stan

Pros of PyMC

• Python-based, integrating seamlessly with the Python ecosystem
• User-friendly API, making it more accessible for beginners
• Extensive documentation and tutorials available

Cons of PyMC

• Generally slower performance compared to Stan
• Less flexibility in model specification for complex hierarchical models

Code Comparison

PyMC example:

import pymc as pm

with pm.Model() as model:
    mu = pm.Normal('mu', mu=0, sigma=1)
    obs = pm.Normal('obs', mu=mu, sigma=1, observed=data)
    trace = pm.sample(1000)

Stan example:

data {
  int<lower=0> N;
  vector[N] y;
}
parameters {
  real mu;
}
model {
  mu ~ normal(0, 1);
  y ~ normal(mu, 1);
}

Both Stan and PyMC are powerful probabilistic programming frameworks, but they cater to different user bases and have distinct strengths. Stan offers superior performance and flexibility for complex models, while PyMC provides a more accessible entry point for Python users and integrates well with the broader Python data science ecosystem.

Pros of TensorFlow Probability

• Seamless integration with TensorFlow ecosystem for deep learning and neural networks
• Supports GPU acceleration for faster computations on large datasets
• Offers a wider range of probabilistic models and distributions

Cons of TensorFlow Probability

• Steeper learning curve, especially for those not familiar with TensorFlow
• Less focus on Bayesian inference compared to Stan
• May be overkill for simpler statistical modeling tasks

Code Comparison

Stan:

parameters {
  real mu;
  real<lower=0> sigma;
}
model {
  y ~ normal(mu, sigma);
}

TensorFlow Probability:

import tensorflow_probability as tfp
tfd = tfp.distributions

model = tfd.Normal(loc=tf.Variable(0.), scale=tf.Variable(1.))
loss = -model.log_prob(y)

Both examples show a simple normal distribution model, but TensorFlow Probability integrates more closely with TensorFlow's computational graph and automatic differentiation system.

Pros of Pyro

• Built on PyTorch, allowing seamless integration with deep learning models
• Supports dynamic computation graphs, enabling more flexible model structures
• Offers a wide range of inference algorithms, including variational inference and MCMC

Cons of Pyro

• Less mature and potentially less stable compared to Stan
• Smaller community and fewer resources for learning and troubleshooting
• May be less efficient for traditional statistical models

Code Comparison

Stan (example of a simple linear regression):

data {
  int<lower=0> N;
  vector[N] x;
  vector[N] y;
}
parameters {
  real alpha;
  real beta;
  real<lower=0> sigma;
}
model {
  y ~ normal(alpha + beta * x, sigma);
}

Pyro (equivalent linear regression):

import pyro
import torch

def model(x, y):
    alpha = pyro.sample("alpha", pyro.distributions.Normal(0, 10))
    beta = pyro.sample("beta", pyro.distributions.Normal(0, 10))
    sigma = pyro.sample("sigma", pyro.distributions.HalfNormal(10))
    mean = alpha + beta * x
    with pyro.plate("data", len(x)):
        pyro.sample("obs", pyro.distributions.Normal(mean, sigma), obs=y)

Pros of DoWhy

• Focused specifically on causal inference and effect estimation
• Python-based, making it more accessible for data scientists familiar with Python ecosystems
• Provides a unified interface for various causal inference methods

Cons of DoWhy

• Less mature and comprehensive compared to Stan's broader statistical modeling capabilities
• Smaller community and ecosystem of extensions/tools
• More limited in terms of advanced probabilistic modeling features

Code Comparison

Stan (probabilistic modeling):

data {
  int<lower=0> N;
  vector[N] x;
  vector[N] y;
}
parameters {
  real alpha;
  real beta;
  real<lower=0> sigma;
}
model {
  y ~ normal(alpha + beta * x, sigma);
}

DoWhy (causal inference):

from dowhy import CausalModel
import pandas as pd

data = pd.read_csv("data.csv")
model = CausalModel(
    data=data,
    treatment='treatment',
    outcome='outcome',
    common_causes=['confounding_variable']
)
identified_estimand = model.identify_effect()
estimate = model.estimate_effect(identified_estimand)