Citation notice #189 · 2026-07-11 03:18:48.592141+00:00

Logistic Credibility with Temporal Decay: Extending B\"uhlmann--Straub for Commercial Lines

cites Vladimir Vovk, Alexander Gammerman, and Glenn Shafer.Algorithmic Learning in a Ran- dom World, which carries a correction notice dated 2016-10-17. One-hop deterministic notice: the citation edge exists in the Pith bibliography graph; no model judged whether the citation was load-bearing.

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01Evidence

Raw extraction · bibliography line · bibliography index 10

doi: 10.1007/s11222-016-9696-4. 50 §A — Nesting Proof and Rolling Bühlmann–Straub Exposition MLE Consistency Under the B-S Data-Generating Process Proposition (MLE recovery under a B-S data-generating process).Suppose the data are generated by the B-S mechanism with true structural parameterK0: that is, the true credibility weight isZi =wi/(wi+K0), the complement is flat, and there is no temporal decay. Then the unconstrained logistic MLE is consistent for the corresponding parameter values: ˆaZ p − →−logK0, ˆbZ p − →1 (on the unstandardisedlogwi scale) as the number of accountsN→∞. Proof sketch.For any observation with true expected rater0 = E[θi|¯fi,wi], Poisson devianceℓ(r) =r−Clogr satisfies E[ℓ(r)] =r−r0 logr +const, which is uniquely minimised atr =r0 (proper scoring rule property). Under the B-S data-generating process (DGP), the Bayesian posterior mean isr0 = (1−Z∗ i )µ+Z∗ i ¯fi with Z∗ i = wi/(wi +K0). For the logistic model to achieveˆri = r0 for every account simultaneously (i.e. for every value ofwi) requiresσ(aZ +bZ logwi) =wi/(wi +K0)to hold identically inwi. Using the identity σ(log(x/K)) = x/(x +K), this is satisfied if and only ifaZ =−logK0 and bZ =

02Event

Type

Correction

Source

Crossref

Original DOI

10.1007/s11222-016-9696-4

Notice DOI

10.1007/s11222-016-9709-3

Date

2016-10-17

Title

Erratum to: Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

Reasons

['Correction']

Work

Vladimir Vovk, Alexander Gammerman, and Glenn Shafer.Algorithmic Learning in a Ran- dom World (2005)

Schema constants (for re-runners): correction · crossref

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