SLOP8412 / Experimental workspace / 01

The distributions stay fixed.
Does the ranking?

Change the sample size, seed or estimator. Run real Python and examine what moves. A smaller reported score need not mean a better underlying distribution.

Enable JavaScript to execute Python. The starter remains readable below.

Run cell: shared variables · Run all: fresh variables, top to bottom · Ctrl / ⌘ + Enter: run focused cell · Tab: leave editor. Deleting a cell does not undo its Python variables; reset or Run all to rebuild state.

01 / Notebook

Python · NumPy

No execution yet.

Cell output / errors

No execution yet.

rng = np.random.default_rng(seed)
population_a = float(gaussian_distance(0, 1, mean_a, variance_a))
population_b = float(gaussian_distance(0, 1, mean_b, variance_b))
estimated_a, estimated_b = [], []
print(f"seed={seed}; repeats={repeats}; reference=N(0, 1)")
print(f"A=N({mean_a}, {variance_a}); B=N({mean_b}, {variance_b}) [mean, variance]")
print(f"Population: A={population_a:.8f}, B={population_b:.8f}")
print("N       mean A       mean B       fraction of trials A < B")
for n in sample_sizes:
    if n < 2 or repeats < 1:
        raise ValueError("Use N >= 2 and repeats >= 1")
    reference = rng.normal(0, 1, (repeats, n))
    a = rng.normal(mean_a, np.sqrt(variance_a), (repeats, n))
    b = rng.normal(mean_b, np.sqrt(variance_b), (repeats, n))
    scores_a, scores_b = estimate(reference, a), estimate(reference, b)
    estimated_a.append(float(scores_a.mean()))
    estimated_b.append(float(scores_b.mean()))
    print(f"{n:<7} {estimated_a[-1]:.8f}   {estimated_b[-1]:.8f}   {np.mean(scores_a < scores_b):.3f}")

No execution yet.

Cell output / errors

No execution yet.

No execution yet.

Cell output / errors

No execution yet.

Export a copy before leaving. Browser storage is not a backup.

02 / Results

No run yet

Your code supplies the evidence.

Run all to compute the starter plot. Cells can change the plot by assigning or modifying the plot dictionary.

The latest plot stays here while you work. Cell outputs appear beneath each editor. Saved cells do not include live Python variables or outputs.

Make one change. Keep the evidence.

Run the starter. Compare the mean estimates with the population distances.
Change only the seed. Does the ordering survive?
Increase the repetitions. This stabilises the average; does it remove finite-sample bias?
Change ddof=1 to ddof=0. Record the implementation change alongside the score.

Continue with Week 5: The bias, or record the result in your measurement log.

Before you run

Python 3.12 / Pyodide 0.27.7 and NumPy download from jsDelivr on first Run. First loading may take a while.
Runs execute locally in your browser. There is no course execution server or submission service. Only run code you trust; Python can access browser networking.
Stop & reset clears variables, not cells. Execution is limited to 30 seconds per cell; runtime loading to 90 seconds.
Individual code cells share variables in execution order. Run all clears variables and runs top to bottom, stopping on the first error. Resetting or leaving this page clears runtime state; saved source cells remain.
Export creates a Python file with # %% cell separators; importing it restores the cells. This is a code-cell notebook, not full .ipynb file support. For plots, assign or update a JSON-compatible plot dictionary as the starter does.