gt;>
>>
>>
>> Gergely Katona, Professor, Chairman of the Chemistry Program Council
>>
>> Department of Chemistry and Molecular Biology, University of Gothenburg
>>
>> Box 462, 40530 Göteborg, Sweden
>>
>> Tel: +46-31-786-3959 / M: +46-70-912-3309
appropriate probability distributions
> and priors. Also, have we got clarity about the question being asked?
>
>
>
> Thanks to all for the interesting points.
>
>
>
> Colin
>
> *From:* CCP4 bulletin board *On Behalf Of *Randy
> John Read
> *Sent:* 21 October 2021
, Email: gergely.kat...@gu.se
From: CCP4 bulletin board On Behalf Of Nave, Colin
(DLSLtd,RAL,LSCI)
Sent: 21 October, 2021 19:21
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Congratulations to James for starting this interesting discussion.
For those who are like me
, Sweden
Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
Web: http://katonalab.eu, Email: gergely.kat...@gu.se
From: CCP4 bulletin board On Behalf Of Nave, Colin
(DLSLtd,RAL,LSCI)
Sent: 21 October, 2021 19:21
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right
for the interesting points.
Colin
From: CCP4 bulletin board On Behalf Of Randy John Read
Sent: 21 October 2021 13:23
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Hi Kay,
No, I still think the answer should come out the same if you have good reason
to believe that all
I am sorry, this was a dead-end idea multinomial distribution with 0 trials is
not defined.
Gergely
From: CCP4 bulletin board On Behalf Of Gergely Katona
Sent: 21 October, 2021 15:29
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Dear Randy and Kay,
My solution would
black belt in statistics so I am not sure what
the closed form of the posterior probabilities would be (if such exist).
Best wishes,
Gergely
From: CCP4 bulletin board On Behalf Of Randy John Read
Sent: 21 October, 2021 14:23
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this
Hi Kay,
No, I still think the answer should come out the same if you have good reason
to believe that all the 100 pixels are equally likely to receive a photon (for
instance because your knowledge of the geometry of the source and the detector
says the difference in their positions is insignifi
Randy,
I must admit that I am not certain about my answer, but I lean toward thinking
that the result (of the two thought experiments that you describe) is not the
same. I do agree that it makes sense that the expectation value is the same,
and the math that I sketched in
https://www.jiscmail.
Just to be a bit clearer, I mean that the calculation of the expected value and
its variance should give the same answer if you're comparing one pixel for a
particular length of exposure with the sum obtained from either a larger number
of smaller pixels covering the same area for the same lengt
I would think that if this problem is being approached correctly, with the
right prior, it shouldn't matter whether you collect the same signal
distributed over 100 smaller pixels or the same pixel measured for the same
length of exposure but with 100 time slices; you should get the same answer.
Hi Ian,
it is Iobs=0.01 and sigIobs=0.01 for one pixel, but adding 100 pixels each with
variance=sigIobs^2=0.0001 gives 0.01 , yielding a 100-pixel-sigIobs of 0.1 -
different from the 1 you get. As if repeatedly observing the same count of 0
lowers the estimated error by sqrt(n), where n is th
Hi Kay
Can I just confirm that your result Iobs=0.01 sigIobs=0.01 is the estimate
of the true average intensity *per pixel* for a patch of 100 pixels? So
then the total count for all 100 pixels is 1 with variance also 1, or in
general for k observed counts in the patch, expectation = variance = k
on
Sent: 18 October, 2021 21:41
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you very much for this Kay!
So, to summarize, you are saying the answer to my question "what is the expectation
and variance if I observe a 10x10 patch of pixels with zero counts?"
James,
I am saying that my answer to "what is the expectation and variance if I
observe a 10x10 patch of pixels with zero
counts?" is Iobs=0.01 sigIobs=0.01 (and Iobs=sigIobs=1 if there is only one
pixel) IF the uniform prior applies. I agree with Gergely and others that this
prior (with its h
e
-Original Message-
From: CCP4 bulletin board On Behalf Of James Holton
Sent: 18 October, 2021 21:41
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you very much for this Kay!
So, to summarize, you are saying the answer to my question "what is the
expect
onfusion of wild ignorance. I've finally realised why.
What I've missed is: what exactly makes the question so important?
I've understood what brought it up, if course, but not the
consequence of getting it wrong.
Frank
Sent from tiny silly touch screen
---
I am not qualified to comment on anything in the rest of this discussion, but
regarding the excerpt quoted below: this way of recording an "image" seems very
similar to the EER (electron event representation) of the Falcon 4 direct
electron detector used in cryoEM. See https://doi.org/10.1107/S2
alised why.
What I've missed is: what exactly makes the question so important?
I've understood what brought it up, if course, but not the
consequence of getting it wrong.
Frank
Sent from tiny silly touch screen
--
Thank you very much for this Kay!
So, to summarize, you are saying the answer to my question "what is the
expectation and variance if I observe a 10x10 patch of pixels with zero
counts?" is:
Iobs = 0.01
sigIobs = 0.01 (defining sigIobs = sqrt(variance(Iobs)))
And for the one-pixel case:
I
All, this was my reply to one of James' emails which I just noticed was to
me only, and I ought to have CC'd it to the BB, since it has relevance to
others' contributions to the discussion.
Cheers
-- Ian
On Mon, 18 Oct 2021 at 11:27, Ian Tickle wrote:
>
> James, no I don't think so, what does
Hi James,
I'm a bit behind ...
My answer about the basic question ("a patch of 100 pixels each with zero
counts - what is the variance?") you ask is the following:
1) we all know the Poisson PDF (Probability Distribution Function) P(k|l) =
l^k*e^(-l)/k! (where k stands for for an integer >=0
onsequence of getting it wrong.
