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February 13th, 2013, 03:23 AM   #1
Joined: May 2012

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Understanding Bayesian statistics, repeated measurements and

I am getting to grips with Bayesian statistics. I understand how to calculate the maximum a posteriori probability (MAP) estimate for the mean, given the sample data and the a priori mean and standard deviation.
However, for my own understanding of Bayesain statistics, i would also like to know how to answer the following question - in a Bayesian paradigm:

The coach of the local american footbal team has a hunch that the field is less than 100 yrds.
He also has an old yardstick, which he uses to measure the field, obtaining n=3 datapoints D={101, 100.5, 101.5}
Question: After each measurement, how should he update his belief about the field length? Specifically, how to re-calculate the probability the field is less then 100 yrds after each measurement?

I know i should start with replacing the 'hunch' with a probability that the field is less than 100 yrds. Then, i assume, i should also assign some measure of uncertainty to my measurements, but i dont know how.

Example taken from this very informative video lecture, series of lectures, really:


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