Mathematische Statistik - Übung Ergänzungsaufgabe 2 Beispiel 3

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Two physiscists, A and B want to determine the value of a physical constant. The physicist A with a large experience in the area specifies his prios as . On the other side, physicist B stated a more uncertain prior . Both physicists agree to make an evaluation of , denoted by X, using a calibrated device with sampling distribution . The value is observed.

(a) What do the physicists infer about ?

Physicist A:

 postmean=function(x,mu,tau,sigma) ((mu/(tau^2)) + (x/(sigma^2))) / (1/(sigma^2) + 1/(tau^2))
 postvar=function(tau,sigma) 1/(1/(sigma^2) + (1/tau^2))

 postmean(850, 900, 20, 40)
 postvar(20, 40)

#

[1] 890
[1] 320

Physicist B:

 postmean=function(x,mu,tau,sigma) ((mu/tau^2) + (x/sigma^2)) / (1/sigma^2 + 1/tau^2)
 postvar=function(tau,sigma) 1/(1/sigma^2 + 1/tau^2)

 postmean(850, 800, 80, 40)
 postvar(80, 40)

#

[1] 840
[1] 1280

(b) Interpret the result.