Suppose that the number of accidents occurring daily in a certain plant has a Po

Question

Suppose that the number of accidents occurring daily in a certain plant has a Poisson distribution with an unknown mean . Based on previous experience in similar industrial plants, suppose that our initial feelings about the possible value of can be expressed by an exponential distribution with parameter =1/2 . That is, the prior density is f() = e^() where [0, ).

(a) Before observing any data (any reported accidents), what is the most likely value for ?

(b)Imagine you now want to predict the number of accidents for tomorrow. How can you use the maximum likelihood estimate computed above? What about the MAP estimate? What would they predict?

(c)For the MAP estimate, what is the purpose of the prior once we observe this data?

(d)Look at the plots of some exponential distributions to better understand the prior chosen on . Imagine that now new safety measures have been put in place and you believe that the number of accidents per day should sharply decrease. How might you change to better reflect this new belief about the number of accidents?

Explanation / Answer

first question explain very nicely about MLE and MAP estimate

Please go through link below

http://www.enriqueareyan.com/files/computer-science/B555%20Machine%20Learning/Solutions/MachineLearning-Assignment-2-Solution.pdf

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