Sam Power

On the other hand, I feel vindicated w.r.t. a past confusion, whereby an Adaptive MCMC paper was more-or-less celebrating replacing "adaptation by stochastic approximation" with "adaptation by reinforcement learning". Even then, my heart told me that no replacement had really occurred.

It certainly makes "highly-offline" learning seem rather quaint by comparison.

Reassuring to read this (www.argmin.net/p/defining-r...) presentation, since I had confused myself a bit in the past w.r.t. i) just how general the attached is (in principle), and ii) observing that "what people mean when they say they're doing RL" has (historically anyways) been rather narrower.

(There are indeed some solutions which are o(N), though not necessarily super simple ones; I am yet to see anything which is O(1). In any case, the answer depends a bit on how well you know Q.)

A fun problem, which I came across recently:

Suppose that you can generate random variates X ~ P by rejection sampling from some Q.

For a given integer N, let X_(N) denote the sample maximum of N independent draws from P.

Can you simulate realisations of X_(N) at a cost of o(N)? Or even O(1)?

Quite fun

It's a fair point! Will keep it in mind.

another day volunteering at the topology museum.

This project was initiated during our residence at a 2024 INI programme on "Stochastic Systems for Anomalous Diffusion" (www.newton.ac.uk/event/ssd/), wherein many presented works treated specific approaches to the 'robustness' issue. It seemed an opportune time to take stock of things.

With Giorgos Vasdekis, we have written a manuscript - arxiv.org/abs/2511.21563 - which surveys the state of affairs within this literature, outlining signals for anticipating non-robustness, principles for improving robustness, and examples of contemporary methods which confront these issues.

In response to this, there have been a range of proposed MCMC strategies which aim to

i) perform acceptably when these conditions hold, but
ii) degrade gracefully when these conditions start to break down,

collectively giving rise to a burgeoning literature on 'robust MCMC'.

Usual MCMC algorithms are typically guaranteed to work well when used to sample from target distributions for which

i) mass is reasonably well-concentrated in the centre of the state space, and
ii) the log-density is smooth and of moderate growth.

Outside of this setting, things can go poorly.

I'll ask around!

On behalf of some friends, let me quickly advertise an event taking place in London, January 12-13 2026 (sites.google.com/view/lpd-tnn), with an overall focus on 'Geometric methods in probability'. Registration is free but required, and closes on December 1 (i.e. next Monday) - exciting stuff!

humans in the 1960s / potentially slightly earlier

(The pictured set is conjecturally optimal for the problem described)

I mean, lol

I'm also slightly reminded of the Beta function, but without any particular conclusions for now.

I like it! It hadn't occurred to me that it is somehow 'really' a product of two (rather than three) factors, but I think that I'm on board. A fan of falling / rising factorials, in any case.

cf. bsky.app/profile/scie...

Tour coming to an end, as I settle in for 5 hours of train journey! Had lots of fun talking about Random Walk Metropolis, Gradient Flows, and Skill Rating in Sports (among other chats). Slides from all talks are saved at github.com/sampower88/t....

🍉

splendid

Super gripping (and fun!) lectures here:
youtu.be/OHDYdmuLMW0?...
"Fourier Analysis & Beyond I" - Mini-course
- Stefan Steinerberger

great stuff, right up my alley:

arxiv.org/abs/2511.11497
'A Recursive Theory of Variational State Estimation: The Dynamic Programming Approach'
- Filip Tronarp

Inference in Stochastic Epidemic Models via Multinomial Approximations We introduce a new method for inference in stochastic epidemic models which uses recursive multinomial approximations to integrate over unobserved variables and thus circumvent likelihood intractabili...

I think this - arxiv.org/abs/2006.13700 - is a good starting point, IIRC.

Very nice! Some of the latter part seemed natural to think of in terms of Markov kernels / channels. A friend had some recent work on epidemiological models where this conjugacy between Poisson / Multinomial and 'colouring' channels was quite computationally useful.

Prompted by glancing at arxiv.org/abs/2511.14200.

One application of this would be to compare the features of different biased random walks, since the convex ordering is preserved under independent summation, and allows for the control of { variance, large deviations, etc. }.

However, this changes if you allow for a dilation factor. In particular, there is always some σ = σ(p, q) such that Z(p) is dominated by σ⋅Z(q). After a bit of book-keeping and changing variables for convenience, one can deduce the attached formula.