A Bayesian Copula Regression Architecture and Workflow
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Abstract: Copula functions let us explicitly handle covariance between the components of a joint product, for example frequency-severity decompositions of expected loss-cost in insurance.
A traditional non-copula joint model (or even worse, sequential separate models) that ignore covariance typically result in a poor fit & predictions, especially in a low-data domain. The required copula transformations are conceptually relatively straightforward, but implementations in the max-likelihood world tend to be quite opaque and full of assumptions and statistical corrections.
Here I’ll describe and demonstrate a flexible, intuitive and performant principled Bayesian architecture for copula regression modeling, using a Bayesian workflow for full model explainability and testing. This is all in the modern and powerful `pymc` & `arviz` ecosystem.
Bio: Jonathan is a Bayesian data scientist and senior consultant with 15+ years varied experience across financial services, tech startups and venture capital in UK, USA, and EMEA. He focusses on commercial & speciality insurance where he delivers bespoke statistical models, designs holistic solutions and advises teams in pricing, performance management and business optimization. He spends too much time daydreaming about his next diving trip.
