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# Statistical Science Seminars

A seminar series covering a broad range of applied and methodological topics in Statistical Science.

#### Talks take place in hybrid format.

Usual time: Thursdays 14:00-15:00 (to be followed by Departmental Tea in the common room).

Location: In Term 2, talks will usually take place in South Wing 9 (Garwood Lecture Theatre) and Zoom. Please use the contact information below to join the mailing list, so you will receive location updates and links to the talks.

Contact info: emma dot simpson at ucl dot ac dot uk

#### Recent talks

Please subscribe to our Youtube channel, to view some recent talks from the series

### Programme for 2022/23

6 October 2022: Alan Rapoport (Utrecht University) - Properties of the gradient squared of the Gaussian free field

The discrete Gaussian free field (DGFF) is a famous model in statistical mechanics, and it is an example of a Gaussian Markov random field in the statistics realm. In this work we study the scaling limit of a non-linear transformation of its gradient. More precisely, we study the (centered) square of the norm of the gradient DGFF at every point of a square lattice. One of the reasons for studying this object stems from the so-called Abelian sandpile, a model which is an example of a dynamical system displaying self-organized criticality. Surprisingly, our real-valued model is connected to the height-one field in the sandpile, which only assumes the values 0 or 1. With different methods we are able to obtain the same scaling limits: on the one hand, we show an identity relating the cumulants of our model to those of the height-one field. Besides, we show our field converges to white noise in the limit, as it happens for the height-one field. Joint work with Alessandra Cipriani (UCL), Rajat Subhra Hazra (Leiden) and Wioletta Ruszel (Utrecht).

13 October 2022: Julia Gog (University of Cambridge) - From maths to COVID-19

I want to introduce some of the things I have learnt from COVID-19: not so much the nitty-gritty of the epidemiological models, but the ways of working that were necessitated and enabled by this emergency. Themes will include (i) contributing to government scientific advice; (ii) large collaborations; (iii) deep uncertainty and consensus and (iv) what happens when the widest public suddenly has huge interest in your niche field. I will probably talk about an epidemic model or two anyway.

20 October 2022: Sam Tickle (University of Bristol) - Detecting national, regional and global changes in terror activity

Changepoint detection has received considerable attention in recent years, with a myriad of methods arising to address data-intensive situations. In particular, there now exist techniques for streaming data; high-dimensional settings; and instances in which a parametric model cannot be known in advance. However, there are relatively few contributions which attempt to address all three of these problems simultaneously. We'll discuss these, alongside a new such method called OMEN; we will talk about the theoretical and empirical properties of OMEN as compared with a suite of standard offline change detectors, before examining the method's performance on the Global Terrorism Database (GTD). The GTD, copyrighted to the University of Maryland, and maintained by the National Consortium of the Study of Terrorism and Responses to Terrorism (START), catalogues terror activity from 1970 to the present. We will use this resource to pass comment on moments in the past fifty years in which the probability of terror activity appeared to shift abruptly, using OMEN to attempt to distinguish between national, regional and global effects.

27 October 2022: James Smith (University of Warwick) - Big data, dynamic Bayesian decision support and the pursuit of criminals

Vast, if patchy, streaming data sets are now available to police serious crime. These leave a shadow of tell tales signs of sequences of tasks criminals must enact before they can perpetrate their plot. Dynamic Bayesian graphical models are proving to be one of the most useful inferential frameworks to support the real time detection of complex crimes. They can embed, in an auditable and formal way, the expert judgements of criminologists and police about the way complex crimes might be committed. These judgements can then guide us in identifying functions of diverse sources of data streams that promise to be the most informative about the existence and progress of a plot. By monitoring these real time signals, police are then able to infer the strength of evidence for a hypothesis that a crime is about to be perpetrated and also about the stage of preparation the plot has reached.
These models are now extant for a number of applications. In this talk I will focus on just two: a Bayesian model of plots to violently attack members of the general public and a model to monitor factories for the possible illicit manufacture of drugs.

