Notation
shorthand for probability
Take
\begin{equation} P(X = 1) = \frac{1}{6} \end{equation}
We can write this in short hand like:
\begin{equation} P(X^{1}) = P(X=1) = \frac{1}{6} \end{equation}
\(P\) vs \(p\)
Upper case \(P\) for probability mass function (one shot chance), lower case \(p\) for probability density functions (integral)
New Concepts
- degrees of belief and describing them using the language of probability
- discrete distribution and continuous distribution and joint probability distribution
- fun probability distributions
- conditional probability and Bayes Theorem
- unique models that leverage conditional probability
- conditional Gaussian models
- linear gaussian model
- conditional linear Gaussian models: use your big brain to add up 1) and 2), with continuous random variables \(X, Y\), and a discrete \(Z\), where \(p(x \mid y, z)\).
- sigmoid model
- unique models that leverage conditional probability
- Baysian Network and conditional independence
Important Results / Claims
- history and impact of decision making
- law of total probability
- fun axioms
- belief axioms:
- probability axioms:
- Methods of Compressing the Parameters of a Distribution
- assuming independence
- using a decision tree
- checking for conditional independence