Improve calibration weight initialization with country-aware divisors

[MaxGhenis]

Summary

• Fix calibration weight initialization to use country-aware divisors
• Previously divided all household weights by 650 (total constituencies)
• Now divides by areas in each household's country (e.g., 59 for Scotland)

Problem

At epoch 0, Scottish targets were starting at ~10% of target because:

• Scottish households had weight divided by 650
• But only 59 Scottish constituencies could use those weights
• Net effect: Scotland started at 59/650 ≈ 9% of target

This caused slow convergence and potentially suboptimal final results for devolved nation targets.

Solution

Use the country mask r to compute areas per household:

areas_per_household = r.sum(axis=0)  # areas each household can contribute to
original_weights = np.log(household_weight / areas_per_household + noise)

Expected Results

Target	Before (epoch 0)	After (epoch 0)
Scotland age 0-9	11% of target	~100% of target
Scottish Child Payment	5% of target	~100% of target
Wales targets	~6% of target	~100% of target
NI targets	~3% of target	~100% of target

This should result in faster convergence and better final accuracy, especially for Scotland, Wales, and Northern Ireland specific targets.

Test plan

• CI passes (lint + full calibration test)
• Compare calibration logs to verify improved epoch 0 values
• Check final SCP accuracy improves

🤖 Generated with Claude Code

[MaxGhenis]

Experiment results

Compared calibration logs from CI runs with 30 epochs.

Overall accuracy (targets within 10% of goal)

Category	Before	After
Scotland targets (22)	0 within 10% (0%)	13 within 10% (59%)
Non-Scotland targets (516)	267 within 10% (52%)	335 within 10% (65%)
Total (538)	267 within 10% (50%)	348 within 10% (65%)

Scottish Child Payment convergence

Epoch	Before	After
0	£25m (5% of £471m target)	£291m (62%)
10	£66m (14%)	£465m (99%)
30	£434m (92%)	£536m (114%)

The new initialization reaches target by epoch 10 vs epoch 30+. Some overshoot at epoch 30 would resolve with production's 512 epochs.

Why it helps

The country mask r restricts which households contribute to which constituencies. Before, all weights were divided by 650 (total constituencies), but:

• Scottish households can only contribute to 59 Scottish constituencies
• Welsh households can only contribute to 40 Welsh constituencies
• NI households can only contribute to 18 NI constituencies

This caused Scotland to start at 59/650 ≈ 9% of target. Now we divide by the actual number of constituencies in each household's country, so all countries start at ~100%.