3 November 2022: Alice Corbella (University of Warwick) - Automatic super-efficiency of the Zig-Zag sampler: a new tool for the analysis of big data

The Zig Zag sampler and other MCMC schemes based on the simulation of Piecewise Deterministic Markov Processes (PDMPs) have been attracting increasing interest mainly due to their appealing super-efficiency property. An algorithm is said to be super-efficient when it draws one independent sample from a posterior target distribution at a lesser cost than evaluating the likelihood of all the N data points. This property is based on the technique of subsampling, whereby only one or a few of the N components of the likelihood are needed for the simulation of each step of the process, whilst still retaining convergence to the correct target distribution. Until recently, super-efficiency has been implemented only in few simple cases. In this talk I will start by introducing PDMPs, the Zig Zag algorithm and its practical implementation; I will then illustrate a way to obtain super efficiency automatically, given any differentiable posterior distribution of interest.  I will present one example of the efficient analysis of big data, and I will describe key tuning decisions that are involved in the implementation of an automatic super-efficient PDMP sampler.

10 November 2022: Kolyan Ray (Imperial College London) - Variational Bayes for high-dimensional linear regression with sparse priors

A core problem in Bayesian statistics is approximating difficult to compute posterior distributions. In variational Bayes (VB), a method from machine learning, one approximates the posterior through optimization, which is typically faster than Markov chain Monte Carlo. We study a mean-field (i.e. factorizable) VB approximation to Bayesian model selection priors, including the popular spike-and-slab prior, in sparse high-dimensional linear regression. We establish convergence rates for this VB approach, studying conditions under which it provides good estimation. We also discuss some computational issues and study the empirical performance of the algorithm.

17 November 2022: Ayush Bharti (Aalto University) - A general method for calibrating stochastic radio channel models with kernels

Calibrating stochastic radio channel models to new measurement data is challenging when the likelihood function is intractable. The standard approach to this problem involves sophisticated algorithms for extraction and clustering of multipath components, following which point estimates of the model parameters can be obtained using specialized estimators. We propose a likelihood-free calibration method using approximate Bayesian computation. The method is based on the maximum mean discrepancy, which is a notion of distance between probability distributions. Our method not only bypasses the need to implement any high-resolution or clustering algorithm but is also automatic in that it does not require any additional input or manual preprocessing from the user. It also has the advantage of returning an entire posterior distribution on the value of the parameters, rather than a simple point estimate. We evaluate the performance of the proposed method by fitting two different stochastic channel models, namely the Saleh–Valenzuela model and the propagation graph model, to both simulated and measured data.

24 November 2022: Takemasa Miyoshi (RIKEN) - Big Data Assimilation revolutionizing numerical weather prediction using Fugaku

At RIKEN, we have been exploring a fusion of big data and big computation in numerical weather prediction (NWP), and now with AI and machine learning (ML). Our group in RIKEN has been pushing the limits of NWP through two orders of magnitude bigger computations using the previous Japan’s flagship “K computer”. The efforts include 100-m mesh, 30-second update “Big Data Assimilation” (BDA) fully exploiting the big data from a novel Phased Array Weather Radar. With the new Fugaku, we achieved a real-time BDA application to predict sudden downpours up to 30 minutes in advance during Tokyo Olympics and Paralympics. Moreover, Fugaku is designed to be efficient for both double-precision big simulations and reduced-precision ML applications, aiming to play a pivotal role in creating super-smart “Society 5.0”. We have been exploring ideas for improving the predicting capabilities by fusing BDA and AI. The data produced by NWP models become bigger and moving the data to other computers for ML or even simply saving them may not be feasible. A next-generation computer like Fugaku may bring a breakthrough toward creating a new methodology of fusing data-driven (inductive) and process-driven (deductive) approaches in meteorology. This presentation will introduce the most recent results from BDA experiments, followed by perspectives toward DA-AI fusion and expanding new applications beyond meteorology.

1 December 2022: Ruda Zhang (University of Houston) - Gaussian process prediction of subspaces, covariance matrices, and phase angles

Gaussian process (GP) is a widely used tool for building statistical surrogates of computer models, where the response is usually one or a few quantities of interest. In this talk I present ongoing development of GP models for predicting complex objects including subspaces, positive semi-definite (PSD) matrices, and angles. These objects live on nonlinear manifolds instead of Euclidean spaces. Complex as they seem, Gaussian distribution is well positioned to capture them: it naturally encodes PSD matrices in its covariance; in singular forms, its support is a linear subspace; and by extension it can also models angles, which are equivalent to the special case of origin-passing lines in the plane. Novelties in these GP models are in the construction of likelihood and the representation of data. These models cover both interpolation and regression types of prediction. I will discuss their applications to computational models in engineering and physics, covering reduced order modeling, uncertainty quantification, and stochastic simulation. They also find use in infrastructure monitoring using satellite data.

