Maybe something to keep in mind, when I’m not feeling motivated to write dissertation is the deep truths that it can touch on. To try and hone in on the ‘foundational’ problem. Or search for the fundamental even if its not really foundational.
I probably need to set up a curriculum to learn statistics.
Research
Trying to portray the breadth of uncertainty that exists. What kind of foundation am I trying to lay wrt uncertainty? I need to settle on some classification and definitions.
- Explication of ontic/epistemic uncertainty (o hagan and igos).
- Practical uncertainty (walker).
- How this practical uncertainty informs modelling (warminik, wolff, I think dee) diagrams needed here.
- Using this structure to zoom in on uncertainty dealt with in this research.
I think it would be wise to read up on representation a bit more tomorrow to help guide my results collecting.
Information Theory
Decoder
If someone tells us r (the received message) and we want to infer what source (s) was sent. We use inverse probability.
It provides a probability measure for all possible source messages provided we know them.
This uses the sum and the product rule. is the total probability across s.
Probability theory
The way I see Bayesian or inverse probability at the moment is you:
- create a paramter space.
- The measure of probability in this space is the likelihood of the data set for each point (often a vector) in that space.
Reading: https://austinrochford.com/posts/intro-prob-prog-pymc.html
I’ve been tentative to lean into the tell the data story aspect of McElreath’s stuff. At the same time, the Bayesian way is to develop a conjecture and posit it against reality.
Is sampling always due to the intractability of computing the integral?
Probabilistic programming is a changing of primitives to distributions not values or functions.
Uncertainty is a personal matter; it is not the uncertainty but your uncertainty.
- Lindley