Activity 3 — Temperature prediction

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What you will do

Each student will predict the daily average temperature (°F) in New York City for the following 5 dates:

December 3, 4, 5, 6, 7 (2025).

You will:

  1. Collect data you consider relevant (e.g., historical weather for NYC, NOAA, ECMWF forecasts, etc.).
  2. Choose a model (Bayesian is required or score will be zero). Any reasonable model is allowed (ARIMA with Bayesian priors, Bayesian linear regression with weather covariates, Bayesian calibration of forecast ensembles, etc.).

  3. Produce for each date $d\in\{3,4,5,6,7\}$:

    • a point prediction (average daily temperature) $\hat{y}_d$ in °F,
    • a two–sided interval $[L_d, U_d]$ in °F (you choose the level, e.g. 80%, 90%, 95%). You can choose the confidence interval (CI) however you prefer, but as explained in the “Score” section below, if it’s too wide or too narrow, you may lose points. Be careful!
  4. Submit two things on Canvas:
    • Submit a PDF with the following constraints:
      • The first part of the pdf is max 2 pages in which you explain: data sources, what data you used, model summary, priors, and how you computed $\hat{y}_d$, $[L_d,U_d]$.
      • The rest of the PDF is your code with the following instructions: no page limit, the final output of the code has to be a table $3 \times 5$. Row 1 is the mean temeperature, row 2 is the lower CI bound and row 3 is the upper CI bound, for a total of 15 predictions. the table has to be a direct output of the code (copy and paste is not allowed).
    • Submit your data into the Excel file provided in Canvas using the following formatting: All temperatures must be in Fahrenheit, numeric with exactly two decimals (e.g., 35.67). For each date, submit 3 numbers divided by comma. \[ \text{ e.g. } \quad 44.13, 40.10, 46.15 \] The first number is the daily average predicted temperature, the second is the lower CI bound, the last is the upper CI bound. An example can be found at the bottom of the Excel file provided in Canvas.

Deadline: Ultimate deadline is Decmeber 1 st, 11:59 PM for both PDF submission and Excel submission. Only Excel submission or PDF will get zero score.

Scoring

The maximim points for this activity is 2.5; divided as follows: 1 point is given to the clearness of the pdf submission. The additional 1.5 is calculated as follows. After each of the five dates passes, we take the true observed NYC average temperature for that day (from a fixed source I disclose in class). For each day (d):

  • If the truth $y^{\text{true}}_d\notin[L_d,U_d]$, your day score is $S_d=0$.
  • If $y^{\text{true}}_d\in[L_d,U_d]$, your score decreases with the absolute error and with the interval length. We propose the smooth, bounded function:

\[ S_d = \exp\big(-\alpha|y^{\text{true}}_d - \hat{y}_d|\big)\times\exp\big(-\beta(U_d-L_d)\big)\times\mathbf{1}\{y^{\text{true}}_d\in[L_d,U_d]\}, \]

with default parameters $\alpha=0.10$ (per °F) and $\beta=0.05$ (per °F). Thus $0\le S_d\le 1$. To help overall students score these parameter might be adjusted.

Final activity score: up to 1 point for the pdf plus \[ \text{Points} = 1.5\times \frac{1}{5}\sum_{d\in\{3,4,5,6,7\}} S_d. \]