New node type for systematic variation

[IzaakWN]

Right now a central/up/down variation might be defined as

{
  'nodetype': "category",
  #'input': "syst",
  'keys': ["nom", "up", "down"],
  'content': [ 1.0, 1.1, 0.9, ],
}

but since this is a frequently used scheme, one could predefine a node type / pydantic model that already generates the keys. One could create different node subtypes depending if the uncertainty is symmetric, asymmetric, or has many variations with different keys.

An uncertainty might be stored with which the reader tool computes the up and down variation, e.g.

{
  'nodetype': "symerr",
  #'input': "syst",
  'content': [ 1.0, 0.1, ],
}

yield 1.0+0.1=1.1 and 1.0-0.1=0.9. The "nom", "up", "down" keys of the "sys" variable are implicit in this node type object.

I don't know if this would improve performance, but it might enforce uniform style, such that the analyzers have to use only one consistent flag/key across all POG SFs ('up', 'down', ...). The default output could be the central one, if no variation key/flag was given.

[nsmith-]

I think introducing a special node type to handle systematics is worthwhile, since it is common to have a mixture of symmetric and asymmetric uncertainties, and some might be better parameterized as shifts from nominal. Probably a type similar to Category. We could have nominal as the default, though its not obvious if requests for a nonexistent systematic should return nominal or throw an error.

[pieterdavid]

Would the systematic category axis (preferably) be the outermost or innermost? In the (much more limited) JSON format we've used in our group for a while, there's only one uncertainty (nominal value, up and down - for multiple uncertainties we'd need to multiply with another one with unit nominal values); that's very readable, but with a high amount of redundancy in the JSON.
Allowing it to be the outermost would make it easier to add systematic variations that are not specified per-bin, but as an overall scaling of the nominal, e.g. something like this (probably too simplistic because I haven't studied the format in detail yet, but essentially a category axis with some extra features):

{
  "nodetype": "systematic",
  #'input': "syst",
  "keys": ["nominal", "stat_up", "stat_down", "syst1_up", "syst1_down"],
  "content": {
    "nominal": {...},
    "stat_up" : {...},
    "stat_down" : {...},
    "syst1_up" : {
      "nodetype": "variation",
      "from" : "nominal",
      "scale" : 1.1
      },
    "syst1_down" : {
      "nodetype": "variation",
      "from" : "nominal",
      "scale" : 0.9
      }
    }
  }
}