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PyMC is a python module that implements Bayesian statistical models and fitting algorithms, including Markov chain Monte Carlo. Its flexibility and extensibility make it applicable to a large suite of problems. Along with core sampling functionality, PyMC includes methods for summarizing output, plotting, goodness-of-fit and convergence diagnostics.
PyMC3 performs Bayesian statistical modeling and model fitting focused on advanced Markov chain Monte Carlo and variational fitting algorithms. It offers powerful sampling algorithms, such as the No U-Turn Sampler, allowing complex models with thousands of parameters with little specialized knowledge of fitting algorithms, intuitive model specification syntax, and optimization for finding the maximum a posteriori (MAP) point. PyMC3 uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed.