All language subtitles for 06 - Solution Perform a Bayesian analysis

(upbeat synth music)

- [Instructor] In the previous movie, I described a problem

where you will determine the probability,

an item is genuine when it's reported genuine.

And an item is counterfeit when reported

counterfeit by museum appraisers and curators

based on the base rate of genuine items,

comprising 70% of the collection

and an appraiser accuracy rate of 90%.

So let's go ahead and fill in the worksheet

and perform our calculations.

I'll click in cell B6.

The probability in item is genuine is given in B3.

So in B6 I'll, type equal and B3.

That means that the probability it is counterfeit

or fake, not real is 1 minus 70%,

so in B7 we'll type equal

one minus and our base rates in B3, so enter.

70 and 30 is 100, which is correct.

Now we need to determine the probability

the appraisers are correct or incorrect.

So in B9, I'll type equal.

The probability they're correct is their accuracy,

so that's in B4.

And as with the probability of an item being counterfeit

the probability of them being incorrect

is 1 minus the probability they are correct.

So in B10

equal 1 minus

B4 and enter,

and we get 10%.

90 plus 10 equals 100,

so we're good there.

Now we can go over to our classification matrix

and calculate the probability of each one of our scenarios.

So we have an item actually being genuine

and being reported genuine.

So in E4 I'll type equal

and the base rate of them being genuine is 70%.

And I have that probability in B6.

And then I want to multiply that

by the probability that the curator is correct,

that's in B9 and enter.

So that's the probability for that scenario.

Now, in E5, I need to give the probability

that an item is reported as genuine

but is actually counterfeit,

so in other words, a mistake was made, so equal.

And I will have an item

is being counterfeit.

that is in B7.

And we'll multiply that by the probability,

that the appraiser is incorrect,

and that is in cell B10 and enter,

so we have 3%.

Now we have reported counterfeit and actually genuine,

so again, a mistake was made.

So we in F4 we'll type in equal sign

and we're multiplying the probability

that the item is actually genuine,

that is in B6.

By the probability that the appraiser made

a mistake that's in B10, enter.

So that's 7%.

And then in F5, we need to calculate the probability

that an appraiser correctly identified a counterfeit object.

So in F5 equal, and we are multiplying the probability

that the item is counterfeit that's in B7.

By the probability that the appraiser is correct,

that's in B9, enter.

And we get 27%.

And we can look at our values

to make sure that everything lines up.

So our correct guesses are 63% and 27%

of the time that's 90, that is our probability, correct.

And 7+3 is 10,

and that is the probability

of the appraiser being incorrect.

Now we can calculate the probability

that an item is genuine when reported genuine

and counterfeit reported counterfeit.

So I'll click in cell E8 type an equal sign.

And we need to calculate the percentage

of times that an item is reported as genuine

and it actually is.

So reported genuine is and cell E4

divide it by the total number of times

an item is identified as genuine,

both right and wrong.

And that is adding E4 and E5.

So I'll type the left parenthesis E4+E5,

right parenthesis and tab,

and we get 95%.

Now we can calculate the probability

an item is actually counterfeit

when it's reported counterfeit.

So in F8 I'll type equal

and we need to divide

the correct guesses by total guesses.

For this column, the correct guesses are in F5,

then I'll type a forward slash for division,

left parentheses and we need to add the total number

of times that an item is reported as counterfeit,

both right and wrong.

So that's F4+ F5, right parentheses and enter,

and we get 79%.

And so it appears that our team will do a very good job

of identifying genuine items with very little error

and still a pretty good

but not quite as good job identifying counterfeits.

I hope you enjoyed this problem.

Bayesian analysis is very different

from other types analysis that we typically do in Excel,

so don't worry if you didn't get it right on the first time.

Take a few minutes, walk away from the workbook,

come back and feel free to try again.