Frank
Sent from tiny silly touch screen
----------------
*From:* James Holton
*Sent:* Saturday, 16 October 2021 20:01
*To:* CCP4BB@JISCMAIL.AC.UK
*Subject:* Re: [ccp4bb] am I doing this right?
Thank you
trap of frequentist thinking and
reduce data one step at the time.
Best wishes,
Gergely
-Original Message-
From: James Holton
Sent: 17 October, 2021 19:25
To: Gergely Katona ; CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you Gergely. That is interestin
bject: Re: [ccp4bb] am I doing this right?
Thank you Gergely. That is interesting!
I don't mind at all making this Bayesian, as long as it works!
Something I'm not quite sure about: does the prior distribution HAVE to be a
gamma distribution? Not that that really narrows things down
es,
Gergely
-Original Message-
From: CCP4 bulletin board On Behalf Of James Holton
Sent: den 16 oktober 2021 21:01
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you everyone for your thoughtful and thought-provoking responses!
But, I am starting t
Bayesian perspective then this will not help,
unfortunately.
Best wishes,
Gergely
-Original Message-
From: CCP4 bulletin board On Behalf Of James Holton
Sent: den 16 oktober 2021 21:01
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you everyone for yo
-----------
*From:* James Holton
*Sent:* Saturday, 16 October 2021 20:01
*To:* CCP4BB@JISCMAIL.AC.UK
*Subject:* Re: [ccp4bb] am I doing this right?
Thank you everyone for your thoughtful and thought-provoking responses!
But, I am starting to think I was not as clear as I
If you write/analyze/improve a data-reduction program in crystallography, then
these questions are important: how to estimate the intensity of a Bragg spot by
evaluating the counts in the pixels of the signal area, and those of the
background area? When calculating mean and standard deviation of
ng it
wrong.
Frank
Sent from tiny silly touch screen<http://www.9folders.com/>
From: James Holton
Sent: Saturday, 16 October 2021 20:01
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Thank you everyone for your thoughtful and thought-pr
looking
for an alternative to the Bayesian perspective then this will not help,
unfortunately.
Best wishes,
Gergely
-Original Message-
From: CCP4 bulletin board On Behalf Of James Holton
Sent: den 16 oktober 2021 21:01
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right
othenburg
Box 462, 40530 Göteborg, Sweden
Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
Web: http://katonalab.eu, Email: gergely.kat...@gu.se
From: CCP4 bulletin board On Behalf Of James Holton
Sent: 15 October, 2021 18:06
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing
>Box 462, 40530 Göteborg, Sweden
>Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
>Web: http://katonalab.eu, Email: gergely.kat...@gu.se
>
>From: CCP4 bulletin board On Behalf Of James
>Holton
>Sent: 15 October, 2021 18:06
>To: CCP4BB@JISCMAIL.AC.UK
>
hemistry and Molecular Biology, University of Gothenburg
>> >Box 462, 40530 Göteborg, Sweden
>> >Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
>> >Web: http://katonalab.eu, Email: gergely.kat...@gu.se
>> >
>> >From: CCP4 bullet
ry and Molecular Biology, University of Gothenburg
> >Box 462, 40530 Göteborg, Sweden
> >Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
> >Web: http://katonalab.eu, Email: gergely.kat...@gu.se
> >
> >From: CCP4 bulletin board On Behalf Of James
> H
Biology, University of Gothenburg
>Box 462, 40530 Göteborg, Sweden
>Tel: +46-31-786-3959 / M: +46-70-912-3309 / Fax: +46-31-786-3910
>Web: http://katonalab.eu, Email: gergely.kat...@gu.se
>
>From: CCP4 bulletin board On Behalf Of James Holton
>Sent: 15 October, 2021 18:06
>
/ M: +46-70-912-3309 / Fax: +46-31-786-3910
Web: http://katonalab.eu, Email: gergely.kat...@gu.se
From: CCP4 bulletin board On Behalf Of James Holton
Sent: 15 October, 2021 18:06
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] am I doing this right?
Well I'll be...
Kay Diederichs pointed o
Well I'll be...
Kay Diederichs pointed out to me off-list that the k+1 expectation and
variance from observing k photons is in "Bayesian Reasoning in Data
Analysis: A Critical Introduction" by Giulio D. Agostini. Granted, that
is with a uniform prior, which I take as the Bayesean equivalent of
I forgot to add probably the most important. James is correct, the expected
value of u, the true mean, given a single observation k is indeed k+1 and
k+1 is also the mean square error of using k+1 as the estimator of the true
mean.
Cheers,
Filipe
On Wed, 13 Oct 2021 at 23:17, Filipe Maia wrote:
Hi,
The maximum likelihood estimator for a Poisson distributed variable is
equal to the mean of the observations. In the case of a single observation,
it will be equal to that observation. As Graeme suggested, you can
calculate the probability mass function for a given observation with
different P
This rang a bell to me last night, and I think you can derive this from first
principles
If you assume an observation of N counts, you can calculate the probability of
such an observation for a given Poisson rate constant X. If you then integrate
over all possible value of X to work out the cen
Hi Ian, James,
I have a strong feeling that I have seen this result
before, and it was due to Andy Hammersley at ESRF. I’ve done a literature
search and there is a paper relating to errors in analysis of counting
statistics (se below), but I had a quick look at this and co
Hi James
What the Poisson distribution tells you is that if the true count is N then
the expectation and variance are also N. That's not the same thing as
saying that for an observed count N the expectation and variance are N.
Consider all those cases where the observed count is exactly zero. Th
All my life I have believed that if you're counting photons then the
error of observing N counts is sqrt(N). However, a calculation I just
performed suggests its actually sqrt(N+1).
My purpose here is to understand the weak-image limit of data
processing. Question is: for a given pixel, if on
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