two small experiments in Bayesian prediction
Bayes posteriorPredictively oriented posterior
Data are drawn from a mixture of Gaussians and are fitted with a single, misspecified N(θ, 0.5²). The predictive distribution after each new datum is observed is shown in orange, with its history in grey. The Bayes posterior (left) identifies the single parameter value best-suited to the data; the predictively oriented posterior (right) concentrates around the predictively-optimal mixture.
→ Predictively oriented posteriors · Markov chain Monte Carlo for predictively oriented posteriors
I am a fourth-year doctoral researcher in the Department of Statistical Science at University College London, supervised by Jeremias Knoblauch and Edwin Fong. Before this, I was a research assistant at Aalto University with Aki Vehtari.
My research develops theory and methodology for Bayesian prediction, model selection, and prior elicitation.
Theme 01
By making parameter inference a function of predictive performance, PrO posteriors make provably more accurate predictions than the Bayes posterior. They only concentrate around a point if it recovers the data-generating distribution exactly, and when the model is wrong they stabilise towards the predictively-optimal mixing distribution.
Theme 02
We are sometimes interested in identifying the model whose out-of-sample predictive performance is best, either in the hope of generalising to future unseen data or recovering an important subset of parameters. In finite data regimes, however, there can be significant uncertainty in differentiating between models of similar performance.
An efficient and asymptotically unbiased computational approach for predictively oriented posteriors.
A statistical principle combining parameter inference and density estimation by expressing parameter uncertainty as a function of predictive ability.
A joint prior over the auto-regressive components of Bayesian time-series models and their induced predictive performance.
Formal evidence for the folklore that, for predictive accuracy, parameter uncertainty is second-order relative to data and model uncertainty.
A survey of projection predictive inference, with a safe, efficient and modular workflow for prediction-oriented model selection.
* Equal contribution
Kullback–Leibler projections for Bayesian model selection
Author
[docs]Wasserstein gradient flows for PrO posteriors
Contributor
[code]Approximate LOO-CV and Pareto smoothed importance sampling
Contributor
[docs]Projection predictive feature selection
Contributor
[docs]Bayesian model-building interface in Python
Contributor
[docs]