Probability
List of probability topics:
- https://en.wikipedia.org/wiki/List_of_probability_topics
- https://en.wikipedia.org/wiki/Outline_of_probability
P(x,y) is the same as
P(x \cap y)A very common notation that you need to understand is that is the same thing as saying .
Learned this to learn about how we can create AI that makes optimal decisions given limited information and uncertainty.
The classical definition of probability:
However, there are 3 problems with this classical definition:
- Logically inconsistent
- Elements in may be difficult to count
- needs to be finite (in the case for example of infinite sample space)
There are two extended interpretations of probability:
4-Part Method
- Identify the sample space (i.e. outcomes) → helps to use a tree
- Define Events of Interest (ex: when you win)
- Determine Outcome Probabilities
- Assign Edge Probabilities
- compute Outcome Probabilities
- Compute Event Probabilities
Variables vs. Events?
Unconditional Probability Unconditional probability is the degree of belief in a proposition in the absence of any other evidence. The result of rolling a die is not dependent on previous events.
Concepts
- Axioms of Probability
- Conditional Probability
- Bayes Rule
- Joint Probability
- Probability Rules
- Law of Total Probability
It’s easy to create an arbitrary distribution over (0,1). Just take any function that doesn’t blow up anywhere between 0 and 1 and stays positive. Then, simply integrate it from 0 to 1 and divide the function with that result.