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Expand Up @@ -279,30 +279,6 @@ In his [PyCon 2017 keynote](https://youtu.be/ZyjCqQEUa8o), Jake VanderPlas gave
In [2022](https://indico.cern.ch/event/1140031/) we created a view for the PyHEP ecosystem
]

---
# Rapid rise of Python for analysis in HEP

<p style="text-align:center;">
<a href="https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf">
<img src="figures/github-language-fullstudy-for-review.svg"; width=85%>
</a>
</p>
.center.large["import XYZ" matches in GitHub repos for users who fork [CMSSW](https://github.com/cms-sw/cmssw) by file]

.footnote[[Modern Python analysis ecosystem for High Energy Physics](https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf), Jim Pivarski, Matthew Feickert, Gordon Watts]

---
# Explosion of Scientific Python (NumPy, etc.)

<p style="text-align:center;">
<a href="https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf">
<img src="figures/github-package-fullstudy-for-review.svg"; width=85%>
</a>
</p>
.center.large["import XYZ" matches in GitHub repos for users who fork [CMSSW](https://github.com/cms-sw/cmssw) by library/tool]

.footnote[[Modern Python analysis ecosystem for High Energy Physics](https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf), Jim Pivarski, Matthew Feickert, Gordon Watts]

---
# Community adoption ...

Expand Down Expand Up @@ -426,7 +402,7 @@ In [2022](https://indico.cern.ch/event/1140031/) we created a view for the PyHEP
---
# Gradients as Computational Tools

- As we'll see later, having access to the gradient while performing minimization is highly beneficial!
- As we'll see later, having access to the gradient while performing minimization is .bold[highly beneficial]!
- Can imagine multiple ways of arriving at gradients for computational functions

.center.width-30[![carbon_f_x](figures/carbon_f_x.png)]
Expand Down Expand Up @@ -540,29 +516,6 @@ Provide constraints on models through setting best limits
---
# HistFactory Template: grammar

$$
f\left(\mathrm{data}\middle|\mathrm{parameters}\right) = f\left(\textcolor{#00a620}{\vec{n}}, \textcolor{#a3130f}{\vec{a}}\middle|\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}\right) = \color{blue}{\prod\_{c \\,\in\\, \textrm{channels}} \prod\_{b \\,\in\\, \textrm{bins}\_c} \textrm{Pois} \left(n\_{cb} \middle| \nu\_{cb}\left(\vec{\eta}, \vec{\chi}\right)\right)} \\,\color{red}{\prod\_{\chi \\,\in\\, \vec{\chi}} c\_{\chi} \left(a\_{\chi}\middle|\chi\right)}
$$

Mathematical grammar for a simultaneous fit with multiple disjoint _channels_ (or regions) of binned distributions with multiple _samples_ contributing to each with additional (possibly shared) systematics between sample estimates

.kol-1-2[
.bold[Main pieces:]
- .blue[Main Poisson p.d.f. for simultaneous measurement of multiple channels]
- .katex[Event rates] $\nu\_{cb}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}})$ (nominal rate $\nu\_{scb}^{0}$ with rate modifiers)
- .red[Constraint p.d.f. (+ data) for "auxiliary measurements"]
- encode systematic uncertainties (e.g. normalization, shape)
<!-- - $\vec{n}$: events, $\vec{a}$: auxiliary data, $\vec{\eta}$: unconstrained pars, $\vec{\chi}$: constrained pars -->
- $\textcolor{#00a620}{\vec{n}}$: .obsdata[events], $\textcolor{#a3130f}{\vec{a}}$: .auxdata[auxiliary data], $\textcolor{#0495fc}{\vec{\eta}}$: .freepars[unconstrained pars], $\textcolor{#9c2cfc}{\vec{\chi}}$: .conpars[constrained pars]
]
.kol-1-2[
.center.width-100[[![SUSY-2016-16_annotated](figures/SUSY-2016-16.png)](https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/SUSY-2016-16/)]
.center[Example: .bold[Each bin] is separate (1-bin) _channel_,<br> each .bold[histogram] (color) is a _sample_ and share<br> a .bold[normalization systematic] uncertainty]
]

---
# HistFactory Template: implementation

$$
f\left(\mathrm{data}\middle|\mathrm{parameters}\right) = f\left(\textcolor{#00a620}{\vec{n}}, \textcolor{#a3130f}{\vec{a}}\middle|\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}\right) = \prod\_{c \\,\in\\, \textrm{channels}} \prod\_{b \\,\in\\, \textrm{bins}\_c} \textrm{Pois} \left(\textcolor{#00a620}{n\_{cb}} \middle| \nu\_{cb}\left(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}\right)\right) \prod\_{\chi \\,\in\\, \vec{\chi}} c\_{\chi} \left(\textcolor{#a3130f}{a\_{\chi}}\middle|\textcolor{#9c2cfc}{\chi}\right)
$$
Expand All @@ -573,10 +526,16 @@ $$
\nu\_{cb}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}) = \sum\_{s \\,\in\\, \textrm{samples}} \underbrace{\left(\sum\_{\kappa \\,\in\\, \vec{\kappa}} \kappa\_{scb}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}})\right)}\_{\textrm{multiplicative}} \Bigg(\nu\_{scb}^{0}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}) + \underbrace{\sum\_{\Delta \\,\in\\, \vec{\Delta}} \Delta\_{scb}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}})}\_{\textrm{additive}}\Bigg)
$$

