Questions for Dr. Weishaus

[AUM]

How do you solve a normal/lognormal or lognormal/lognormal (model/prior) problem? I didn't see this combination addressed in your manual and according to what you wrote for the normal/normal pair, none of the textbooks actually address this type of questions.
How do you solve a kernel smoothing question which is neither triangular, uniform nor gamma? The only thing given was the density function.

This exam was absolutely insane...

Thanks!

[carryme]

You're getting too specific dude. Moderator1 is around, watching you very closely.

[Abraham Weishaus]

I answered the second question, but that answer was deleted. Perhaps this answer won't be deleted: the ASM manual covers some other possibiities for kernels, as have some old released exam questions. See exercises 24.6 and 24.15. An exam question asking a question on an arbitrary kernel should not puzzle you, and is testing to see if you can go beyond formulas.

[pcramirez]

Originally Posted by AUM

How do you solve a normal/lognormal or lognormal/lognormal (model/prior) problem? I didn't see this combination addressed in your manual and according to what you wrote for the normal/normal pair, none of the textbooks actually address this type of questions.
How do you solve a kernel smoothing question which is neither triangular, uniform nor gamma? The only thing given was the density function.

This exam was absolutely insane...

Thanks!

Integrate the kernel density function, and multiply that integral by the probability of that point being chosen (1/N, N the number of points). Also, you could determine the bandwidth by looking at the density function. I had a better written response, but I just shortened it in hopes that it won't be deleted. If you want more specifics, you can PM me .

[AUM]

Originally Posted by Abraham Weishaus

I answered the second question, but that answer was deleted. Perhaps this answer won't be deleted: the ASM manual covers some other possibiities for kernels, as have some old released exam questions. See exercises 24.6 and 24.15. An exam question asking a question on an arbitrary kernel should not puzzle you, and is testing to see if you can go beyond formulas.

Thanks for your reply. I will recheck teh manual!

[AUM]

Originally Posted by pcramirez

Integrate the kernel density function, and multiply that integral by the probability of that point being chosen (1/N, N the number of points). Also, you could determine the bandwidth by looking at the density function. I had a better written response, but I just shortened it in hopes that it won't be deleted. If you want more specifics, you can PM me .

Thanks!!

[Abraham Weishaus]

Originally Posted by AUM

Thanks!!

About your other question - of course I have no idea what the exam question was. But if X is lognormal, then ln X is normal. If the parameters of the lognormal are theta and v and the mean theta varies according to another normal distribution with parameters mu and a, then the posterior for ln X is normal (by the normal/normal conjugate prior), and then X itself is lognormal with the same parameters as the posterior ln X.

In general with conjugate priors, you can do reparametrizations like that. In Loss Models 3rd edition, instead of exponential/inverse gamma conjugate prior, they feature exponential/gamma. They simply use 1/theta as the exponetial's parameter instead of theta. If X is gamma, then X^{-1} is inverse gamma, so it's the same idea.

[AUM]

Originally Posted by Abraham Weishaus

About your other question - of course I have no idea what the exam question was. But if X is lognormal, then ln X is normal. If the parameters of the lognormal are theta and v and the mean theta varies according to another normal distribution with parameters mu and a, then the posterior for ln X is normal (by the normal/normal conjugate prior), and then X itself is lognormal with the same parameters as the posterior ln X.

In general with conjugate priors, you can do reparametrizations like that. In Loss Models 3rd edition, instead of exponential/inverse gamma conjugate prior, they feature exponential/gamma. They simply use 1/theta as the exponetial's parameter instead of theta. If X is gamma, then X^{-1} is inverse gamma, so it's the same idea.

thanks again for your clarification!

[atkinsmt]

Originally Posted by AUM

thanks again for your clarification!

Are you going to remember all that for next time? Oh wait, you won't need to because something more evil awaits.

[badmaj5]

I'll worry about remembering it in a few months. I feel like this will not be the end of that topic.