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# Visualizing Uncertainty
## CAPP 30239
---
![bg fit](climate1.png)
<!--
What is this trying to show?
source: https://www.ipcc.ch/report/ar6/wg1/figures/chapter-3/figure-3-4/
-->
---
![bg fit](climate2.png)
<!--
These are showing essentially the same thing, one shows individual models and the other uses some aggregates with confidence intervals.
These are from the same page of the IPCC report.
-->
---
## What causes uncertainty?
1) **measurement error** - An instrument used has some non-perfect degree of accuracy. In a survey, this could be a poorly-worded question.
2) **model uncertainty** - Models make assumptions and simplifications, different assumptions lead to different outcomes.
3) **sampling variability** - Differences between sample & population.
4) **missing data** - How missing data is accounted for & represented.
The result is that we have a range or distribution, where we want a number to use with one of our channels (Hue, X, Y, etc.).
---
## Challenges of Uncertainty
Often left out, in part due to being hard to understand, and even harder to visualize.
Omission however misleads audiences, especially where a lot of significant figures are included.
![width:100%](clock.png)
*Global Population Uncertainty: ±160 million people (2%)*
---
## Challenges of Uncertainty
Uncertainty estimates are simplified, often out of necessity.
![](weather.png)
30% chance of rain: "A 30% chance that at least 0.01" of rain will fall somewhere within a given area over a 12 hour period."
**Do I bring an umbrella?**
---
## Challenges of Uncertainty
Complexity of visualization can overwhelm audience, obscure other meaning.
![](matplotlib.png)
From a data-ink ratio perspective, it is understandable why if the error bars do not seem relevant to a narrative, that they would be omitted.
---
## Including Uncertainty
If omitting uncertainty misleads, it violates our prime directive of **graphical integrity**.
The job then, is to find ways that are **audience appropriate** & **don't obfuscate the meaning**.
The difficulty will be in resolving this tension.
---
## Common Techniques
- Uncertainty as Probability
- Error Bars
- Confidence Bands
---
## Uncertainty As Probability
![width:100%](probability-waffle.png)
Random waffle chart: works for cases with discrete outcomes.
---
## Uncertainty As Probability
In practice, we often care about more than boolean outcome.
![](election-prediction.png)
---
![bg fit](election-quantile.png)
<!--
We can convert this to discrete measurements: quantile dot plot.
-->
---
![bg fit](biden-trump.webp)
<!-- source: fivethirtyeight -->
---
## Uncertainty of Point Estimates
These work when we're focused on uncertainty around a particular outcome.
Sometimes we need to show uncertainty around discrete measurements, or projections.
---
### Error Bars
![](data-ci.png)
---
### Error Bands
![bg left](altair-errorband.png)
```python
line = alt.Chart(source).mark_line().encode(
x='Year',
y='mean(Miles_per_Gallon)'
)
band = alt.Chart(source).mark_errorband(extent='ci').encode(
x='Year',
y=alt.Y('Miles_per_Gallon').title('Miles/Gallon'),
)
band + line
```
---
### Issues with Error Bars & Confidence Bands
1) There is no pre-defined meaning of these intervals.
**If error bars or bands are included, the legend must include information on the meaning.**
2) Error bars are common in scientific & academic literature, other audiences cannot be assumed to understand them.
3) Restricted to 1D/2D dots. If variable being expressed is mapped to color, area, etc. then alternative presentations needed.
---
![bg fit](2016.jpg)
---
### Variations on Error Bars & Intervals
![](ci-2.png)
<!-- when appropriate, can also be used to show multiple intervals -->
---
![bg fit](ci-3.png)
<!--care should be taken that distribution is indeed normal if curves/etc. chosen -->
---
![](2d-bars.png)
---
### Regression Uncertainty
![width:900px](multiple-reg.png)
---
### Regression Uncertainty
![width:900px](translucent-band.png)
---
## Other Approaches
---
### Showing Multiple Futures
![](multiple-outcomes.webp)
---
![width:900px](climate1.png)
---
### Hurricane Uncertainity
<div class="container">
<div class="col">
![width:450](hurricane2.png)
</div>
<div class="col">
![width:450px](hurricane1.png)
</div>
</div>
<!-- source: https://tamucoa.b-cdn.net/app/uploads/2021/10/House2011TrackUncertaintyVisualization.pdf -->
---
### On Maps
![bg fit](map-uncertainity.png)
<!-- source: https://www.e-education.psu.edu/geog486/sites/www.e-education.psu.edu.geog486/files/Lesson_07/Images/ex_vs_ont.PNG -->
---
### "Sketchiness"
![](sketchy.gif)
---
### Animating Uncertainty
-
- HOP Plot: <https://vallandingham.me/animating_uncertainty.html>
---
## References & Acknowledgements
- <https://clauswilke.com/dataviz/visualizing-uncertainty.html>
- <https://www.mjskay.com/presentations/aalto2020-uncertainty.pdf>
- <https://nightingaledvs.com/dark-sky-weather-data-viz/>
- <https://mucollective.co/uncertainty_collection/>

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