What is a hierarchical probability model?
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. Hierarchical modeling is used when information is available on several different levels of observational units.
What is Bayesian multilevel modeling?
In addition to standard reasons for Bayesian analysis, Bayesian multilevel modeling is often used when the number of groups is small or in the presence of many hierarchical levels. When the comparison of groups is of main interest, Bayesian multilevel modeling can provide entire distributions of group-specific effects.
What is NumPyro?
NumPyro is a small probabilistic programming library that provides a NumPy backend for Pyro. We rely on JAX for automatic differentiation and JIT compilation to GPU / CPU. This is an alpha release under active development, so beware of brittleness, bugs, and changes to the API as the design evolves.
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 to create a hierarchical binominal model in PyMC3?
Computing the marginal posterior directly is a lot of work, and is not always possible for sufficiently complex models. On the other hand, creating heirarchichal models in pymc3 is simple. We can use the samples obtained from the posterior to estimate the means of α and β. Auto-assigning NUTS sampler… Initializing NUTS using jitter+adapt_diag…
How is hierarchical linear regression used in psychology?
Hierarchical modeling allows the best of both worlds by modeling subjects’ similarities but also allowing estimiation of individual parameters. As an aside, software from our lab, HDDM, allows hierarchical Bayesian estimation of a widely used decision making model in psychology.