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EnglishVoice Age
Middle Aged (35-54)Accents
North American (General)Transcript
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Chapter 16 causes Trump statistics consider the following scenario and note your intuitive answer to the question. A cab was involved in a hit and run accident at night. Two cab companies, the green and the blue operate in that city. You are given the following data. 85% of the cabs in the city are green and 15% are blue. A witness identified the cab as blue. The court tested the reliability of the witness under the circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors, 80% of the time and failed 20% of the time. What is the probability that the cab involved in the accident was blue rather than green? This is a standard problem of Bayesian inference. There are two items of information. A base rate and an imperfectly reliable testimony of a witness in the absence of a witness. The probability of the guilty cab being blue is 15%,, which is the base rate of that outcome. If the two cab companies had been equally large, the base rate would be uninformative and you would consider only the reliability of the witness concluding that the probability is 80%. The two sources of information can be combined by Bay's rule. The correct answer is 41 per cent. However, you can probably guess what people do when faced with this problem, they ignore the base rate and go with the witness. The most common answer is 80%.