@Axel Vogt 

Thanks a lot for such a lucid explanation. Really do appreciate it. 

But, in giving you the information, I missed a very crucial piece of information. Which is the following that - the function j() is dependent on z. i.e.  j(e,y,z).

Now, does it make sense for me to use Gauss-Hermite approximation?

Thanks once again for your help.

@Axel Vogt 

Thanks a lot for such a lucid explanation. Really do appreciate it. 

But, in giving you the information, I missed a very crucial piece of information. Which is the following that - the function j() is dependent on z. i.e.  j(e,y,z).

Now, does it make sense for me to use Gauss-Hermite approximation?

Thanks once again for your help.

I am not absolutely sure what your saying. But, I am asuuming the following is what you mean

gauss_hermite_analys.mw

Thanks a lot for your patience. 

I am not absolutely sure what your saying. But, I am asuuming the following is what you mean

gauss_hermite_analys.mw

Thanks a lot for your patience. 

Hopefully, this explains what I am trying to do

gauss_hermite_analys.mw

Thank you once again.

Hopefully, this explains what I am trying to do

gauss_hermite_analys.mw

Thank you once again.

I deepl appreciate all the help.

gauss_hermite.mw

I have added the comments in bold font to as many things as I can. Hope it make sense. Please feel free to ask any other questions that you might have.

Thanks!

I deepl appreciate all the help.

gauss_hermite.mw

I have added the comments in bold font to as many things as I can. Hope it make sense. Please feel free to ask any other questions that you might have.

Thanks!

Classic mistake. Here it is.

gauss-hermite.mw

Thank you

Classic mistake. Here it is.

gauss-hermite.mw

Thank you

Here is the code. It is uploaded as .mw file

I am fairly new to Maple (close to three weeks). So you might find the code little childish and not nearly as elegant as it should be.

Thank you.

Here is the code. It is uploaded as .mw file

I am fairly new to Maple (close to three weeks). So you might find the code little childish and not nearly as elegant as it should be.

Thank you.

@Carl Love

My Problem is the following. I have 

Y ~ Normal(a,b)

and also 

X|Y=y ~Normal( f(y,j*))

where j* is to be choosen that will maximize the int(int(j*.x|y . f(x|y)).f(y)).

Therefore, I am using the Gauss-hermite procedure

a) to calculate the nodes

b) for those nodes evalue the optimal j* - using the optimization routine

c) then evalute conditional expectation for all the nodes

d) Then use the weights to compute the unconditinal expectation.

So, I am not sure if I can just straight away use the standard numerical integration package - because the function that I have to integrate over has to be endogeously determined. 

I am sorry if I am not clear about things or being a little dense. Any advice/comments/suggestions to make this procedure faster is appreciated.

Thanks once again!

@Carl Love

My Problem is the following. I have 

Y ~ Normal(a,b)

and also 

X|Y=y ~Normal( f(y,j*))

where j* is to be choosen that will maximize the int(int(j*.x|y . f(x|y)).f(y)).

Therefore, I am using the Gauss-hermite procedure

a) to calculate the nodes

b) for those nodes evalue the optimal j* - using the optimization routine

c) then evalute conditional expectation for all the nodes

d) Then use the weights to compute the unconditinal expectation.

So, I am not sure if I can just straight away use the standard numerical integration package - because the function that I have to integrate over has to be endogeously determined. 

I am sorry if I am not clear about things or being a little dense. Any advice/comments/suggestions to make this procedure faster is appreciated.

Thanks once again!

@Carl Love I apologize for the delay in getting back to you. Been away from the computer.

Yes, it is related to what I was asking about earlier in thw week. I have currently shelved it and instead have to address something related to that before I get back to previous problem. 

I genuinely appreciate your generousity and willingness to share your knowledge.

Thanks!