Many times when you perform a test and analyze it using Bayesian analysis, you can repeat your analysis based on the results of a different test. In this video, learn how to update your analysis to reflect the circumstances.
- [Instructor] Many times when you perform a test and analyze it using Bayesian analysis, you'll be able to repeat your analysis based on the results of a different test. In this movie, I will show you how to update your analysis to reflect those circumstances. The example we've been working with uses Kaheneman's Cabs which asks for the chance a cab reported as blue is actually blue. We have an 85% base rate for green cabs, that means 15% are blue, and 80% accuracy. Based on that analysis, we've seen that a blue cab is identified correctly as blue about 41.38% of the time.
However, what if you can test using another method? In other words, we are assuming that you have this witness testimony which is accurate 41.38% of the time. If you have another test, how does that affect the probability? Let's assume to extend the argument that a security camera filmed the accident and that the security camera is 90% accurate at distinguishing green from blue at the time the hit and run occurred. So the question is, does the 85% green base rate for the entire city still apply? And the answer is no and that's because the witness said that the cab was blue and that witness' testimony is deemed to be 41.38% accurate.
Do we use 41.38% as our base rate then? That is the base rate for blue cabs based on the information we have, but the correct base rate for green is one minus 41.38% or 58.62% and that is the value that we will use in Excel. I've switched over to Excel. My sample file is the updating workbook and you can find it in the chapter six folder of the exercise files collection. The existing base rate is 85% which you can see in the cell B3 which I already have selected, but the new base rate for green cabs based on the explanation I gave earlier is 58.62%.
So in cell B3, I will type 58.62 and Enter and you can see how the probabilities change. The accuracy of this new test is 90%, thus the security camera, so I'll type 90 and Enter and we can see how it changes. Now note that combining the two tests, one that is 80% accurate based on witness testimony and the second based on a camera that is 90% accurate, we see a big change in the values.
As you can see, the change in the base rate makes the probability that a cab being blue when reported blue go up substantially and while the probability a cab is green when it's reported green goes down a bit because of the new base rate, it's still quite high.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.