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Part 14: When to use which method — the decision framework

Part 14: When to use which method — the decision framework

This framework assumes you have already decided that naive observed rates are not appropriate. Some form of partial pooling is needed. The question is which form.

Use Bühlmann-Straub when:

  • One grouping variable. Schemes, vehicle classes, or postcode districts in isolation. B-S is a one-dimensional method; it handles one grouping at a time.
  • Many groups. At least 5, ideally 20+. With fewer groups, the estimate of between-group variance (a_hat) is unreliable. Five groups gives a very noisy a_hat, and a noisy a_hat makes K unreliable.
  • Speed matters. B-S runs in milliseconds. PyMC takes minutes. For daily monitoring, real-time pricing, or exploratory analysis, B-S wins.
  • Regulatory transparency. Bühlmann-Straub has a 55-year track record in actuarial methodology documentation. The FCA Consumer Duty pack can cite Bühlmann & Straub (1970) and explain Z without specialist software. A documented, auditable methodology is substantially stronger than an undocumented one, even if the undocumented approach is technically superior.
  • Downstream of a main model. If you are applying credibility to residuals from a GLM or GBM, B-S is the natural tool.

Use full Bayesian hierarchical models when:

  • Multiple crossed grouping variables simultaneously. Area AND vehicle group AND NCD band, all with partial pooling. B-S handles one dimension at a time; PyMC handles arbitrary combinations.
  • Few groups. With fewer than 10 affinity schemes, the uncertainty in the structural parameters is material. Bayesian propagates it correctly.
  • Credible intervals are required. B-S gives point estimates of Z and the credibility estimate. Bayesian gives the full posterior distribution — 90% credible intervals, probability that a rate exceeds a threshold, etc.
  • Two-level geographic hierarchy. Districts nest within areas. The nested model in Exercise 2 handles this correctly.
  • Proper Poisson or Gamma likelihood. B-S is derived from a Normal observation model. Full Bayesian uses the correct likelihood for the data type.

The two-stage approach

For most UK personal lines pricing projects, the correct architecture is:

  1. Stage 1: CatBoost or GLM on the full dataset for main effects — driver age, vehicle group, NCD, area bands
  2. Stage 2: Bühlmann-Straub on district-level O/E residuals from Stage 1, with log_transform=True

This is not a shortcut. It is the principled decomposition: the main model handles the rating factors the GLM/GBM can identify from large samples; credibility handles the district-level departures that require pooling.

Reserve full Bayesian for cases where Stage 2 is insufficient — multiple crossed groupings, very few groups, or explicit uncertainty quantification requirements.