All language subtitles for 03 - Create a classification matrix

- [Instructor] In the previous movie,

I showed you a way to draw a graph

that visualizes the way probability

is combined to perform Bayesian analysis.

In this movie, I will show you how to create

a classification matrix,

which will take us one step closer

to implementing this analysis in Excel.

So let's review what we know

about our base rates and our accuracy.

First, we know that the base rate of green cabs is 85%.

That means that 15% of the cabs will be blue.

Also, we know that witnesses are accurate

as for color identification, 80% of the time.

And again, the cab can be green or blue.

Also, the witness can be accurate or not.

And those are the factors that we will use

to create a two by two probability

or a classification matrix.

So we know the probability

of arriving at each combination.

So let's take a look at a classification matrix.

Here's the data again, I won't repeat it,

but here is what the matrix look like.

And it is the compound probability

of reaching each of these four states.

So a green cab will be reported as green 68% of the time.

And that's the multiple of 0.85 times 0.8.

In a similar way, if a cab is blue,

it will be reported as blue 12% of the time or 0.12.

Adding those two values reflects

the amount of time that the witness

will be correct 80% of the time.

And you can see that the other two cells

have the values 0.17 and 0.03.

Those add to 0.2, and those are the incorrect guesses.

Now let's take a look at the probabilities

of each of these scenarios.

From the standpoint of witness accuracy.

Here again is the classification matrix.

And let's do the calculation that we did

for reporting a cab is blue

and finding the probabilities actually blue

for each of the four scenarios.

So we have the probability

of a cab being blue and reported as blue as 41%.

That's the calculation I described earlier.

On the other hand,

the witness will identify a blue cab is green.

That's the second item 59% of the time.

And you can see that 41% and 59 add up to 100%.

So if the cab's blue, that's the percent

of the time that the witness will be correct.

Then at the bottom, we have the same scenarios

but we're assuming the cab is green.

So if the cab is green and the witness report

it is green, that will happen 96% of the time.

On the other hand, the witness will identify

a green cab as blue only 4% of the time.

And what makes these calculations

so different is the base rate.

Only 15% of cabs are blue

and that makes the impact of the probability

of an improper identification that much greater.