All language subtitles for 04 - Calculate Bayesian probabilities in Excel

- [Instructor] Microsoft Excel worksheets

are very well suited to performing Bayesian analysis.

In this movie, I will show you how to implement our analysis

of the Kahneman's Cabs problem.

My sample file is 07_04_Calculating

and you can find it in the Chapter07 folder

of the exercise files collection.

We've gone through the parameters

of the problem several times in this chapter,

so I'll just go ahead

and start entering in the values and formulas.

In cell B3, we need to establish the base rate

of green cabs, and that is 85%.

So in cell B3, I will type 85

and I have already formatted the cell

with a percentage format,

so I'll just press Enter.

You don't need to type in the percent sign.

And in B4, I'll type the accuracy

and remember that the court established

that the witnesses were accurate 80% of the time.

So 80 and Enter.

Now we can find the probability a cab is green or blue.

And then the probability the witness

is correct or incorrect.

So in B6, we need the probability

that the cab is actually green.

So I'll type an equal sign

and that will be equal to B3,

which is the base rate for green.

The probability the cab is blue

is one minus the probability it's green.

So in B7, I'll type equal.

One minus B3 and Enter.

And 85 plus 15 is 100.

So I know that those formulas are correct.

Now we can do the same

for the witness being correct or incorrect.

So in B9, I'll type equal

and their accuracy is 80%.

That's in B4. Enter.

And then in B10, probability they are incorrect.

So equal one minus the probability they're correct.

That's in B4, Enter,

and we get 20% and 80 plus 20 is 100.

We can now use those probabilities

to find the probability of a particular scenario happening.

And we'll do that over here in our classification matrix.

In cell E4, I want to know the probability

that a cab is reported green when it's actually green.

So I'll type an equal sign.

And the probability a cab is green is in B6

and we'll multiply that

by the case where the witness is correct.

And that's in B9 and Enter.

Now in E5, we need to know the probability

that the cab is actually blue

but was reported as being green.

So

type equal and then the cab is actually blue.

So that's in B7, the probability of it being blue.

Multiplied by the probability

that the witness is incorrect and that's in B10.

And Enter, and I get 3%.

Same thing for the cab being reported as blue.

So in F4, I'll type equal.

In this case, the cab is actually green

and that is in cell B6.

And we'll multiply that by the probability

that the witness is incorrect.

That's in B10 and we get 17%.

And finally, we want to find the probability

of the case where the cab is blue

and it's reported as blue.

So in F5, I'll type equal.

The probability it's blue is in B7

multiplied by the probability the witness is correct.

That's in B9, Enter and we get 12%.

One way to check to make sure

that your classification matrix has been done correctly

is that you can add the probability of correct guesses,

so we have 68 and 12, that's 80%,

which equals the accuracy,

and then inaccurate guesses, 17 plus 3 is 20%,

which is also the probability the witness is incorrect.

Now we can perform calculations

to find the probability the cab is green

when reported green

and the probability the cab is blue when reported blue.

So in cell E8,

we need to type an equal sign

and then find the number of times

that a cab is correctly reported as being green.

And that is in cell E4.

And we need to divide that by the total number of times

that the cab is reported as being green,

even if it's actually blue.

So after the division sign,

I'll type a left parentheses

and we'll have E4 plus E5,

right parentheses and Tab.

And we'll see that that percentage

or probability is 96%.

Now we can perform the calculation

that we did in previous movies as part of the example,

and find the probability the cab is blue

when it's reported blue.

So in F8, I'll type equal,

and the probability that the cab is actually blue

and is reported as blue is in cell F5.

It can be very easy to use F4 as your basis

but remember that that is an incorrect guess.

So now we have the number of times

that the cab is correctly reported as being blue

and we need to divide that by the total number

of times it is reported as being blue,

both right and wrong.

So left parentheses, F4, plus F5,

right parentheses and Enter.

And we get 41%, which is the value

that we saw earlier in this chapter.