0, 5); // a non-informative prior
##   theta ~ normal(mu, tau);
##   y ~ normal(theta, sigma);
##   mu ~ normal(0, 5);
## }

We can get additional information about the model by using info().

info(sc)

## Model: eight_schools_centered
## A centered hiearchical model for 8 schools
## Frameworks: 'stan', 'pymc3'

To access data for a specific posterior, we can use pdb_data()

dat <- pdb_data(po)
dat

## $J
## [1] 8
## 
## $y
## [1] 28  8 -3  7 -1  1 18 12
## 
## $sigma
## [1] 15 10 16 11  9 11 10 18

Again, we can get additional information about the data by using info().

info(dat)

## Data: eight_schools
## The 8 schools dataset of Rubin (1981)

Finally, we can access reference posterior draws for the given posterior.

rpd <- reference_posterior_draws(po)

The posterior is based on the posterior R package structure and can easily be summarized and transformed using the posterior R package.

library(posterior)

## This is posterior version 0.1.2

summarize_draws(rpd)

## # A tibble: 10 x 10
##    variable  mean median    sd   mad     q5   q95  rhat ess_bulk ess_tail
##    <chr>    <dbl>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>    <dbl>    <dbl>
##  1 theta[1]  6.15   5.59  5.62  4.56 -1.68  16.3   1.00   10095.    9732.
##  2 theta[2]  4.94   4.77  4.65  4.14 -2.22  12.8   1.00   10049.   10139.
##  3 theta[3]  3.91   4.11  5.28  4.48 -4.91  11.8   1.00    9533.    9339.
##  4 theta[4]  4.80   4.70  4.77  4.22 -2.67  12.6   1.00   10026.    9666.
##  5 theta[5]  3.61   3.82  4.61  4.15 -4.26  10.6   1.00    9922.   10207.
##  6 theta[6]  4.05   4.16  4.80  4.32 -3.87  11.5   1.00    9783.   10039.
##  7 theta[7]  6.32   5.80  5.00  4.39 -0.855 15.3   1.00   10039.    9690.
##  8 theta[8]  4.88   4.79  5.32  4.47 -3.32  13.5   1.00    9605.    9871.
##  9 mu        4.41   4.36  3.31  3.30 -0.936  9.83  1.00   10041.    9973.
## 10 tau       3.60   2.75  3.20  2.55  0.257  9.73  1.00    9989.    9992.

Using info(), we can access more detailed information on the reference posterior draws.

info(rpd)

## Posterior: eight_schools-eight_schools_noncentered
## Method: stan_sampling (rstan 2.21.1)
## Arguments:
##   chains: 10
##   iter: 20000
##   warmup: 10000
##   thin: 10
##   seed: 4711
##     adapt_delta: 0.95

It is also possible to access only information for models, data, and draws as follows.

pdb_model_info(po)

## Model: eight_schools_centered
## A centered hiearchical model for 8 schools
## Frameworks: 'stan', 'pymc3'

pdb_data_info(po)

## Data: eight_schools
## The 8 schools dataset of Rubin (1981)

pdb_reference_posterior_draws_info(po)

## Posterior: eight_schools-eight_schools_noncentered
## Method: stan_sampling (rstan 2.21.1)
## Arguments:
##   chains: 10
##   iter: 20000
##   warmup: 10000
##   thin: 10
##   seed: 4711
##     adapt_delta: 0.95

Using the posterior database from python

See python README

Using the posterior database from R (extensive)

See R README

Design choices (so far)

The main focus of the database is simplicity, both in understanding and in use.

The following are the current design choices in designing the posterior database.

1. Priors are hardcoded in model files as changing the prior changes the posterior. Create a new model to test different priors.
2. Data transformations are stored as different datasets. Create new data to test different data transformations, subsets, and variable settings. This design choice makes the database larger/less memory efficient but simplifies the analysis of individual posteriors.
3. Models and data has (model/data).info.json files with model and data specific information.
4. Templates for different JSONs can be found in content/templates and schemas in schemas (Note: these don’t exist right now and will be added later)
5. Prefix ‘syn_’ stands for synthetic data where the generative process is known and found in content/data-raw.
6. All data preprocessing is included in content/data-raw.
7. Specific information for different PPL representations of models is included in the PPL syntax files as comments, not in the model.info.json files.