Add a Student-t likelihood for robust regression

[thomaspinder]

Category: literature · Severity: medium
Location: gpjax/likelihoods.py (module)

Problem

The robust Student-t likelihood — standard in GPflow/GPyTorch and analysed by Jylänki, Vanhatalo & Vehtari (2011, JMLR) — is absent (npd.StudentT appears only as a Matérn spectral density, kernels/stationary/utils.py:38). It is a natural, low-cost addition given the existing quadrature machinery.

Recommendation

Add a StudentT likelihood as a ~20-line class using npd.StudentT as the link and the existing GHQuadratureIntegrator(20) for the expected log-likelihood.

_{Filed from the 2026-07-02 GPJax codebase audit (medium tier). Companion spec for the high-severity items: plans/2026-07-02-audit-high-severity-remediation-design.md.}