M.Eng. Chengkun Li defends his PhD thesis "Surrogate-based methods for efficient Bayesian posterior computation" on Wednesday the 1st of April 2026 at 13 in the University of Helsinki Main Building, Small Hall (F4050, Fabianinkatu 33, 4th floor). His opponent is Professor Umberto Picchini (Chalmers University of Technology and University of Gothenburg, Sweden) and custos Associate Professor Luigi Acerbi (University of Helsinki). The defence will be held in English.
The thesis of Chengkun Li is a part of research done in the Department of Computer Science and in the Machine and Human Intelligence group at the University of Helsinki. His supervisor has been Associate Professor Luigi Acerbi (University of Helsinki).
Surrogate-based methods for efficient Bayesian posterior computation
Bayesian inference provides a principled framework for quantifying uncertainty in parameter estimation and model selection. Despite advances in algorithms such as Markov chain Monte Carlo (MCMC) and improvements in both software and hardware, applying Bayesian methods to complex models remains computationally demanding, particularly when likelihood evaluations are mildly to very expensive, or noisy, or when inference must be repeated across many observed datasets. This thesis addresses these challenges by developing two classes of surrogate-based methods for efficient Bayesian posterior computation.
The first article included in this thesis presents a software implementation of the variational Bayesian Monte Carlo (VBMC) method, which employs a Gaussian process as a regression surrogate for the log-density function and combines variational inference with Bayesian quadrature to approximate the posterior distribution. The software is extensively tested and facilitates Bayesian inference in scenarios where the total number of feasible likelihood evaluations is typically limited to a few hundred.
The second and third articles develop methodologies for approximating the posterior log-density using alternative regression-based surrogates, namely sparse Gaussian processes and normalizing flows. Sparse Gaussian processes mitigate the cubic computational scaling limitation of standard Gaussian processes. Normalizing flows, on the other hand, are proper flexible probability distributions and enable a direct posterior sampling after regression. We show that both surrogate families can often yield accurate posterior approximations by purely post-processing evaluations obtained from maximum a posteriori (MAP) optimization traces.
Finally, the fourth article introduces an amortized inference workflow based on the conditional normalizing flow surrogate trained on simulated datasets. Unlike regression-based surrogates, which fit log-density evaluations for a single dataset, the amortized surrogate takes an observed dataset as input and directly outputs a posterior approximation. The workflow integrates amortized inference, Pareto-smoothed importance sampling, and MCMC samplers, enabling flexible and reliable posterior computation across many observed datasets. We validate the workflow on a range of benchmark problems and demonstrate its improved computational efficiency while maintaining accuracy.
Availability of the dissertation
An electronic version of the doctoral dissertation will be available in the University of Helsinki open repository Helda at
Printed copies will be available on request from Chengkun Li: