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Lesson 9 presents the conjugate model for exponentially distributed data.
Lesson 10 discusses models for normally distributed data, which play a central role in statistics.
For example, a simple probability question may ask: "What is the probability of Amazon.com, Inc., (NYSE: AMZN) stock price falling?
" Conditional probability takes this question a step further by asking: "What is the probability of AMZN stock price falling If A is: "AMZN price falls" then P(AMZN) is the probability that AMZN falls; and B is: "DJIA is already down," and P(DJIA) is the probability that the DJIA fell; then the conditional probability expression reads as "the probability that AMZN drops given a DJIA decline is equal to the probability that AMZN price declines and DJIA declines over the probability of a decrease in the DJIA index. This is also the same as the probability of A occurring multiplied by the probability that B occurs given that A occurrs, expressed as P(AMZN) x P(DJIA|AMZN).
This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.
In this module, you will learn methods for selecting prior distributions and building models for discrete data.
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Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities.
Bayes' theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability.
The theorem provides a way to revise existing predictions or theories (update probabilities) given new or additional evidence.
Bayes' theorem follows simply from the axioms of conditional probability.
Conditional probability is the probability of an event given that another event occurred.
The probability that the card is a king is 4 divided by 52, which equals 1/13 or approximately 7.69%. Now, suppose it is revealed that the selected card is a face card.