Post Introductory Metaculus Comment on Question 22307 about forecasting-tornadoes

[AFg6K7h4fhy2]

See here:

I understand that this question closes in less than a day and that the observed preliminary count of 310 exceeds the open upper boundary of 300, but I would really appreciate if some Metaculites could take a look at this multilevel model I built and provide some thoughts and or feedback. 

Some quick links:

- [The repository](https://github.com/AFg6K7h4fhy2/Forecasting-Tornadoes)
- [The NOAA data, if anyone wants a cleaned csv file](https://github.com/AFg6K7h4fhy2/Forecasting-Tornadoes/blob/main/data/clean/cleaned_NOAA_SPC.csv)
- [The model, in code](https://github.com/AFg6K7h4fhy2/Forecasting-Tornadoes/blob/main/model_E414_01/src/model.py)
- __[A document for the model](https://github.com/AFg6K7h4fhy2/Forecasting-Tornadoes/blob/main/model_E414_01/docs/output/out.pdf)__

The most important aspects of the above, in math and writing, for those who do not want to visit the last link:

---

Let \(\alpha_i\) denote the random effect of the location of state \(i\) on expected tornado count. Further, let \(\gamma_j\) and \(\delta_k\) denote the random of effects of month \(j\) on and year \(k\), respectively, on expected tornado count. Let the expected tornado count for state \(i\), month \(j\), and year \(k\) be called \(Y_{ijk}\).

The tornado count \(T_{ijk}\) for state \(i\), month \(j\), and year \(k\) can be modelled via \(T_{ijk} \sim \text{Poisson}(Y_{ijk})\), where \(\log (Y_{ijk}) = \alpha_{\text{state}[i]} + \gamma_{\text{month}[j]} + \delta_{\text{year}[i]}\), i.e. \(Y_{ijk}\) is [log-linear](https://en.wikipedia.org/wiki/Log-linear_model).

Adaptive priors:

$$
\begin{aligned}
\alpha_{l} &\sim \text{Normal}(\overline{\alpha}, \sigma_{\alpha}) \quad \text{for} \quad l = 1, 2, \dotsc, 50 \\
\gamma_{l} &\sim \text{Normal}(\overline{\gamma}, \sigma_{\gamma}) \quad \text{for} \quad l = 1, 2, \dotsc, 12  \\
\delta_{l} &\sim \text{Normal}(\overline{\delta}, \sigma_{\delta}) \quad \text{for} \quad l = 1, 2, \dotsc, 5
\end{aligned}
$$

where

$$
\begin{aligned}
\overline{\alpha} &\sim \text{Normal}(0, 3.0) \\
\overline{\gamma} &\sim \text{Normal}(0, 1.0) \\
\overline{\delta} &\sim \text{Normal}(0, 2.0)
\end{aligned}
$$

and

$$\sigma_{\alpha}, \sigma_{\gamma}, \sigma_{\delta} \sim \text{Exponential}(1.0)$$

---

Around a week ago, I began created it, but had to pause working on it due to my job. The posterior samples gave me around a mean US tornado count of 275 (summing across individual states), so this is not too bad relative to other commented predictions and considering the turn of events. 

I expect to create more modelling repositories in the future, if anyone wants to join (worth noting that I am fairly particular about how my repositories are run and setup). Also, it's worth noting that there are likely going to be more files for visualization, sensitivity analyses, forecast-output creation, saving of posterior samples and other values, etc... in the near term as I scope out this Forecasting-Tornadoes repository further. The README needs to be worked on more as well; I expect to include some visualizations (tornado data, priors, prior predictive, posterior predictive, MCMC trace, etc...) later next week (these will be in the last link in the aforementioned list).

Mostly, I am looking for others to lean towards either "_yes, this model makes some sense_" or "_no, this is silly, why would you do this?_" or "_this model would make sense if X was changed_" or something else similar. 

@(skmmcj) @(Haiku) @kqr @(katifish) 

[AFg6K7h4fhy2]

Done, save for some of the first task. Completely now in the interest of time.