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PyMC is a probabilistic programming library for Python that allows users to build Bayesian models with a simple Python API and fit them using state of the art algorithms such as Markov chain Monte Carlo (MCMC) methods and variational inference.

Features#

PyMC strives to make Bayesian modeling as simple and painless as possible, allowing users to focus on their problem rather than the methods.

Here is what sets it apart:

Modern: Includes state-of-the-art inference algorithms, including MCMC (NUTS) and variational inference (ADVI).
User friendly: Write your models using friendly Python syntax. Learn Bayesian modeling from the many example notebooks.
Fast: Uses PyTensor as its computational backend to compile through C, Numba or JAX, run your models on the GPU, and benefit from complex graph-optimizations.
Batteries included: Includes probability distributions, Gaussian processes, ABC, SMC and much more. It integrates nicely with ArviZ for visualizations and diagnostics, as well as Bambi for high-level mixed-effect models.
Community focused: Ask questions on discourse, join MeetUp events, follow us on Twitter, and start contributing.

Get started#

Example from Linear Regression#

This example demonstrates how to perform Bayesian inference for a linear regression model to predict plant growth based on environmental factors.

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

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.

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)

# 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

Params	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
betas[sunlight hours]	4.972	0.054	4.866	5.066	0.001	0.001	3003	1257	1
betas[water amount]	19.963	0.051	19.872	20.062	0.001	0.001	3112	1658	1
betas[soil nitrogen]	1.994	0.055	1.899	2.107	0.001	0.001	3221	1559	1
sigma	0.511	0.037	0.438	0.575	0.001	0	2945	1522	1

# 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:

Output	mean	sd	hdi_3%	hdi_97%
plant growth[0]	14.229	0.515	13.325	15.272
plant growth[1]	24.418	0.511	23.428	25.326
plant growth[2]	-6.747	0.511	-7.740	-5.797

# 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:

Output	mean	sd	hdi_3%	hdi_97%
plant growth[0]	12.149	0.515	11.193	13.135
plant growth[1]	29.809	0.508	28.832	30.717
plant growth[2]	-0.131	0.507	-1.121	0.791

Cite PyMC#

If you use PyMC in your research, please cite the following paper:

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}
}