compute-constrained-bayes/index.md

## Dependencies

nimble install print
https://github.com/treeform/print

## Dependencies

The data folder is not included, but its contents are:
.
├── data
│   ├── stripped
│   └── stripped.gz

Where stripped.gz can be found at <https://oeis.org/wiki/JSON_Format,_Compressed_Files>

## Gotchas

Nimble doesn't play well with relative directories. Ignore and use make instead?

## To do

- [x] Exploration of OEIS data
- [ ] Subdivide subsequent tasks into steps
  - [x] Simple prediction of the next integer
    - [x] Simple predictions v1
    - [x] Wrangle the return types to something semi-elegant
    - [-] Maybe add some caching, e.g., write continuations to file, and read them next time.
  - [ ] JIT Bayesianism:
    - [x] Function to predict with a variable number of hypotheses
    - [x] Function to start predicting with a small number of hypotheses, and get more if the initial ones aren't enough. 
    - [x] Add the loop of: start with some small number of sequences, and if these aren't enough, read more.
    - [x] Clean-up
  - [ ] Infrabayesianism
      - [ ] Infrabayesianism x1: Predicting interleaved sequences.
        - Yeah, actually, I think this just captures an implicit assumption of Bayesianism as actually practiced.
      - [ ] Infrabayesianism x2: Deterministic game of producing a fixed deterministic prediction, and then the adversary picking whatever minimizes your loss
        - I am actually not sure of what the procedure is exactly for computing that loss. Do you minimize over subsequent rounds of the game, or only for the first round? Look this up.
        - Also maybe ask for help from e.g., Alex Mennen.
    - [ ] Write the actor 

--- 

An implementation of Infrabayesianism over OEIS sequences.
<https://oeis.org/wiki/JSON_Format,_Compressed_Files>

Or "Just-in-Time bayesianism", where getting a new hypothesis = getting a new sequence from OEIS which has the numbers you've seen so far. 

Implementing Infrabayesianism as a game over OEIS sequences. Two parts:
1. Prediction over interleaved sequences. I choose two OEIS sequences, and interleave them: a1, b1, a2, b2.
  - Now, you don't have hypothesis over the whole set, but two hypothesis over the 
  - I could also have a chemistry like iteration:
    a1
    a2 b1
    a3 b2 c1
    a4 b3 c2 d1
    a5 b4 c3 d2 e1
    .................
  - And then it would just be computationally absurd to have hypotheses over the whole 

2. Game where: You provide a deterministic procedure for estimating the probability of each OEIS sequence giving a list of trailing examples.