Random thoughts 2012 comp 066
This presentation is the property of its rightful owner.
Sponsored Links
1 / 15

Random Thoughts 2012 (COMP 066) PowerPoint PPT Presentation


  • 64 Views
  • Uploaded on
  • Presentation posted in: General

Random Thoughts 2012 (COMP 066). Jan-Michael Frahm Jared Heinly. Assignment. Calculate the probability of being pregnant with a positive pregnancy test for a women with age 27 and for a women of age 44 in 2008. Use the Bayes rule to compute the probability.

Download Presentation

Random Thoughts 2012 (COMP 066)

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


Random thoughts 2012 comp 066

Random Thoughts 2012(COMP 066)

Jan-Michael Frahm

Jared Heinly


Assignment

Assignment

  • Calculate the probability of being pregnant with a positive pregnancy test for a women with age 27 and for a women of age 44 in 2008. Use the Bayes rule to compute the probability.

  • Read in the Moldinov book chapter 6.


Pregnancy rate by age group

Pregnancy rate by age group


Bayes rule

Bayes Rule

  • Bayes rule


Bayes rule for pregnancy test

Bayes Rule for Pregnancy Test

Age 27: [99.99%, 84.16%]

Age 44: [ 99.96%, 37.67%]


Spam filtering

Spam filtering

  • Often done based on black list

    • too restrictive

    • easy to evade by putting false sender e-mail

  • Bayes rule can be used to perform spam filtering

  • Filtering based on words in the e-mail

    • “viagra” has high probability of spam

    • “Bayes-rule” has low probability of spam

  • can be learned from e-mails


Probability rules

Probability Rules

  • Probability of event = p

    • ex. probability of rolling a 1 on a die: p = 1/6

  • Probability of event not happening = 1 – p

    • ex. probability of not rolling a 1: p = 5/6

  • Probability of event happening n times in a row = pn

    • ex. probability of rolling five 1s in a row: p = (1/6)5

  • Probability of event happening at least once during n attempts = Inverse of probability of event not happening n times in a row = 1 – (1 – p)n

    • ex. probability of rolling a 1 at least once in 5 rolls: p = 1 – (5/6)5


Probability rules1

Probability Rules

  • Probability of event happening k times in n attempts

    • Binomial

  • Can only add probabilities when you want to know if any one of a set of outcomes occurred and it is impossible for the outcomes to occur at the same time

    • ex. probability of rolling a 1 or a 2 on a die: p = 2/6


Expected value

Expected Value

Σ

  • Expected value = probability of event * value of event

  • Ex: pay $1 to play a game, 10% chance of winning $5, 40% chance of winning $1

  • Expected Value = -1 + 0.1 * 5 + 0.4 * 1 = $-0.10


Perceptual pitfalls

Perceptual Pitfalls

  • The probability that two events will occur can never be greater than the probability that each will occur individually.

    • “a good story is often less probable than a less satisfying … [explanation]”

  • Missing information

  • Availability bias

    • recallable prior knowledge influences our estimates


Odds vs probability

Odds vs. Probability

  • Odds vs Probability


Binomial distribution

Binomial distribution

  • Binomial distribution: For events with K successes in N trials

  • Properties of a Binomial distribution:

    • Fixed number of trials

    • Only outcomes are success and fail?

    • Same probability for success in each trial

    • Independent trials (no influence of previous trials to current trial)


Description of data

Description of Data

  • Mean

    • Average

  • Median

    • Middle value

  • Standard deviation

    • Variability or spread of the data

  • Percentile

    • Position within ordered list of values


Confidence interval

Confidence Interval

  • Margin of error of N samples

z*=

Number of samples needed:


How many trials

How many trials?

  • Margin of error for a population proportion

    • Depends on proportion in the population that had the characteristic we searched for


  • Login