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tijana-zrnic authored Oct 1, 2023
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Expand Up @@ -30,9 +30,9 @@ The gold-standard labels and model predictions from the dataset will be download
The labels, $Y$, are binary indicators of whether or not the galaxy is a spiral galaxy.
The model predictions, $\hat{Y}$, are the model's estimated probability of whether the galaxy image has spiral arms.
The inference target is $\theta^* = \mathbb{E}[Y]$, the fraction of spiral galaxies.
You will produce a confidence interval, $\mathcal{C}^{\mathrm{PP}}_\alpha$, which contains $\theta^*$ with probability $1-\alpha=90\%$, i.e.,
You will produce a confidence interval, $\mathcal{C}^{\mathrm{PP}}_\alpha$, which contains $\theta^*$ with probability $1-\alpha=0.9$, i.e.,
```math
\mathbb{P}\left( \theta^* \in \mathcal{C}^{\mathrm{PP}}_\alpha\right) \geq 90\%.
\mathbb{P}\left( \theta^* \in \mathcal{C}^{\mathrm{PP}}_\alpha\right) \geq 0.9.
```

The code for this is below. It can be copy-pasted directly into the Python REPL.
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