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Introduction to Bayesian Learning: Basic Terms and Notations

Learn the key terms and notations in Bayesian Learning, such as prior probability, conditional probability, posterior probability, and Bayes theorem. Understand how these concepts are used in machine learning problems.

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Introduction to Bayesian Learning: Basic Terms and Notations

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  1. Co2 Session 1

  2. Bayesian Learning

  3. As Bayes Learning is based on Probability , we have to learn the basic terms and notationslike • Prior probability • Conditional probability • Posterior probability • Bayes theorem etc.

  4. Prior probability Theprior probability of an event is its probability calculated from some prior information about the event. • ex: P(A) is 40 %.

  5. Prior information: • No of customers =100 • 20% of customers buys computer. • 50% customers are age is >35. So P(buys computer)=0.2 P(age=35)=0.5

  6. Conditional probability • Conditional probabilities expresses the probability that Event-A will occur when you assume (or know) that Event-B has already occurred. • notation: P(A|B)

  7. Posterior probability:(Inference): • is a Conditional probability which represents the updated prior probability after taking into account some new piece of information.-P(A|B)

  8. P(h) to denote the initial probability that hypothesis h holds, before we have observed the training data. • P(h) is often called the prior probability of h. • P(D) to denote the prior probability that training data D .The probability of D given no knowledge about which hypothesis holds • P(D|h) to denote the probability of observing data D given some world in which hypothesis h holds.

  9. But In machine learning problems we are interested in the probability P (h| D) that h holds given the observed training data D. • P (h| D) is called the posterior probability of h, as it reflects our confidence that h holds after we have seen the training data D. • The posterior probability P(h|D) reflects the influence of the training data D, in contrast to the prior probability P(h) , which is independent of D.

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