Stan

"Thousands of users rely on Stan for statistical modeling, data analysis, and prediction in the social, biological, and physical sciences, engineering, and business.

Users specify log density functions in Stan’s probabilistic programming language and get:

• full Bayesian statistical inference with MCMC sampling (NUTS, HMC)
  
• approximate Bayesian inference with variational inference (ADVI)
  
• penalized maximum likelihood estimation with optimization (L-BFGS)
  

Stan’s math library provides differentiable probability functions & linear algebra (C++ autodiff). Additional R packages provide expression-based linear modeling, posterior visualization, and leave-one-out cross-validation."

http://mc-stan.org/

"PyStan provides an interface to Stan, a package for Bayesian inference using the No-U-Turn sampler, a variant of Hamiltonian Monte Carlo."

https://pystan.readthedocs.io/en/latest/