Re: [ccp4bb] am I doing this right?

[Gergely Katona]

Dear James,

Uniform distribution sounds like “I have no idea”, but a uniform distribution 
does not go from -inf to +inf. If I believe that every count from 0 to 65535 
has the same probability, then I also expect counts with an average of 32768 on 
the image. It is not an objective belief in the end and probably not a very 
good idea for an X-ray experiment if the number of observations are small. 
Concerning which variance is the right one, the frequentist view requires 
frequencies to be observed. In the absence of frequencies, there is no error 
estimate. Bayesians at least can determine a single distribution as an answer 
without observations and that will be their prior belief of the variance. 
Again, I would avoid a uniform a priori distribution for the variance. For a 
Poisson distribution the convenient conjugate prior is the gamma distribution. 
It can control the magnitude of k and strength of belief with its location and 
scale parameter, respectively.

Best wishes,

Gergely

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 / 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 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 have no idea".

So, if I'm looking to integrate a 10 x 10 patch of pixels on a weak detector 
image, and I find that area has zero counts, what variance shall I put on that 
observation?  Is it:

a) zero
b) 1.0
c) 100

Wish I could say there are no wrong answers, but I think at least two of those 
are incorrect,

-James Holton
MAD Scientist
On 10/13/2021 2:34 PM, Filipe Maia wrote:
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 
mailto:fil...@xray.bmc.uu.se>> 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 Poisson 
parameters (i.e. true means) and see that function peaks when the parameter 
matches the observation.

The root mean squared error of the estimation of the true mean from a single 
observation k seems to be sqrt(k+2). Or to put it in another way, mean squared 
error, that is the expected value of (k-u)**2, for an observation k and a true 
mean u, is equal to k+2.

You can see some example calculations at 
https://colab.research.google.com/drive/1eoaNrDqaPnP-4FTGiNZxMllP7SFHkQuS?usp=sharing

Cheers,
Filipe

On Wed, 13 Oct 2021 at 17:14, Winter, Graeme (DLSLtd,RAL,LSCI) 
<6a19cead4548-dmarc-requ...@jiscmail.ac.uk>
 wrote:
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 central value of the rate constant 
which is most likely to result in an observation of N I think you get X = N+1

I think it is the kind of calculation you can perform on a napkin, if memory 
serves

All the best Graeme


On 13 Oct 2021, at 16:10, Andrew Leslie - MRC LMB 
mailto:and...@mrc-lmb.cam.ac.uk>> wrote:

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 could not find the 
(N+1) correction, so it must have been somewhere else. I Have cc’d Andy on this 
Email (hoping that this Email address from 2016 still works) and maybe he can 
throw more light on this. What I remember at the time I saw this was the 
simplicity of the correction.

Cheers,

Andrew

Reducing bias in the analysis of counting statistics data
Hammersley, AP 
(Hammersley, AP) Antoniadis, 
A (Antoniadis, A)
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS 

[ccp4bb] Structural Biology researcher position at St. Jude

[Marcus Fischer]

The lab of Dr. Taosheng Chen is recruiting a Structural Biologist to join
the efforts in structural determination of protein-ligand complexes and
contribute structural biology insights into the mechanism of action of
novel chemical probes. The Chen Laboratory (https://www.stjude.org/chen) uses
multidisciplinary approaches to study transcriptional regulation by nuclear
receptors, including chemical biology approaches to develop chemical
modulators, with a goal to understand nuclear receptor-regulated
transcription networks and design therapeutic approaches to overcome drug
resistance and tumorigenesis in cellular and animal models. The structural
biology efforts are expected to synergize with our chemical biology efforts
and enable completion of impactful projects (*Nat Commun* 8:741, 2017; *J
Am Chem Soc**2021, DOI: 10.1021/jacs.1c07066*). The Chen Laboratory
provides a unique research environment: in addition to basic research, lab
members will learn and gain experience in small molecule drug discovery
from target validation, chemical probe discovery and optimization to
preclinical mechanistic studies. The *Senior or Lead Researcher* will work
in a collaborative and multidisciplinary environment by collaborating with
biologists, chemists, and technologists.



The successful candidate will have proved experience in expression
construct design, molecular cloning, protein expression and purification,
optimization of crystallization conditions, crystallization and structural
determination of protein-ligand complexes using X-ray crystallography.



