How to use PyMC3 for Bayesian modeling?

How to use PyMC3 for Bayesian modeling?

This post is devoted to give an introduction to Bayesian modeling using PyMC3, an open source probabilistic programming framework written in Python. Part of this material was presented in the Python Users Berlin (PUB) meet up.

What does zero inflated Poisson mean in PyMC3?

Zero-inflated Poisson log-likelihood. Negative binomial log-likelihood. ZeroInflatedNegativeBinomial (name, *args, …) Zero-Inflated Negative binomial log-likelihood. Discrete uniform distribution.

How is the negative binomial distribution parametrized in PyMC3?

The negative binomial distribution can be parametrized either in terms of mu or p, and either in terms of alpha or n. The link between the parametrizations is given by Poission distribution parameter (mu > 0). Gamma distribution parameter (alpha > 0). Alternative probability of success in each trial (0 < p < 1).

When to use PyMC3 in a case study?

Here we use PyMC3 on two Bayesian inference case studies: coin-toss and Insurance Claim occurrence. My last post was an introduction to Baye’s theorem and Bayesian inference by hand.

What can you learn from hierarchical Bayesian modeling?

With PyMC3, I have a 3D printer that can design a perfect tool for the job. One of the simplest, most illustrative methods that you can learn from PyMC3 is a hierarchical model. Many problems have structure. On different days of the week (seasons, years, …) people have different behaviors. Climate patterns are different.

How is hierarchical linear regression used in PyMC3?

This is the 3rd blog post on the topic of Bayesian modeling in PyMC3, see here for the previous two: Gelman et al.’s (2007) radon dataset is a classic for hierarchical modeling. In this dataset the amount of the radioactive gas radon has been measured among different households in all counties of several states.

How many levels of hierarchy are there in PyMC3?

This hierarchy has 3 levels (some would say it has 2 levels, since there are only 2 levels of parameters to infer, but honestly whatever: by my count there are 3). 3 levels is fine, but add any more levels, and it becomes harder for to sample. Try out a taller hierarchy to see if it works, but err on the side of 3-level hierarchies.

Which is the central problem in Bayesian modelling?

The central problem in Bayesian modelling is this: given data and a probabilistic model that we think models this data, how do we find the posterior distribution of the model’s parameters? There are currently two good solutions to this problem.

How to build a logistic regression using PyMC3?

We are going to begin with the simplest possible logistic model, using just one independent variable or feature, the duration. With the data in the right format, we can start building our first and simplest logistic model with PyMC3: Centering the data can help with the sampling.

How are generalised linear models used in PyMC3?

We will briefly describe the concept of a Generalised Linear Model (GLM), as this is necessary to understand the clean syntax of model descriptions in PyMC3. Subsequent to the description of these models we will simulate some linear data with noise and then use PyMC3 to produce posterior distributions for the parameters of the model.

Why do we use probabilities in Bayesian statistics?

And Bayesian’s use probabilities as a tool to quantify uncertainty. Therefore, the answers we get are distributions not point estimates. Step 1: Establish a belief about the data, including Prior and Likelihood functions.

How to fit a Bayesian linear regression to data?

Lets fit a Bayesian linear regression model to this data. As you can see, model specifications in PyMC3 are wrapped in a with statement. Here we use the awesome new NUTS sampler (our Inference Button) to draw 2000 posterior samples. Auto-assigning NUTS sampler…

How to create a linear regression in PyMC3?

Essentially we are creating a regression line defined by intercept and slope and add data points by sampling from a Normal with the mean set to the regression line. Lets fit a Bayesian linear regression model to this data. As you can see, model specifications in PyMC3 are wrapped in a with statement.