# Graphical Models

https://en.wikipedia.org/wiki/Bayesian_network bayesian networks directed edges express conditional rpobablity. Hopefully acyclic. https://en.wikipedia.org/wiki/Graphical_model graphical models https://en.wikipedia.org/wiki/Markov_random_field

# Statistics

I should have more to say here? Probability Experimental design Hypothesis testing Goodness of fit metrices Bayes rules Regularization Bayes rule and regularization can be seen to be related. Regularization corresponds to a prior that the values of your parameters arenâ€™t going to be ridiculous. A Gaussian prior and guassian distrubtion of error

$e^{ -\frac{\eps^2}{\sigma^2} }$ $y_j = \eps_j + \sum a_i f_i(x_j)$

Machine learning

Measure theory stochastic calculus

Combinatorics

Markov decision processes Monte carlo algos las vegas algos

## Bayesian

bayesian vs freqeuntist Priors as regularization

# Distributions

Gaussian Poisson Binomial

# Mathematical

https://en.wikipedia.org/wiki/Cox%27s_theorem

from z3 import *
E = Sort("Event")
P = Function("P", E, RealSort())

# Proof system for probability theory?


https://en.wikipedia.org/wiki/Probability_axioms Kolmogorov axioms

Sets and probability. You need to know an ambient space X to be working in.

https://en.wikipedia.org/wiki/Probabilistic_logic

Law of Total Probability $P(A) = \sum P(A \cap B_i) = \sum P(A | B_i) P(B_i)$ if $B_i$ is a partition of the sample space

https://en.wikipedia.org/wiki/Law_of_total_expectation

Central limit theorem

Markov bound Chernoff bound