Bayesian statistics with PyMC3: brief overview Frequency stati | Big Data Science

Bayesian statistics with PyMC3: brief overview
Frequency statistics rely on long-term event rates (data points) to calculate the desired variable. The Bayesian method can also work without a lot of events, even with a single data point. Frequency analysis gives a point estimate, while Bayesian analysis gives a distribution that can be interpreted as the confidence that the mean of the distribution is a good estimate for the variable. However, there is an uncertainty in the form of the standard deviation.
The Bayesian approach is useful in ML problems where estimates and validity are important. For example, today it could rain with a 60% chance.” The main formula underlying the Bayesian approach is Bayes' theorem, which allows you to calculate the posterior probability P(A|B ) of event A depending on event B.
• P(B|A) is called the probability that if event A happened, how likely is event B to happen?
• P(A) – probability of event A, a prior (initial) assumption about the variable of interest.
• P(B) is the probability of event B (evidence), which is usually difficult to calculate when estimating the posterior probability.
You can quickly calculate the Bayesian probability using the PyMC3 Python library https://docs.pymc.io/en/v3/. It allows you to write models using an intuitive syntax to describe the data generation process. PyMC3 allows you to tune an ML model with gradient-based MCMC algorithms like NUTS, with ADVI for fast approximate inference, including a mini-batch ADVI for scaling to large datasets, or with Gaussian processes to build Bayesian non-parametric models. PyMC3 includes a complete set of predefined statistical distributions that can be used as the building blocks of a Bayesian model.
This probabilistic programming package for Python allows users to fit Bayesian models using various numerical methods, most notably Markov Chain Monte Carlo (MCMC) and Variational Inference (VI). Instead of providing a basic model specification and fitting functions, PyMC3 includes functions for summarizing output and diagnosing the model.
PyMC3 aims to make Bayesian modeling as simple and painless as possible by allowing users to focus on their scientific problem rather than the methods used to solve it. The package uses Theano as a computational backend to quickly evaluate an expression, compute the gradient automatically, and perform computations on the GPU.
PyMC3 also has built-in support for modeling Gaussian processes, allowing you to generalize models and build graphs. There's model validation and convergence detection, custom stepwise methods, and unusual probability distributions. Bayesian models obtained using PyMC3 can be embedded in larger programs, and the results can be analyzed using any Python tools.
https://medium.com/@akashkadel94/bayesian-statistics-overview-and-your-first-bayesian-linear-regression-model-ba566676c5a7