Bayesian Notions and False Positives
Download
1 / 19

Bayesian Notions and False Positives - PowerPoint PPT Presentation


  • 74 Views
  • Uploaded on

Bayesian Notions and False Positives. In the 2004, presidential election, of those Texans who voted for either Kerry or Bush, 62% voted for Bush and 38% for Kerry. Of the Massachusetts residents who voted for either Kerry or Bush, 37% voted for Bush and 63% for Kerry.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Bayesian Notions and False Positives' - keala


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

In the 2004, presidential election, of those Texans who voted for either Kerry or Bush,

62% voted for Bush and

38% for Kerry.

Of the Massachusetts residents who voted for either Kerry or Bush,

37% voted for Bush and

63% for Kerry.

Bill was a Kerry voter. He comes from either Texas or Massachusetts but I know nothing more about him.

Is it more likely that he comes from Texas or from Massachusetts?


I need to tell you that: voted for either Kerry or Bush,

in Texas there were 7.4 million voters for either Kerry or Bush and

in Massachusetts there were only 2.9 million such voters.




Bayes theorem
Bayes’ Theorem Texas and only 39% came from Massachusetts.

Where:

Is the probability of Event B given that Event A has occurred

Is the probability of Event A given that Event B has occurred

Is the probability of Event B

Is the probability of Event A


Bayes theorem for kerry voter vs texan
Bayes’ Texas and only 39% came from Massachusetts. Theorem for Kerry_voter vs. Texan


False positives in medical tests
False Positives in Medical Tests Texas and only 39% came from Massachusetts.

Suppose that a test for a disease generates the following results:

  • if a tested patient has the disease, the test returns a positive result 99.9% of the time, or with probability 0.999

    2. if a tested patient does not have the disease, the test returns a negative result 99.5% of the time, or with probability 0.995.

    Suppose also that only 0.2% of the population has that disease, so that a randomly selected patient has a 0.002 prior probability of having the disease.


False positives in medical tests1
False Positives in Medical Tests Texas and only 39% came from Massachusetts.

Suppose that a test for a disease generates the following results:

  • if a tested patient has the disease, the test returns a positive result 99.9% of the time, or with probability 0.999

    2. if a tested patient does not have the disease, the test returns a negative result 99.5% of the time, or with probability 0.995.

    Suppose also that only 0.2% of the population has that disease, so that a randomly selected patient has a 0.002 prior probability of having the disease.

What is the probability of a “false positive”:

The patient does not have the disease

given that the test was positive?


Let’s begin with Texas and only 39% came from Massachusetts.

What is the probability of a “true positive”:

The patient does have the disease

given that the test was positive?

A: Patient Tests Positively

B: Patient Has Disease

Is the probability Patient Has Disease given that Patient Tests Positively

Is the probability Patient Tests Positively given that Patient Has Disease

Is the probability Patient Has Disease

Is the probability Patient Tests Positively


Let’s begin with Texas and only 39% came from Massachusetts.

What is the probability of a “true positive”:

The patient does have the disease

given that the test was positive?

A: Patient Tests Positively

B: Patient Has Disease

Is the probability Patient Has Disease given that Patient Tests Positively

Is the probability Patient Tests Positively given that Patient Has Disease

Is the probability Patient Has Disease

Is the probability Patient Tests Positively


Let’s begin with Texas and only 39% came from Massachusetts.

What is the probability of a “true positive”:

The patient does have the disease

given that the test was positive?

A: Patient Tests Positively

B: Patient Has Disease

Is the probability Patient Has Disease given that Patient Tests Positively

.999

.002

Is the probability Patient Tests Positively


What is the Texas and only 39% came from Massachusetts.

probability that the Patient Tests Positively?

Is the probability Patient Has Disease given that Patient Tests Positively

.999

.002

.006988


What is the probability of a “false positive”: Texas and only 39% came from Massachusetts.

The patient does not have the disease

given that the test was positive?

A: Patient Tests Positively

B: Patient Has Disease

.2859 and P(not B|A) is 1-.2859 = .7141

.999

.002

.006988


+ Texas and only 39% came from Massachusetts.

TEST NEGATIVE

+



ad