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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.

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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.
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
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