up:: Rationality
Baye’s rule
Posterior Probability (credence in an idea) can be estimated by Prior(how much credence the idea had before you even looked at the evidence) multiplied by Likelihood(if the hypothesis is in fact true, how likely is it that you’re going to see the evidence that is currently being presented) divide the product by Evidence(commonality of the data found).
- Prior can be theories so far, anything relevant, data gathered.
- We want to decide the realms in which we want to be Bayesian.
Bayes’ Rule, also known as Bayes’ Theorem or Bayes’ Law, is a mathematical formula that describes the probability of an event based on prior knowledge or information. It is named after the Reverend Thomas Bayes, an 18th-century British mathematician and theologian who developed the formula.
Bayes’ Rule is expressed as:
P(A|B) = P(B|A) * P(A) / P(B)
where:
- P(A|B) is the conditional probability of event A given event B has occurred.
- P(B|A) is the conditional probability of event B given event A has occurred.
- P(A) is the prior probability of event A.
- P(B) is the probability of event B.
In other words, Bayes’ Rule tells us how to update our beliefs about the probability of an event A given new evidence B. We start with a prior probability of A, and then update this probability based on the likelihood of observing B given A and the overall probability of observing B.
Bayes’ Rule has many applications in fields such as statistics, artificial intelligence, and machine learning. It is used, for example, in Bayesian inference, which is a method for estimating parameters of statistical models based on observed data.
― #genAI/chatgpt