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{doc}PyMC <pymc:index> is a probabilistic programming library for Python that allows users to build Bayesian models with a simple Python API and fit them using Markov chain Monte Carlo (MCMC) methods.

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 {doc}PyTensor <pytensor:index> 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 {doc}ArviZ <arviz:index> for visualizations and diagnostics, as well as {doc}Bambi <bambi:index> for high-level mixed-effect models.
  • Community focused: Ask questions on discourse, join MeetUp events, follow us on Twitter, and start contributing.

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

Get started

Announcements

:::::{container} full-width ::::{grid} 1 2 2 3 :gutter: 3

:::{grid-item-card} PyMC forked Aesara to PyTensor :link: pytensor_announcement :link-type: ref :class-header: bg-pymc-three

Release announcement ^^^ PyTensor will allow for new features such as labeled arrays, as well as speed up development and streamline the PyMC codebase and user experience. :::

:::{grid-item-card} PyMC 4.0 is officially released! :link: v4_announcement :link-type: ref :class-header: bg-pymc-three

Release announcement ^^^ PyMC 4.0 is a major rewrite of the library with many great new features while keeping the same modeling API of PyMC3. :::

:::{grid-item-card} PyMC - Office Hours :link: https://discourse.pymc.io/tag/office-hours :class-header: bg-pymc-one

Event ^^^ The PyMC team has recently started hosting office hours regularly. Subscribe on Discourse to be notified of the next event! :::

:::{grid-item-card} Probabilistic Programming in PyMC :link: https://austinrochford.com/posts/intro-prob-prog-pymc.html :class-header: bg-pymc-two

Talk ^^^ Austin Rochford gave the coolest talk on Probabilistic Programming in PyMC 4.0 :::

:::{grid-item-card} Sprint testimonials :link: sprint_testimonial :link-type: ref :class-header: bg-pymc-one

Blog post ^^^ Read about the recent PyMC-Data Umbrella sprint in this interview with Sandra Meneses, one of the participants who submitted a PR :::

:::: :::::

Sponsors

:::::{container} full-width ::::{grid} 1 2 2 2 :gutter: 2

:::{grid-item-card} NumFOCUS :link: https://numfocus.org

NumFOCUS is our non-profit umbrella organization. :::

:::{grid-item-card} PyMC Labs :link: https://pymc-labs.io

PyMC Labs offers professional consulting services for PyMC. ::: :::{grid-item-card} Mistplay :link: https://www.mistplay.com/

Mistplay is the world's leading Loyalty Program for mobile gamers. ::: :::{grid-item-card} ODSC :link: https://odsc.com/california/?utm_source=pymc&utm_medium=referral

The future of AI gathers here. ::: :::{grid-item-card} Adia Lab :link: https://www.adialab.ae/

Dedicated to basic and applied research in data and computational sciences. :::

:::: :::::

:::{toctree} :hidden:

about/ecosystem about/history about/testimonials :::

:::{toctree} :hidden: :caption: External links

Discourse https://discourse.pymc.io Twitter https://twitter.com/pymc_devs YouTube https://www.youtube.com/c/PyMCDevelopers LinkedIn https://www.linkedin.com/company/pymc/ Meetup https://www.meetup.com/pymc-online-meetup/ GitHub https://www.github.com/pymc-devs/pymc :::