Gaussian Random Number Generation

[JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST)]

Dear ImageJ community,


You are an intelligent group of people so I would like to ask this...


Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).


For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?


Many thanks,


Greg.


__________________________________________
Gregory James
Clinical Scientist (Nuclear Medicine)
Department of Physics and Nuclear Medicine
City Hospital
Dudley Road
Birmingham
B18 7QH

0121 507 4043


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[Arne Seitz]

Dear Greg,

the RandomJ plugin from Eric Meijering looks to me what you are asking for.
https://imagescience.org/meijering/software/randomj/

The only limitation it works on images. However it is macro recordable and the source code can be found on GitHub.

Best
Arne


-----Original Message-----
From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST)
Sent: mercredi 19 septembre 2018 14:09
To: [hidden email]
Subject: Gaussian Random Number Generation

Dear ImageJ community,


You are an intelligent group of people so I would like to ask this...


Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).


For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?


Many thanks,


Greg.


__________________________________________
Gregory James
Clinical Scientist (Nuclear Medicine)
Department of Physics and Nuclear Medicine City Hospital Dudley Road Birmingham
B18 7QH

0121 507 4043


********************************************************************************************************************

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[Mark Osborne]

Greg

Something like the following macro should work...

var U; var V;

function normal(){
S = 2;
        while(S >= 1){
        U = -1+2*random; // uniform random no. -1..1
        V = -1+2*random;
        S = U*U+V*V;
}
}

X = U * sqrt(-2*log(S)/S);   //or
Y = V * sqrt(-2*log(S)/S);   // where log in ImageJ is natural ln

X and Y are independent standard normally distributed random numbers, so you can multiply by a finite standard deviation to spread beyond unit STD and add to a mean to get the Gaussian.  Check against the Marsaglia polar method of generating normally distributed random numbers. Bit wasteful finding S<1, but easy to check and rather more intuitive than some.

Mark

-----Original Message-----
From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of Seitz Arne
Sent: 19 September 2018 13:33
To: [hidden email]
Subject: Re: Gaussian Random Number Generation

Dear Greg,

the RandomJ plugin from Eric Meijering looks to me what you are asking for.
https://imagescience.org/meijering/software/randomj/

The only limitation it works on images. However it is macro recordable and the source code can be found on GitHub.

Best
Arne


-----Original Message-----
From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST)
Sent: mercredi 19 septembre 2018 14:09
To: [hidden email]
Subject: Gaussian Random Number Generation

Dear ImageJ community,


You are an intelligent group of people so I would like to ask this...


Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).


For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?


Many thanks,


Greg.


__________________________________________
Gregory James
Clinical Scientist (Nuclear Medicine)
Department of Physics and Nuclear Medicine City Hospital Dudley Road Birmingham
B18 7QH

0121 507 4043


********************************************************************************************************************

This message may contain confidential information. If you are not the intended recipient please inform the sender that you have received the message in error before deleting it.
Please do not disclose, copy or distribute information in this e-mail or take any action in relation to its contents. To do so is strictly prohibited and may be unlawful. Thank you for your co-operation.

NHSmail is the secure email and directory service available for all NHS staff in England and Scotland. NHSmail is approved for exchanging patient data and other sensitive information with NHSmail and other accredited email services.

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[Michael Schmid]

Hi Greg,

when programming in Java or JavaScript:
the Java Random generator has a method to create random numbers with a
Gaussian distribution, standard deviation 1, and mean=0.
 
https://docs.oracle.com/javase/7/docs/api/java/util/Random.html#nextGaussian()

As usual for generating Gaussian-distributed random numbers, it uses the
polar method to generate the final random number from two independent
random numbers, one for the 'radius' and one for the 'angle'
   https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform

So, you can translate the code for the polar method from one of the two
links above to the macro language.

As an alternative, call JavaScript in the macro (rather slow).

   seed=round(random()*2e9);
   a=eval("script", "rnd=new java.util.Random("+seed+");
rnd.nextGaussian()");
   print(a);

[Note that the 2nd line of the macro should be one line starting with
'a=' and ending with 'nextGaussian()");']

Or as a further possibility, if you need n random numbers, create a
32-bit image with n pixels and 'random' initial values, then access them
pixel by pixel.


In any case, multiply by the desired stddev and add the desired mean.

Michael
________________________________________________________________


On 19/09/2018 14:09, JAMES, gregory (SANDWELL AND WEST BIRMINGHAM
HOSPITALS NHS TRUST) wrote:

> Dear ImageJ community,
>
>
> You are an intelligent group of people so I would like to ask this...
>
>
> Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).
>
>
> For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?
>
>
> Many thanks,
>
>
> Greg.
>
>
> __________________________________________
> Gregory James
> Clinical Scientist (Nuclear Medicine)
> Department of Physics and Nuclear Medicine
> City Hospital
> Dudley Road
> Birmingham
> B18 7QH
>
> 0121 507 4043
>
>
> ********************************************************************************************************************
>
> This message may contain confidential information. If you are not the intended recipient please inform the
> sender that you have received the message in error before deleting it.
> Please do not disclose, copy or distribute information in this e-mail or take any action in relation to its contents. To do so is strictly prohibited and may be unlawful. Thank you for your co-operation.
>
> NHSmail is the secure email and directory service available for all NHS staff in England and Scotland. NHSmail is approved for exchanging patient data and other sensitive information with NHSmail and other accredited email services.
>
> For more information and to find out how you can switch, https://portal.nhs.net/help/joiningnhsmail
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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[Ewing James]

Mark’s suggestion is the Box and Muller algorithm: Box G, Muller M. A Note on the Generation of Random Normal Deviates. Ann Math Stat. 1958;29:610-611.  It works well, but I’ve found that with many random number generators X and Y tend to be correlated.  You can check this by plotting X vs Y for a few hundred calculations. If there is a recognizable pattern (stripes, clusters) on the plot, X and Y are correlated (and thus not random).  I generally use only one of the pair if I really need a set of pseudorandom numbers that look truly random.

