This morning I’m trying to look a bit at Bayesian Modelling so I can message Liam about a general plan to incorporate it into the current LCA uncertainty tool.
What are the goals of using a probabilistic modelling package?
In the LCA work, we have a set of functions. Each of these functions variables and it’s output are uncertain. We need to capture this uncertainty throughout the calculation. We won’t be using much data, so Bayesian techniques, where we might have one or two cases or be able to reasonably assume a prior.
I want to spend large chunks of my day working with probability. I should try and write about it!
At a high-level we can describe the process of constructing Bayesian modeling in 3 steps.
- Given some data and some assumptions on how this data could have been generated, we design a model by combining and transforming random variables.
- We use Bayes’ theorem to condition our models to the available data. We call this process inference, and as a result we obtain a posterior distribution. We hope the data reduces the uncertainty for possible parameter values, though this is not a guarantee of any Bayesian model.
- We criticize the model by checking whether the model makes sense according to different criteria, including the data and our expertise on the domain-knowledge. Because we generally are uncertain about the models themselves, we sometimes compare several models.
The goal is to produce a robust model. One that can be update with new data. It doesn’t specifically require Bayesian inference to make the model. The model can be constructed from some granularity of linear functions.
There are numerous methods to communicate the architecture of statistical models. These can be, in no particular order:
- Spoken and written language
- Conceptual diagrams (like DAG’s).
- Statistical notation.
- Computer Code
For a modern Bayesian practitioner it is useful to be literate across all these mediums.
https://www.youtube.com/watch?v=9SEIYh5BCjc
motivation for PPL The hope is to combine the structure of the world we have (in the form of a model of the world) which we can codify and then imbue it with the uncertainty, the lack of isomorphism of our model with reality.
”Concepts have a language like compositionality and encode probabilistic knowledge. These features allow them to be extended productively to new situations and support flexible reasonig and learning by inference.”
- The ability to build things up ??