Research Fellow in the Department of Statistics at the University of Warwick, working with Gareth Roberts under the ProbAI Hub
Ciao! I am Nicola Branchini, a Research Fellow in the Department of Statistics at the University of Warwick, working with Gareth Roberts under the ProbAI Hub. Sometimes I blog as well here.
Previously, I was a PhD student in Statistics in the School of Mathematics at the University of Edinburgh, advised by Víctor Elvira, and an ELLIS PhD student co-advised by Aki Vehtari at Aalto University.
My real interests are broad, spanning computational statistics and statistical/probabilistic machine learning, with a focus on methodology. For my PhD, I have been focussing on developing methodology in Monte Carlo.
A sample of some specific interests:
- Importance sampling ∩ Markov chain Monte Carlo: IS is often viewed as a classical, somewhat “naive” method that struggles with complex problems such as high dimensions. Yet it remains central to applications ranging from Boltzmann generators and LLM training to estimating rare outputs of generative models. More advanced methods, such as Sequential Monte Carlo, are fundamentally based on IS. I remain interested in the mathematical properties of IS estimators: when they can work in high dimensions, which population- and sample-based metrics are appropriate, how they behave with infinite variance or heavy-tailed targets, and how combinations such as MCMC-IS can be understood. Ultimately, MC methods are used wherever an accurate answer matters, and understanding how much an answer can be trusted requires mathematics.
- Monte Carlo ∩ generative models: What is the role of Monte Carlo methods in understanding the properties of generative models, like LLMs, diffusion models, etc.? For instance, we have been working on estimating probabilities of rare outputs in masked diffusion language models.
- …and adjacent ideas: I like continuously learning new concepts from neighbouring fields. There are so many interesting ideas still to explore!
Please do not hesitate to contact me for talking about research.
- My PhD thesis, On self-normalized importance sampling, is now publicly available.
- Glad to announce that we got two workshop papers accepted at NeurIPS. The first is Robust monitoring of changes in sequential Bayesian experimental design, with Sara Pérez-Vieites, to appear in the E-Values: From Statistics to ML workshop. The second is Estimating rare event probabilities in masked diffusion language models with Francesco Vinciguerra (first author), to appear in the AI4GOOD workshop.
- Pleased to announce that our paper on adaptive SNIS via MCMC was rejected (yes, you read it right) by NeurIPS 2026 with superficial feedback! Looking forward to submit to a journal.
- Happy to share that I passed my PhD viva in June! Many thanks to my examiners Art Owen and Grégoire Clarté.
- Happy to be invited for a talk at StaTalk 2026 in Torino.
- Happy to give a contributed talk at the London Meeting on Computational Statistics at UCL.