Is there a function in Stan analogous to the convolve() function in R?

[Jon Fawcett]

Dear User Group,

I am trying to fit a model in Stan that views a particular time-series as arising from the convolution of several “pulses” of varying strength along with a particular response function. As a starting point, I am interested in recreating the analysis reported here by another research tea, (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3365158/) with original scripts in R provided here (http://www.pnas.org/content/suppl/2012/05/11/1201858109.DCSupplemental/sd02.txt and http://www.pnas.org/content/suppl/2012/05/11/1201858109.DCSupplemental/sd03.txt). I have an intuition as to how I should proceed, but a critical step in the original R calculations involves the command:

convolve(i,rev(h),type="open")

Where i represents the pulses and h represents the response function. Does Stan have an equivalent command to convolve(x, y, type='open')? I have been unable to find one.

Cheers!

Jon

[Ben Goodrich]

On Sunday, January 15, 2017 at 3:16:27 PM UTC-5, Jon Fawcett wrote:

Does Stan have an equivalent command to convolve(x, y, type='open')? I have been unable to find one.

If there were one, it would be returned by

rstan::lookup("convolve")

Ben

[Bob Carpenter]

We don't have any Fourier transform functions available
from within the Stan language. We've been planning to
add the basic FFT because there's an implementation in
Eigen (which we, by the way, use for autocorrelation estimates
as part of effective sample size estimation).

- Bob

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[Jon Fawcett]

Thanks for weighing in, Ben and Bob!

I should have specified more clearly that I had already searched for functions named convolve or any obvious sign of there being such a function and found nothing. I was checking to see whether there were perhaps something less obvious I missed. From your answers, I gather that there is not at this time. Do you know when FFT will be implemented? Or is that low on the list?

[Bob Carpenter]

I think Thel may implement the discrete FFT very soon (maybe in
the next couple of months). I don't think there's anything standing
in the way.

- Bob

[Mike Lawrence]

I believe that the purpose to which convolve was used in that model was merely to prepare the predictor matrix. You can create that matrix yourself outside Stan, where each column is the response function shifted by a different amount for each column. You then do a standard regression and the weights associated with each column reflect the evidence for a pulse at the time-point corresponding to the shift of that column. 

--
Mike Lawrence
Graduate Student
Department of Psychology & Neuroscience
Dalhousie University

~ Certainty is (possibly) folly ~

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[Mike Lawrence]

Note: an improvement on the model could include modeling the column coefficients as a Gaussian Process rather than independent weights

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[Sebastian Weber]

Hi!

Depending on the details of the problem you could abuse the ode solver to do the integration...just a thought.

Sebastian

[Bob Carpenter]

This wasn't enough for me to understand the function:

each column is the response function shifted by a different amount
for each column.

Can you define convolve() as a function in Stan itself? If
so, it'll be easy for us to add to the language itself.

- Bob

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[Mike Lawrence]

I made up an example data set and analysis for this. See the attached "pulse.R", which generates a fake data set comprised of the additive combination of a single reference function shifted to varying degrees plus noise. The analysis takes the resulting timeseries and successfully retrieves the three shift values used to make the data.

On Fri, Jan 20, 2017 at 1:58 PM, Bob Carpenter <ca...@alias-i.com> wrote:

This wasn't enough for me to understand the function:

  each column is the response function shifted by a different amount
  for each column.

Can you define convolve() as a function in Stan itself?  If
so, it'll be easy for us to add to the language itself.

- Bob

> On Jan 15, 2017, at 8:05 PM, Mike Lawrence <mike....@gmail.com> wrote:
>
> I believe that the purpose to which convolve was used in that model was merely to prepare the predictor matrix. You can create that matrix yourself outside Stan, where each column is the response function shifted by a different amount for each column. You then do a standard regression and the weights associated with each column reflect the evidence for a pulse at the time-point corresponding to the shift of that column.
>
> --
> Mike Lawrence
> Graduate Student
> Department of Psychology & Neuroscience
> Dalhousie University
>
> ~ Certainty is (possibly) folly ~
>
> On Sun, Jan 15, 2017 at 4:16 PM, Jon Fawcett <jmfa...@gmail.com> wrote:
> Dear User Group,
>
> I am trying to fit a model in Stan that views a particular time-series as arising from the convolution of several “pulses” of varying strength along with a particular response function. As a starting point, I am interested in recreating the analysis reported here by another research tea, (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3365158/) with original scripts in R provided here (http://www.pnas.org/content/suppl/2012/05/11/1201858109.DCSupplemental/sd02.txt and http://www.pnas.org/content/suppl/2012/05/11/1201858109.DCSupplemental/sd03.txt). I have an intuition as to how I should proceed, but a critical step in the original R calculations involves the command:
>
> convolve(i,rev(h),type="open")
>
> Where i represents the pulses and h represents the response function. Does Stan have an equivalent command to convolve(x, y, type='open')? I have been unable to find one.
>
> Cheers!
> Jon
>
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[Bob Carpenter]

Thanks for sharing.

- Bob

P.S. Those semicolons look so lonely being separated from their statements!

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> <pulse.R><pooled_regression.stan>

[Christopher Fisher]

I came across this post while searching for something similar to convpow() in the distr package, which is used for efficiently convolving random variables. So I will chime in and say this could also be useful for my purposes as well. 

Best regards,

Chris 

[Bob Carpenter]

Thanks --- we're working on it (or I should say, Thel's
working on it).

- Bob