pymc 6.3.2

Features

• Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal('x',0,1)

• Powerful sampling algorithms, such as the No U-Turn Sampler, allow complex models with thousands of parameters with little specialized knowledge of fitting algorithms.

• Variational inference: ADVI for fast approximate posterior estimation as well as mini-batch ADVI for large data sets.

• Relies on PyTensor which provides:

  • Computation optimization and dynamic C or JAX compilation

  • NumPy broadcasting and advanced indexing

  • Linear algebra operators

  • Simple extensibility

• Transparent support for missing value imputation

Linear Regression Example

Plant growth can be influenced by multiple factors, and understanding these relationships is crucial for optimizing agricultural practices.

Imagine we conduct an experiment to predict the growth of a plant based on different environmental variables.

import pymc as pm

# Taking draws from a normal distribution
seed = 42
x_dist = pm.Normal.dist(shape=(100, 3))
x_data = pm.draw(x_dist, random_seed=seed)

# Independent Variables:
# Sunlight Hours: Number of hours the plant is exposed to sunlight daily.
# Water Amount: Daily water amount given to the plant (in milliliters).
# Soil Nitrogen Content: Percentage of nitrogen content in the soil.


# Dependent Variable:
# Plant Growth (y): Measured as the increase in plant height (in centimeters) over a certain period.


# Define coordinate values for all dimensions of the data
coords={
 "trial": range(100),
 "features": ["sunlight hours", "water amount", "soil nitrogen"],
}

# Define generative model
with pm.Model(coords=coords) as generative_model:
   x = pm.Data("x", x_data, dims=["trial", "features"])

   # Model parameters
   betas = pm.Normal("betas", dims="features")
   sigma = pm.HalfNormal("sigma")

   # Linear model
   mu = x @ betas

   # Likelihood
   # Assuming we measure deviation of each plant from baseline
   plant_growth = pm.Normal("plant growth", mu, sigma, dims="trial")


# Generating data from model by fixing parameters
fixed_parameters = {
 "betas": [5, 20, 2],
 "sigma": 0.5,
}
with pm.do(generative_model, fixed_parameters) as synthetic_model:
   idata = pm.sample_prior_predictive(random_seed=seed) # Sample from prior predictive distribution.
   synthetic_y = idata.prior["plant growth"].sel(draw=0, chain=0)


# Infer parameters conditioned on observed data
with pm.observe(generative_model, {"plant growth": synthetic_y}) as inference_model:
   idata = pm.sample(random_seed=seed)

   summary = pm.stats.summary(idata, var_names=["betas", "sigma"])
   print(summary)

From the summary, we can see that the mean of the inferred parameters are very close to the fixed parameters

# Simulate new data conditioned on inferred parameters
new_x_data = pm.draw(
   pm.Normal.dist(shape=(3, 3)),
   random_seed=seed,
)
new_coords = coords | {"trial": [0, 1, 2]}

with inference_model:
   pm.set_data({"x": new_x_data}, coords=new_coords)
   pm.sample_posterior_predictive(
      idata,
      predictions=True,
      extend_inferencedata=True,
      random_seed=seed,
   )

pm.stats.summary(idata.predictions, kind="stats")

The new data conditioned on inferred parameters would look like:

# Simulate new data, under a scenario where the first beta is zero
with pm.do(
 inference_model,
 {inference_model["betas"]: inference_model["betas"] * [0, 1, 1]},
) as plant_growth_model:
   new_predictions = pm.sample_posterior_predictive(
      idata,
      predictions=True,
      random_seed=seed,
   )

pm.stats.summary(new_predictions, kind="stats")

The new data, under the above scenario would look like:

Getting started

Installation

To install PyMC on your system, follow the instructions on the installation guide.

Citing PyMC

Please choose from the following:

• PyMC: A Modern and Comprehensive Probabilistic Programming Framework in Python, Abril-Pla O, Andreani V, Carroll C, Dong L, Fonnesbeck CJ, Kochurov M, Kumar R, Lao J, Luhmann CC, Martin OA, Osthege M, Vieira R, Wiecki T, Zinkov R. (2023)

  • BibTex version

    @article{pymc2023,
      title = {{PyMC}: A Modern and Comprehensive Probabilistic Programming Framework in {P}ython},
      author = {Oriol Abril-Pla and Virgile Andreani and Colin Carroll and Larry Dong and Christopher J. Fonnesbeck and Maxim Kochurov and Ravin Kumar and Junpeng Lao and Christian C. Luhmann and Osvaldo A. Martin and Michael Osthege and Ricardo Vieira and Thomas Wiecki and Robert Zinkov },
      journal = {{PeerJ} Computer Science},
      volume = {9},
      number = {e1516},
      doi = {10.7717/peerj-cs.1516},
      year = {2023}
    }

• A DOI for all versions.

• DOIs for specific versions are shown on Zenodo and under Releases

Contact

We are using discourse.pymc.io as our main communication channel.

To ask a question regarding modeling or usage of PyMC we encourage posting to our Discourse forum under the “Questions” Category. You can also suggest feature in the “Development” Category. Requests for non-technical information about the project are also welcome on Discourse, we also use Discourse internally for general announcements or governance related processes.

You can also follow us on these social media platforms for updates and other announcements:

• LinkedIn @pymc

• YouTube @PyMCDevelopers

• X @pymc_devs

• Mastodon @pymc@bayes.club

To report an issue with PyMC please use the issue tracker.

License

Apache License, Version 2.0

Software using PyMC

Papers citing PyMC

See Google Scholar here and here for a continuously updated list.

Contributors

The GitHub contributor page shows the people who have added content to this repo which includes a large portion of contributors to the PyMC project but not all of them. Other contributors have added content to other repos of the pymc-devs GitHub organization or have contributed through other project spaces outside of GitHub like our Discourse forum.

If you are interested in contributing yourself, read our Code of Conduct and Contributing guide.

Support

PyMC is a non-profit project under NumFOCUS umbrella. If you want to support PyMC financially, you can donate here.

Professional Consulting Support

You can get professional consulting support from PyMC Labs.

Sponsors

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