machine learning - MAP estimation (predictive distribution) -

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yes, old exam question unfortunately can't find solution.

suppose part of team has trained n temperature prediction models. models use readings set of sensors measure weather conditions on given day , predict temperature following day. i-th model determined vector of parameters wi , estimates conditional probability p(y | x, wi) of observing temperature y if sensor state x. furthermore, based on historical data team has prior belief on models given p(wi) = 2i/(n(n+1)) ∈ {1, . . . , n}. given measured sensor state today x* please write down predictive distribution p(y*| x*) temperature tomorrow using map estimation.

we didn't cover predictive distributions. map estimate want estimate parameters wi on basis of observed sensor data x. how can fit y in here?

any hints appreciated :-)


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