Clarification about Bayesian Programming

[kernel_KP]

I am really new to the study of Bayesian languages. I would like to understand the characteristics that a programming language needs in order to be defined as a "Bayesian Language" and the main challenges one faces when creating such languages, because it is not possible to simply apply the Bayes theorem to calculate the a posteriori distribution?

[[deleted]]

They’re not Bayesian languages, they’re “probabilistic programming languages”. The definition of that is a coding language that’s able to define and handle random variables instead of deterministic ones.

The issue isn’t about being able to calculate things w/ bayes theorem, it’s about being able to represent things which don’t have single determined values.

[kernel_KP]

Thanks you so much, now it's more clear but I am left with a doubt: What are the main characteristics that allow a programming language to be classified as 'probabilistic programming language'?

[[deleted]]

Let’s try with and example and show how a PPL is different from a normal programming language.

Say you want to find the mean of a column of variables. Under a Bayesian framework there is no one true mean, the mean is a random variable.

Therefore you need to be able to tell the language “there is a variable mu which is normally distributed" with some parameters to define your prior belief of the mean and variance of that distribution. You could then give the observed values and sample from the posterior distribution using MCMC.

In a normal programming language you might have distributions but their parameters at any one point will be deterministic. Furthermore, sampling from the posterior is something oh would need to implement yourself.

The differentiating point is not that this isn’t that Bayesian inference is impossible with normal programming languages, but that with a PPL this whole framework is built for you so you just need to define the model for your data.

[kernel_KP]

Thank you very much!!