Approaches & Interpretations

Probability is the quantitative measurement of the likelihood of events in a random experiment.

  • Frequentist:
  • Bayesian:

Frequentist

Bayesian

Types of Probability

  • Conditional Probability
  • Frequentist Approach
  • Marginal Probability: Calculating probability of an event using contingency table(when it’s irrespective of the outcome of another event).
  • Joint Probability: The chance of a variable on X happening with another variable on the Y of the contingency table(When more than one event can happen at the same time).

Events and Rules of Probability

  • The events are formalized by sets within an event space denoted by .
  • Probability Function takes a set and returns a number between 0 and 1.
  • The probability of the entire event space must be 1:
  • the probability of mutually exclusive events(events that can't occur at the same time) is the sum of their probabilities: and
  • When events are not mutually exclusive: when two events can occur at the same time.
  • When events are independent: Two events which the occurrence of one is in no way influenced by the occurrence of the other.
    Two events are said to be independent of each other, if the probability that one event occurs in no way affects the probability of the other event occurring, or in other words if we have observation about one event it doesn’t affect the probability of the other.
  • Conditional Independent event: Two events A and B are conditionally independent given a third event C precisely if the occurrence of A and the occurrence of B are independent events in their conditional probability distribution given C. In other words, A and B are conditionally independent given C if and only if, given knowledge that C already occurred, knowledge of whether A occurs provides no additional information on the likelihood of B occurring, and knowledge of whether B occurs provides no additional information on the likelihood of A occurring.

Learning Material: