pyhf:统计不确定性的实现

Question

关于统计不确定性的实施，我有一个问题。在pyhf文档https://scikit-hep.org/pyhf/likelihood.html#sample中，您提到了推断统计不确定性的方法是使用带有"type"："staterror“和data field=0.1的修饰符。

所以让我们假设我有一个来自MC的背景频道，我把我的发行分成三个回收箱：

"name": "background",
"data": [300., 50., 60.]

你如何正确地解释统计不确定性？从Poissonian的构建，我想说，通过建设，你已经考虑了统计的不确定性。还是我必须有一个包含状态错误的修饰符？统计错误的数据字段到底是什么？

Answer 1

I有一个来自MC的背景频道

考虑到由于Monte样本大小有限，您想要对形状的不确定性进行建模，最好使用的修改器是staterror。staterror在所有样本(有一个staterror修饰符)之间共享，它是在正常约束下应用的，约束的强度是在正交中添加的每个样本的不确定性。在这里，data键表示样本中每个桶中的绝对不确定性(在本例中是bin计数的泊松不确定性)：

因此，考虑到一个带有3个回收箱的单个背景示例，示例规范可能如下所示(我将命名为bkg_only_spec.json)。

{
    "channels": [
        {
            "name": "single_channel",
            "samples": [
                {
                    "name": "background",
                    "data": [
                        300.0,
                        50.0,
                        60.0
                    ],
                    "modifiers": [
                        {
                            "name": "uncorr_bkguncrt",
                            "type": "staterror",
                            "data": [
                                17.32051,
                                7.07107,
                                7.74597
                            ]
                        }
                    ]
                }
            ]
        }
    ],
    "observations": [
        {
            "name": "single_channel",
            "data": [
                300.0,
                50.0,
                60.0
            ]
        }
    ],
    "measurements": [
        {
            "name": "Measurement",
            "config": {
                "poi": "mu",
                "parameters": []
            }
        }
    ],
    "version": "1.0.0"
}

我们可以看到(注意，constrained_by_normal)仍然是CLI's inspect的一个有效规范(当然，您也需要一个信号样本来进行任何推断)

$ pyhf --version
pyhf, version 0.5.1
$ python answer.py
$ pyhf inspect bkg_only_spec.json
          Summary       
    ------------------  
       channels  1
        samples  1
     parameters  1
      modifiers  1

       channels  nbins
     ----------  -----
 single_channel    3  

        samples
     ----------
     background

     parameters  constraint              modifiers
     ----------  ----------              ----------
uncorr_bkguncrt  constrained_by_normal   staterror

    measurement           poi            parameters
     ----------        ----------        ----------
(*) Measurement            mu            (none)

下面的answer.py生成规范。

# answer.py
import numpy as np
import json


def main():
    bins = [300.0, 50.0, 60.0]
    # rounding, as keeping full floating point is maybe a bit silly
    poisson_uncert = np.sqrt(bins).round(decimals=5).tolist()

    # just set the observations to be the same as the bin count here
    # as a placeholder
    spec = {
        "channels": [
            {
                "name": "single_channel",
                "samples": [
                    {
                        "name": "background",
                        "data": bins,
                        "modifiers": [
                            {
                                "name": "uncorr_bkguncrt",
                                "type": "staterror",
                                "data": poisson_uncert,
                            }
                        ],
                    }
                ],
            }
        ],
        "observations": [{"name": "single_channel", "data": bins}],
        "measurements": [
            {"name": "Measurement", "config": {"poi": "mu", "parameters": []}}
        ],
        "version": "1.0.0",
    }

    with open("bkg_only_spec.json", "w") as spec_file:
        json.dump(spec, spec_file, indent=4)


if __name__ == "__main__":
    main()