Some fun news: We're hiring! Lectureship (analogous to Assistant Prof.) in Statistical Science and AI, in the School of Mathematics, University of Bristol. Closing date 13 October 2025; link below! www.bristol.ac.uk/jobs/find/de...

The first talk of the season will be this coming Tuesday (23 September), given by Alexandre Bouchard-Côté from UBC. Alex is a great speaker, so do join if you have the chance! See sites.google.com/view/monte-c... for details, links, and so on.

Returning soon - stay tuned! sites.google.com/view/monte-c...

Perhaps a bit orthogonally to the main point here, I have certainly had the experience of reading something out of { duty / necessity / etc. }, and found it remarkable how this context can amplify all sorts of frustrations about the style, even those which could otherwise be quite minor.

On my way home after a splendid couple of days at this workshop up in Newcastle! Slides are up on the workshop website (sites.google.com/view/probai-...) and videos will follow in due course. Excited for the possibility to host a follow-up!

Quite funny:

Sometimes it feels naive to expect a paper to exist with exactly the title which you need, and sometimes a miracle occurs:

Doing a bit of reading about 'Phase-Type Distributions' for modelling non-negative random variables on N or R_+. They seem to be an interesting family, with a bit of nice flexibility (though still reading to learn what the favoured applications are where it really makes a difference).

Birb of the day

Quite fun: one of the early and important works on self-exciting point processes is authored by Hawkes and Oakes, a pair of names which are clearly distinct in some (but not all!) accents.

Gearing up for this workshop next week, with the finalised schedule attached! For those who are unable to attend in person, but are interested in watching the talks, they will be streamed live on MS Teams. Please do get in touch with me if you'd like to stay informed about the stream.

super cool: www.arxiv.org/abs/2509.00881 'An Elementary Proof of the Hanson-Wright Inequality' - Ingvar Ziemann

An announcement, which might be of some interest: In the period 2022-2024, myself and a number of other postdocs on the "CoSInES" and "Bayes4Health" EPSRC grants were involved in organising a number of internal tutorial workshops, on topics relevant to researchers in computational statistics.

I don't have strong feelings on how to represent autoencoders in particular (though as an aside, this does make me wonder about how to usefully depict PCA), but this did remind me of some of my prior complaints about NN diagrams, and how I don't care much for the 'node-to-node' computation graph.

Not to be ignored! 'Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon' (Lecture Notes) - Justin Salez arxiv.org/abs/2508.21055

Just finished delivering a course on 'Robust and scalable simulation-based inference (SBI)' at Greek Stochastics. This covered an introduction to SBI, open challenges, and some recent contributions from my own group. The slides are now available here: fxbriol.github.io/pdfs/slides-....

In reading research papers, it's somewhat inevitable to occasionally have the wrong mental pronunciation of an author's name. Easily corrected, not a big deal, etc. What I find funny is that for me, the most common source of making such mistakes is to erroneously assume that the author is French.

The registration deadline for this workshop is coming up soon (Sunday, Aug 31) - make sure to register ASAP, and we'll see you in Newcastle before long!

Rebranding as a researcher in (Markov) Kernel Methods.

Pretty cool: the "Fundamental Examples" of independence structures in Non-Commutative Probability.

Proud fan with the merch:

Something pretty cool which I learned recently: Schoenberg's theorem says that if K is a stationary, isotropic, positive-definite kernel, then it necessarily takes the form of (the density of) a Gaussian scale mixture, up to a possible scaling factor.

Really sweet stuff here; makes you wonder whether there are other similar combinatorial tricks that could be used in the same context. "Fast Computation of Leave-One-Out Cross-Validation for k-NN Regression" - Motonobu Kanagawa openreview.net/forum?id=SBE...

Effective captioning:

A bit of an under-developed thought: there are some foundational results in probability which are stated in ways which 1) are very natural from the point of applications or intuition, but in achieving this, 2) somewhat obscure the mathematical naturality of the underlying result.

Very sweet annotations:

I want to advertise some relatively recent work which I really like, and have been fortunate to play a small role in. The paper is titled "A New Proof of Sub-Gaussian Norm Concentration Inequality" (arxiv.org/abs/2503.14347), led by Zishun Liu and Yongxin Chen at Georgia Tech.

A tangential quote (in as much as it's from Diaconis talking about collaboration):

A random old one: "Kernels and Decision Trees" hackmd.io/@sp-monte-ca...

I was reminded of this earlier, and I mention it partially as an incentive for me to maintain it a bit better: I have a blog of sorts (sites.google.com/view/sp-mont...) on a variety of topics (though more-or-less the ones you might expect, if you already know what sort of work I do).

Pretty nice little trove of notes: benchugg.com/research_not...

Something which I occasionally find to be a bit unfortunate in the literature on Bayesian computation is a certain type of conflation which takes place around the Bernstein-von Mises Theorem (BvM), which leads to reasonable conclusions but through slightly spurious justification.

The same notes contain this nice encapsulation of what I think of as being one of the "points" of things like { measurability, adaptedness, etc. }: information flow!

This looks very neat to me: arxiv.org/abs/2508.10782 'Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling' - Galen Reeves

Very fun and excitingly illustrated: arxiv.org/abs/2508.10597 'Crocheting Mathematics' - Hanne Kekkonen

Niche, but: from an optimisation perspective, one of the really nice things about Hilbertian norms is that you can do easy 'maintenance' on sums of the form sum_i w_i || x - a_i ||^2 in a way that is not really feasible for most (all?) other norms. This is a neat flexibility to have in some cases.

A favoured personal blunder illustrating why, even for more theoretical work, one should consider running a simulation from time to time:

Deterministic branching process:

Big fan of this perspective:

Applied Fluid Dynamics:

In terms of computation, two of the best-honed tools are iterative methods and recursive methods. It's well worth taking the time to understand how each become relevant in a specific application domain.

A cute result: • let d be a natural number • let P be a probability measure over R_+ so that v^{-d/2} P(v) is log-concave • define a random variable X by sampling V ~ P, and then sampling X | V ~ 𝒩(0, v⋅𝐈_d) • then the law of X is log-concave!

vowels were in short supply that day, one has to assume

Very cheeky here (I think)!

A fun one: let V > 0 be a random volatility, and then conditional on V, let X_t = B_{Vt}, with B a standard Brownian motion. Describe the Markovian projection of X (with V integrated out) as an Itô SDE.

Sorensen (2012) giving the business to the field of metaheuristics:

Putting up some interesting numbers here!

A glance at the schedule and speaker list, for the interested:

A really nice work. Controlled SMC is a great tool in the right contexts, and it's very satisfying to identify well-suited applications in this way.

A funny point about optimisation algorithms (and their theory, in particular) which is not discussed so often is that there is not a universal relationship between i) convergence of iterates, ii) convergence of function values, and iii) convergence of gradients.