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These are replies submitted by sand15

@Thomas Richard 

Thanks Thomas



Sorry !
Thanks for the answer, I'm going to look to the like you gave

@Carl Love


"the likelihood function is only properly defined for distributions with at least one symbolic parameter" 

Right, the likelihood function... is a function which must depend upon some parameters (those of the traget distribution).

In effect, Maple help pages says that: 

[likelihood] n. (Statistics) the probability of a given sample being randomly drawn, regarded as a function of the parameters of the population. 


So I should have read more carefuly those pages...

If S is a sample, D some distribution with parameters P and L denotes the likelihood (function), the expression of L is often written
L(D(P) ; S) to emphasize L is considered as a function of P (or D(P)). 
Once P is instanciated to some values P*, L(D(P*) ; S) becomes a number.
My mistake comes from the common usage of the term likelihood, which may represent at the same timeeither  the likelihood function itself L(D(P) ; S) , or either its value L(D(P*) ; S)... and in this later case we often talk about the "likelihood of the sample S" (as it is the probability density of S given D(P*)).



When you write "What is the likelihood, or probability, that you've correctly estimated the parameters when there are no parameters? Of course it's 1."
I'm not completely sure of that.
Admittedly, from a bayesian perspective, we can write something like p(S) =int( p(S | P)*p(P), dP) where p(P) is some prior on P.
Rewriting this integral in terms of the likelihood we have  p(S) =int( L(P ; S)*p(P), dP)=1... which seems to confirm your claim, excepted that there exist no distribution without parameters: then "... when there are no parameters? Of course it's 1." doesn't seem to make sense.
Maybe Maple uses some shortcut to return the value 1 ?



"What I'm wondering is What happened to the factors of 1/sqrt(2*Pi) that usually appear in the Normal PDF?"
Here again we face some approximations of the Statistics language: in many situations we use to consider the likelihood is defined up to an arbitrary multiplicative constant.
This comes from the fact that the infotùation which really matters is generally the ratio of two different likelihood.
For instance Likelihood(Normal(m, s), S) / Likelihood(Normal(m', s'), S)

In any event, thanks for your clarification which had have the merit to bring me back to my student years


@Carl Love 


By the way, thanks for making me discover the syntax op([2, 1, 1, 2], ...)
It is shorter (maybe slightly less clear) than op(2, op(1, ....) that I used to use


Than you.
It is exactly what I was expecting.

So I take it that Maple implicitely selects the first interval [-Pi/2, +Pi/2] when   solve(sin(x)=y,x)    returns   arcsin(y)


You write
 "First note that there is not such thing as "global inverse" of f, unless f (supposed to be C^1) is strictly monotonic."
Thank you vv for this quick math reminder but I know this perfectly.

Maybe I should have written
I want to construct some kind of pseudo global inverse of f over R by putting "side by side" local inverse functions
instead of
I want to construct the global inverse of f over R by putting "side by side" local inverse functions
to be clearer ?

I had thought that I was clear enough when saying
     The idea is to define the global inverse g of f over R by
     g := y ->  piecewise(y < f(a__1), g__0(y), ..., y < f(a__n), g__(n-1)(y))
    where g__p(y), is the inverse function of the restriction of f to ] a__p, a__(p+1) [

I realize it was not the case ...  or maybe you where too scandalized (with good reason) by reading the first lines (find the inverse of a non monotonic function) that you did not keep reading the rest of my question ?
I do not hold this against you: "This function is not strictly monotonic over R [and] I want to construct [its] global inverse" is really disturbing and I guess that hearing this would make me hit the roof too.

@Carl Love 


Thank you Carl.
My today problem concerns a polynomial function f, then your answer will be very valuable.

By the way: I have always been surprised that  solve(sin(x)=y, x)  returns arcsin(y), just as if the inverse of "sin" was defined everywhere.
If it is not too much to ask could you say a little more about this ?

Thank for all


Thank you Kitonum.

I'm often puzzled with the differences of behavior between  -> and unapply ... I guess I have to read more carefully the dedicated helps pages ...


Thanks acer
Loading 2015.2 here is not easily due to the very strict safety policy 

Nevertheless I will test this tomorrow with (some) version 2016.
Maybe I will join you later on from home, where I use 2015.2 on a imac.

Thanks again


Here it is

@Daniel Skoog 

Thanks Daniel,

I have just gave some info to acer.

About point 1 : this is a very interesting way to customize the DataSummary procedure
Concerning  your point 2 : right, a screenshot is a roundabout way to answer the question.

Thanks also for your last line, I appreciate that


Thank you acer.

I had aleady tried the plotsetup(jpeg, ...) command but I had got an error saying the embeded summary was not of plot type (did not tried textplot : I'm going to see righr now).
What do I mean by "save this table" : you are right, this is not clear. I mean "ideally" save the appearance of the table as an image ... just like some image capture tool could do.
Of course I could use fprintf to save these informations in a text file in a "smart" form, but I found that the appearance of
DataSummarize(...summarize=embed) was realy very smart.



It looks like our replies have crossed


I found myself the solution :-)
I just  declared  use plots  within the procedure and it  works correctly now.

(I thought that loading the package plots in the worksheet itself would be sufficient)

Sorry for the inconvenience



This works well but your answer made me realize that  I oversimplified my problem.
If it's not too much to ask, could you answer this one please ?

 f := proc(DrawThis)
     plotsetup(jpeg, plotoutput=SomeJpegFile);
end proc;

MyPlot := plot(x, x=0..1)
f(MyPlot);   # That's fine, thank you,

MyPlot := display(plot(x, x=0..1), plot(x^2, x=0..1))
f(MyPlot);   # No file is created

Even this simplified procedure
 f := proc(DrawThis)
end proc;

returns what I would have obtained by writting
MyPlot := display(plot(x, x=0..1), plot(x^2, x=0..1)) ;

Could you help me please ?

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