Experience in the following areas is a plus: purification and
crystallization of nuclear receptors; synchrotron data collection;
biophysical assays; *in silico* modeling of protein-ligand interactions;
preparation of manuscripts; along with a strong publication record.



Please direct your inquiries and current CV to Dr. Taosheng Chen (
taosheng.c...@stjude.org) or *apply online* (
https://careers-stjude.icims.com/jobs/8708/sr-researcher/job?hub=15=false=1180=500=true=false=-360=-300
 ).



*Minimum Education*

Bachelor's or Master's degree in biology, chemistry, or a related field
required. PhD in structural biology is essential, and relevant postdoctoral
training is preferred.



*Contact*

Taosheng Chen, PhD

Member (Professor), Department of Chemical Biology and Therapeutics

Director, High Throughput Bioscience Center

St. Jude Children's Research Hospital

262 Danny Thomas Place

Memphis, TN 38105-2794

USA

Phone: 1-901-595-5937

Fax: 1-901-595-5715

Email: taosheng.c...@stjude.org

Website: https://www.stjude.org/chen



To unsubscribe from the CCP4BB list, click the following link:
https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB=1

This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list 
hosted by www.jiscmail.ac.uk, terms & conditions are available at 
https://www.jiscmail.ac.uk/policyandsecurity/

Re: [ccp4bb] am I doing this right?

[James Holton]

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 
have no idea".


So, if I'm looking to integrate a 10 x 10 patch of pixels on a weak 
detector image, and I find that area has zero counts, what variance 
shall I put on that observation?  Is it:


a) zero
b) 1.0
c) 100

Wish I could say there are no wrong answers, but I think at least two of 
those are incorrect,


-James Holton
MAD Scientist

On 10/13/2021 2:34 PM, Filipe Maia wrote:
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 Poisson parameters (i.e.
true means) and see that function peaks when the parameter matches
the observation.

The root mean squared error of the estimation of the true mean
from a single observation k seems to be sqrt(k+2). Or to put it in
another way, mean squared error, that is the expected value of
(k-u)**2, for an observation k and a true mean u, is equal to k+2.

You can see some example calculations at

https://colab.research.google.com/drive/1eoaNrDqaPnP-4FTGiNZxMllP7SFHkQuS?usp=sharing



Cheers,
Filipe

On Wed, 13 Oct 2021 at 17:14, Winter, Graeme (DLSLtd,RAL,LSCI)
<6a19cead4548-dmarc-requ...@jiscmail.ac.uk
> wrote:

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 central value of the rate constant which
is most likely to result in an observation of N I think you
get X = N+1

I think it is the kind of calculation you can perform on a
napkin, if memory serves

All the best Graeme


On 13 Oct 2021, at 16:10, Andrew Leslie - MRC LMB
mailto:and...@mrc-lmb.cam.ac.uk>>
wrote:

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 could not find the
(N+1) correction, so it must have been somewhere else. I Have
cc’d Andy on this Email (hoping that this Email address from
2016 still works) and maybe he can throw more light on this.
What I remember at the time I saw this was the simplicity of
the correction.

Cheers,

Andrew


Reducing bias in the analysis of counting statistics data


  Hammersley, AP
  
(Hammersley,
  AP) Antoniadis, A
  
(Antoniadis,
  A)


  NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION
  A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT


  Volume


  394


  Issue

1-2


  Page

219-224


  DOI

10.1016/S0168-9002(97)00668-2


  Published

JUL 11 1997


On 12 Oct 2021, at 18:55, Ian Tickle mailto:ianj...@gmail.com>> wrote:


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.  That
can arise from any number of true counts, though as you
noted larger values become increasingly unlikely.  However
those true counts are all >= 0 which means that the mean and
variance of those true counts must be positive and
non-zero.  From 

[ccp4bb] PDB-REDO downtime

[Robbie Joosten]

Dear BB-ers,

Due to electrical maintenance at our host institute pdb-redo.eu will be 
unavailable from 20:00h (Amsterdam) on October 15th to roughly 12:30h on 
October 16th. Apologies for the inconvenience.

Best wishes,
Robbie Joosten



To unsubscribe from the CCP4BB list, click the following link:
https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB=1

This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list 
hosted by www.jiscmail.ac.uk, terms & conditions are available at 
https://www.jiscmail.ac.uk/policyandsecurity/