This repository contains data and models to produce posteriors based on different probabilistic programming languages (PPL). Currently, the focus is Stan, but it should be possible to use it with other frameworks as well.
There are many purposes with the PDB
- A simple repository to access many models and datasets in a structured way from R and Python
- Store models and data in a structure that lends itself for testing inference algorithms on a large number of posteriors.
- A structure that makes it easy for students to access models and data for courses in Bayesian data analysis.
- A structure that is framework agnostic (although now Stan is in focus) and can be used with many different probabilistic programming frameworks.
- A structure that simplifies regression testing of probabilistic programming frameworks.
- Providing reliable gold standards for use in inference method development.
The long term goal is to move the posterior database to an open RESTful NoSQL database for easy access.
See DATABASE_CONTENT.md for the details content of the posterior database.
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.
Install the package from github
remotes::install_github("MansMeg/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"
## [2] "arma-arma11"
## [3] "eight_schools-eight_schools_centered"
## [4] "eight_schools-eight_schools_noncentered"
## [5] "garch-garch11"
## [6] "gp_pois_regr-gp_pois_regr"
po <- posterior("eight_schools-eight_schools_centered", pdb = pd)
po## Posterior
##
## Data: eight_schools
## The 8 schools dataset of Rubin (1981)
##
## Model: eight_schools_centered
## A centered hiearchical model for 8 schools
From the posterior we can easily access data and models as
sc <- stan_code(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);
## }
dat <- get_data(po)
dat## $J
## [1] 8
##
## $y
## [1] 28 8 -3 7 -1 1 18 12
##
## $sigma
## [1] 15 10 16 11 9 11 10 18
Finally we can access gold standard posterior draws and information on how those were computed as follows.
rp_info <- reference_posterior_info(po)
rp_info## Posterior: eight_schools-eight_schools_noncentered
## Method: stan_sampling (rstan 2.19.2)
## Arguments:
## chains: 10
## iter: 20000
## warmup: 10000
## thin: 10
## seed: 4711
## adapt_delta: 0.95
gsd <- reference_posterior_draws(po)
gsd## Posterior: eight_schools-eight_schools_noncentered
## # A tibble: 10 x 10
## variable mean median sd mad q5 q95 rhat ess_bulk ess_tail
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 theta[1] 6.23 5.59 5.72 4.48 -1.56 16.4 1.00 10116. 9946.
## 2 theta[2] 5.03 4.90 4.67 4.16 -2.40 12.8 1.000 9908. 9992.
## 3 theta[3] 3.99 4.26 5.29 4.44 -4.71 11.8 1.000 10329. 9872.
## 4 theta[4] 4.78 4.68 4.84 4.29 -2.80 12.7 1.00 10448. 10079.
## 5 theta[5] 3.68 3.97 4.70 4.19 -4.47 10.9 1.00 10324. 9788.
## 6 theta[6] 3.99 4.13 4.83 4.30 -4.12 11.5 1.000 10195. 9682.
## 7 theta[7] 6.40 5.89 5.12 4.37 -0.888 15.6 1.00 9505. 9991.
## 8 theta[8] 4.89 4.77 5.28 4.44 -3.23 13.5 1.00 9869. 9515.
## 9 mu 4.44 4.47 3.36 3.34 -1.09 10.0 1.000 10374. 9871.
## 10 tau 3.60 2.72 3.26 2.53 0.250 9.92 1.00 9866. 10035.
The posterior is based on the posterior R package structure and can easily be summarized and transformed using the mentioned R package.
draws_df <- posterior::as_draws_df(gsd$draws)
head(draws_df)## # A tibble: 6 x 13
## .chain .iteration .draw `theta[1]` `theta[2]` `theta[3]` `theta[4]`
## <int> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 1 3.83 3.23 4.68 1.89
## 2 1 2 2 1.99 3.66 -0.296 -0.115
## 3 1 3 3 -3.57 5.64 3.70 7.68
## 4 1 4 4 9.40 17.4 8.35 10.9
## 5 1 5 5 2.01 3.43 3.74 1.32
## 6 1 6 6 5.95 6.08 7.68 6.25
## # … with 6 more variables: `theta[5]` <dbl>, `theta[6]` <dbl>,
## # `theta[7]` <dbl>, `theta[8]` <dbl>, mu <dbl>, tau <dbl>
See python README
See R README
The main focus of the database is simplicity in data and model, both in understanding and in use.
The following are the current design choices in designing the posterior database.
- Priors are hardcoded in model files as changing the prior changes the posterior. Create a new model to test different priors.
- Data transformations are stored as different datasets. Create new data to test different data transformations, subsets, and variable settings. This makes the database larger/less memory efficient but simplifies the analysis of individual posteriors.
- Models and data has (model/data).info.json files with model and data specific information.
- 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)
- Prefix ‘syn_’ stands for synthetic data where the generative process is known and can be found in content/data-raw.
- All data preprocessing is included in content/data-raw.
- Specific information for different PPL representations of models is included in the PPL syntax files as comments, not in the model.info.json files.