.center[.bold[This is a _mathematical_ representation!] Nowhere is any software spec defined]
Mathematical grammar for a simultaneous fit with multiple disjoint _channels_ (or regions) of binned distributions with multiple _samples_ contributing to each with additional (possibly shared) systematics between sample estimates

<!-- .center[.bold[This is a _mathematical_ representation!] Nowhere is any software spec defined] -->
.center[.bold[Until 2018] the only implementation of HistFactory was in `C++` framework for physics analysis ([`ROOT`](https://root.cern.ch/))]

.center.width-70[[![ROOT_HistFactory](figures/ROOT_HistFactory.png)](https://root.cern/doc/v628/group__HistFactory.html)]
<p style="text-align:center;">
<a href="https://root.cern/doc/v628/group__HistFactory.html">
<img src="figures/ROOT_HistFactory.png"; width=55%>
</a>
</p>

---
# `pyhf`: HistFactory in pure Python
Expand Down Expand Up @@ -1164,6 +1123,30 @@ class: end-slide, center

.center[[ATLAS](https://cds.cern.ch/record/2803119?ln=en) and [CMS](https://cds.cern.ch/record/2815292?ln=en) software and computing reviews]

---
# Rapid rise of Python for analysis in HEP

<p style="text-align:center;">
<a href="https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf">
<img src="figures/github-language-fullstudy-for-review.svg"; width=85%>
</a>
</p>
.center.large["import XYZ" matches in GitHub repos for users who fork [CMSSW](https://github.com/cms-sw/cmssw) by file]

.footnote[[Modern Python analysis ecosystem for High Energy Physics](https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf), Jim Pivarski, Matthew Feickert, Gordon Watts]

---
# Explosion of Scientific Python (NumPy, etc.)

<p style="text-align:center;">
<a href="https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf">
<img src="figures/github-package-fullstudy-for-review.svg"; width=85%>
</a>
</p>
.center.large["import XYZ" matches in GitHub repos for users who fork [CMSSW](https://github.com/cms-sw/cmssw) by library/tool]

.footnote[[Modern Python analysis ecosystem for High Energy Physics](https://matthewfeickert.github.io/talk-doepy-python-exchange-2022/2022-06-29.pdf), Jim Pivarski, Matthew Feickert, Gordon Watts]

---
# Automatic Differentiation: Forward and Reverse

Expand Down Expand Up @@ -1239,6 +1222,30 @@ $$
- encode systematic uncertainties (e.g. normalization, shape)
- .red[Constraint p.d.f. (+ data) for "auxiliary measurements"]

---
# HistFactory Template: grammar

$$
f\left(\mathrm{data}\middle|\mathrm{parameters}\right) = f\left(\textcolor{#00a620}{\vec{n}}, \textcolor{#a3130f}{\vec{a}}\middle|\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}}\right) = \color{blue}{\prod\_{c \\,\in\\, \textrm{channels}} \prod\_{b \\,\in\\, \textrm{bins}\_c} \textrm{Pois} \left(n\_{cb} \middle| \nu\_{cb}\left(\vec{\eta}, \vec{\chi}\right)\right)} \\,\color{red}{\prod\_{\chi \\,\in\\, \vec{\chi}} c\_{\chi} \left(a\_{\chi}\middle|\chi\right)}
$$

Mathematical grammar for a simultaneous fit with multiple disjoint _channels_ (or regions) of binned distributions with multiple _samples_ contributing to each with additional (possibly shared) systematics between sample estimates

.kol-1-2[
.bold[Main pieces:]
- .blue[Main Poisson p.d.f. for simultaneous measurement of multiple channels]
- .katex[Event rates] $\nu\_{cb}(\textcolor{#0495fc}{\vec{\eta}}, \textcolor{#9c2cfc}{\vec{\chi}})$ (nominal rate $\nu\_{scb}^{0}$ with rate modifiers)
- .red[Constraint p.d.f. (+ data) for "auxiliary measurements"]
- encode systematic uncertainties (e.g. normalization, shape)
<!-- - $\vec{n}$: events, $\vec{a}$: auxiliary data, $\vec{\eta}$: unconstrained pars, $\vec{\chi}$: constrained pars -->
- $\textcolor{#00a620}{\vec{n}}$: .obsdata[events], $\textcolor{#a3130f}{\vec{a}}$: .auxdata[auxiliary data], $\textcolor{#0495fc}{\vec{\eta}}$: .freepars[unconstrained pars], $\textcolor{#9c2cfc}{\vec{\chi}}$: .conpars[constrained pars]
]
.kol-1-2[
.center.width-100[[![SUSY-2016-16_annotated](figures/SUSY-2016-16.png)](https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/SUSY-2016-16/)]
.center[Example: .bold[Each bin] is separate (1-bin) _channel_,<br> each .bold[histogram] (color) is a _sample_ and share<br> a .bold[normalization systematic] uncertainty]
]


---
# HistFactory Template: systematic uncertainties

Expand Down

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