nnpdf / mcpdf

MCPDF

Sample the PDF posterior distribution.

• notes contains any kind of annotation, including considerations and intermediate results
• project contains the roadmap
• experiments are just small, self-contained experiments, mainly to check properties or to play with tools (including any half-baked solution)
• src contains the source for all the various intermediate attempts, but full attempts (possibly on simplified problems)

Name

The name mcpdf is just the temporary identifier for the project, chosen to be "compatible" with nnpdf (since the deliverable will be once more an MC set, but also because at some point MCMC will be involved).

In some sense, it comes just from a generalization, since no neural network is going to be involved.

mcpdf's Issues

Data

Roadmap for closure and actual data implementation.

• 0: PDF level fake data (PDF uncertainty)
• 1: closure test data through actual DIS theory (PDF uncertainty)
• 2: actual data (actual covmat)

Gaussian Processes: `lsqfitgp`

Roadmap for GP track

• 0: design the GP regression (with fake data and theory)
• ...

HMC

Here the roadmap for HMC implementation:

• 0: basic GP regression with model and NUTS from pymc3

ZEUS very large-x data

Allen Caldwell presented at DIS2022 an extremely similar work.

PDFs were sampled from the Bayesian posterior, with the only difference (wrt the basic idea) of assuming an extremely restrictive parametrization, and to consume only some DIS data.

In that case, the main point was actually about the data themselves, that are potentially extremely useful, giving a direct handle on the very large-x PDF.
The reason why they have not been implemented in NNPDF yet is that they have Poissonian statistics (with a quite small count for a few bins), so they were violating Gaussian assumptions. This is almost a non-reason, since Poissonian are easy to use for pseudodata generation (sampling), and Gaussian are a good enough approximation in the loss function.

However, we can implement them and compare one-to-one in a similar environment to Caldwell's group result, within two scenarios:

• the "apples with apples" comparison, based on the exact same dataset, and
• the "full" dataset sampling, where the dataset is extended to MCPDF/NNPDF baseline + these ZEUS data

Analytic formula

Here the roadmap for analytic formula implementation, as per https://arxiv.org/abs/2111.05787

• 0: setup the project
• 1: improve FkTables
  • reinterpolate x grid
• 2: mask PDF flavor and luminosities

Generate vp reports

Since we have no comparable fit data (wrt n3fit ones) there are a few things we can't reproduce from a full comparison report. But most things only rely on an LHAPDF grid, so we just need to generate that one.

• evolve a fit (essentially the resulting NumPy array) with evolven3fit
• First generate a brief one
  • this is already based just on an LHAPDF grid, so once we have one, we can make it
• Then try to get as many elements from the complete one as possible, purging the template
  • essentially the only things to suppressed are those related to training lengths

Thanks @RoyStegeman for all the explanations and the references.