 - Jim

> On Sep 19, 2018, at 9:09 AM, Mark Osborne <[hidden email]> wrote:
>
> Greg
>
> Something like the following macro should work...
>
> var U; var V;
>
> function normal(){
> S = 2;
> while(S >= 1){
> U = -1+2*random; // uniform random no. -1..1
> V = -1+2*random;
> S = U*U+V*V;
> }
> }
>
> X = U * sqrt(-2*log(S)/S);   //or
> Y = V * sqrt(-2*log(S)/S);   // where log in ImageJ is natural ln
>
> X and Y are independent standard normally distributed random numbers, so you can multiply by a finite standard deviation to spread beyond unit STD and add to a mean to get the Gaussian.  Check against the Marsaglia polar method of generating normally distributed random numbers. Bit wasteful finding S<1, but easy to check and rather more intuitive than some.
>
> Mark
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of Seitz Arne
> Sent: 19 September 2018 13:33
> To: [hidden email]
> Subject: Re: Gaussian Random Number Generation
>
> Dear Greg,
>
> the RandomJ plugin from Eric Meijering looks to me what you are asking for.
> https://imagescience.org/meijering/software/randomj/
>
> The only limitation it works on images. However it is macro recordable and the source code can be found on GitHub.
>
> Best
> Arne
>
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST)
> Sent: mercredi 19 septembre 2018 14:09
> To: [hidden email]
> Subject: Gaussian Random Number Generation
>
> Dear ImageJ community,
>
>
> You are an intelligent group of people so I would like to ask this...
>
>
> Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).
>
>
> For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?
>
>
> Many thanks,
>
>
> Greg.
>
>
> __________________________________________
> Gregory James
> Clinical Scientist (Nuclear Medicine)
> Department of Physics and Nuclear Medicine City Hospital Dudley Road Birmingham
> B18 7QH
>
> 0121 507 4043
>
>
> ********************************************************************************************************************
>
> This message may contain confidential information. If you are not the intended recipient please inform the sender that you have received the message in error before deleting it.
> Please do not disclose, copy or distribute information in this e-mail or take any action in relation to its contents. To do so is strictly prohibited and may be unlawful. Thank you for your co-operation.
>
> NHSmail is the secure email and directory service available for all NHS staff in England and Scotland. NHSmail is approved for exchanging patient data and other sensitive information with NHSmail and other accredited email services.
>
> For more information and to find out how you can switch, https://portal.nhs.net/help/joiningnhsmail
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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[Cammer, Michael-2]

What about addingsubtracting or multiplying a random by a perfect Gaussian?  This could also be scaled as per the distance from the mean.

Michael Cammer, Sr Research Scientist, DART Microscopy Laboratory
NYU Langone Health, 540 First Avenue, SK2 Microscopy Suite, New York, NY  10016
[hidden email]  http://nyulmc.org/micros  http://microscopynotes.com/ 
Voice direct only, no text or messages:  1-914-309-3270 and 1-646-501-0567



-----Original Message-----
From: JAMES, gregory (SANDWELL AND WEST BIRMINGHAM HOSPITALS NHS TRUST) [mailto:[hidden email]]
Sent: Wednesday, September 19, 2018 8:09 AM
To: [hidden email]
Subject: Gaussian Random Number Generation

Dear ImageJ community,


You are an intelligent group of people so I would like to ask this...


Does anyone have a clever way of generating a random set of numbers that conform to a normal (Gaussian) distribution for a given mean and standard deviation using the 'random' macro function? I acknowledge that the ImageJ macro language is a slightly strange place to do this but I cannot use Excel because my data sets are so large and I would rather not learn a new scripting language (e.g. R).


For what it's worth, it is quite straightforward to do in Excel using =NORMINV(RAND(), mean, stdev). Does anyone have a clever way of replicating this function in ImageJ?


Many thanks,


Greg.


__________________________________________
Gregory James
Clinical Scientist (Nuclear Medicine)
Department of Physics and Nuclear Medicine
City Hospital
Dudley Road
Birmingham
B18 7QH

0121 507 4043


********************************************************************************************************************

This message may contain confidential information. If you are not the intended recipient please inform the
sender that you have received the message in error before deleting it.
Please do not disclose, copy or distribute information in this e-mail or take any action in relation to its contents. To do so is strictly prohibited and may be unlawful. Thank you for your co-operation.

NHSmail is the secure email and directory service available for all NHS staff in England and Scotland. NHSmail is approved for exchanging patient data and other sensitive information with NHSmail and other accredited email services.

For more information and to find out how you can switch, https://urldefense.proofpoint.com/v2/url?u=https-3A__portal.nhs.net_help_joiningnhsmail&d=DwIFAw&c=j5oPpO0eBH1iio48DtsedbOBGmuw5jHLjgvtN2r4ehE&r=vfUn-WSoz3z11I1Wutm3wYYMExfQInQ6nJuvEPYzlnE&m=zwreGc0NZ6s6BW8-g5d8NGAU6igblX0VMTnh84JZN0k&s=fh4GlqAYP7AQJmuScTNK9sQRNNOp7eXHr-8GiWCECrA&e=


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