1 / 8

Bayesian analysis with a discrete distribution

Bayesian analysis with a discrete distribution. Source: Stattrek.com. Bayes Theorem. Probability of event A given event B depends not only on the relationship between A and B but on the absolute probability of A not concerning B and the absolute probability of B not concerning A.

fia
Download Presentation

Bayesian analysis with a discrete distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bayesian analysis with a discrete distribution Source: Stattrek.com

  2. Bayes Theorem • Probability of event A given event B depends not only on the relationship between A and B but on the absolute probability of A not concerning B and the absolute probability of B not concerning A. Start with --P(Ak∩B)=P(Ak).P(B|Ak)

  3. Bayes Theorem • If A1, A2, A3…An are mutually exclusive events of sample space S and B is any event from the same sample space and P(B)>0. then, • P(Ak|B)= P(Ak). P(B|Ak) P(A1). P(B|A1)+P(A2). P(B|A2)+… P(An). P(B|An)

  4. Sufficient conditions for Bayes • The sample space is partitioned into a set of mutually exclusive events { A1, A2, . . . , An }. • Within the sample space, there exists an event B, for which P(B) > 0. • The analytical goal is to compute a conditional probability of the form: P( Ak | B ). • We know at least one of the two sets of probabilities described below. • P( Ak ∩ B ) for each Ak • P( Ak ) and P( B | Ak ) for each Ak

  5. Eg. of Discrete Distribution • Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year.

  6. Eg. of Discrete Distribution • The weatherman has predicted rain for tomorrow. • When it actually rains, the weatherman correctly forecasts rain 90% P( B | A1 )of the time. • When it doesn't rain, he incorrectly forecasts rain 10% P( B | A2 ) of the time. • What is the probability that it will rain on the day of Marie's wedding (P(A1))? • A2==does not rain on wedding.

  7. Values for calculation • P( A1 ) = 5/365 =0.0136985 [It rains 5 days out of the year.] • P( A2 ) = 360/365 = 0.9863014 [It does not rain 360 days out of the year.] • P( B | A1 ) = 0.9 [When it rains, the weatherman predicts rain 90% of the time.] • P( B | A2 ) = 0.1 [When it does not rain, the weatherman predicts rain 10% of the time.]

  8. Applying the Bayes theorem • P(Ak|B)= P(Ak). P(B|Ak) P(A1). P(B|A1)+P(A2). P(B|A2)+… P(An). P(B|An) • P(A1|B)= P(A1). P(B|A1) P(A1). P(B|A1)+P(A2). P(B|A2) • P(A1|B)= 0.111

More Related