8 December 2022: Neil Davies (University College London) - Estimating causal effects on healthcare costs using genetics

Health economic evaluations aim to estimate the costs and benefits of interventions to treat ill-health and disease. A key limitation of most studies to date is that the costs of disease are extremely challenging to estimate comprehensively. The vast majority of studies have attempted to use a limited range of conditions to estimate the burden of disease and healthcare costs. As a result, these studies are likely to substantially underestimate the costs of disease, as only a handful of conditions are explicitly measured. Furthermore, it is generally impossible using observational data to reliably estimate the causal effects of different risk factors (e.g. BMI, blood pressure, smoking, drinking) on healthcare costs. In this seminar, I will describe how an approach known as Mendelian randomization can be used to overcome these limitations. Mendelian randomization is the use of genetic variants as instrumental variables, which has been widely applied in genetic epidemiology, and has applications in health economics. I will conclude with outlining the next steps for this programme of research.

•    Harrison, S. et al. Long-term cost-effectiveness of interventions for obesity: A mendelian randomisation study. PLoS Med 18, e1003725 (2021).
•    Dixon, P., Hollingworth, W., Harrison, S., Davies, N. M. & Davey Smith, G. Mendelian Randomization analysis of the causal effect of adiposity on hospital costs. Journal of Health Economics 70, 102300 (2020).
•    Dixon, P., Davey Smith, G., von Hinke, S., Davies, N. M. & Hollingworth, W. Estimating Marginal Healthcare Costs Using Genetic Variants as Instrumental Variables: Mendelian Randomization in Economic Evaluation. PharmacoEconomics (2016) doi:10.1007/s40273-016-0432-x.

12 January 2023: Alessandra Luati (Imperial College London / University of Bologna) - On optimality of score-driven models

Score-driven models have been recently introduced to specify time varying parameters of conditional densities, as a function of the score of the associated loglikelihood. According to which conditional density is assumed, the score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Although score-driven models have been empirically and theoretically validated multiple times, also in the case of a misspecified conditional density, a rigorous motivation for the use of the score in the updating equation has not been fully formalised.
This paper shows that score-driven updates are optimal in that, at each time step, they reduce the Euclidean distance between the expected updated parameter and the pseudo-true parameter. Optimality is intended as the property of an estimator to arise as the solution of an optimisation problem. As a matter of fact, optimality in conditional expected variation can be naturally viewed as a generalisation of the monotonicity property of the stochastic gradient descent scheme.
Several examples illustrate how the results derived in the paper apply to specific models under different, easy to check, assumptions, and provide a formal method to select the scaling coefficient that multiplies the score in the updating equation.

(joint with Paolo Gorgi, Vrije Universiteit Amsterdam, and Sacha Lauria, University of Bologna)

19 January 2023: Badr-Eddine Chérief-Abdellatif (CNRS) - Bayes meets Bernstein in Meta-Learning

Bernstein assumption is a crucial assumption under which PAC-Bayes methods can learn $n$ observations at the fast rate of convergence $O(d_\pi/n)$, as opposed to the slow rate $O(\sqrt{d_\pi/n})$ without it, where $d_\pi$ is a parameter which depends on the prior $\pi$. Coming to the process of learning $T$ tasks each composed of $n$ observations, meta learning takes advantage of the commonality of the $T$ tasks to learn more efficiently. In this paper, we show that Bernstein assumption is always satisfied at the meta level (between the $T$ tasks) when learning the prior and therefore, that PAC-Bayes techniques achieve the fast rate of convergence $O(\inf_\pi d_\pi/n + 1/T)$ if Bernstein assumption is satisfied at the observation level (between the $n$ observations), and the rate $O(\inf_\pi \sqrt{d_\pi/n} + 1/T)$ otherwise, improving upon the existing $O(\inf_\pi \sqrt{d_\pi/n} + \sqrt{1/T})$ rate. We apply this result to the finite, Gaussian and mixtures of Gaussian cases, and show that under some regularity condition on the distribution of the tasks, the very fast rate $O(1/T)$ is achieved in practice.

26 January 2023: Maud Lemercier (University of Oxford) - Training continuous space-time generative models using signature kernel score minimization

In this talk, I will present a new approach for modelling systems that vary both in space and in time using Neural SPDEs, a variant of Neural SDEs, a class of generative adversarial networks that are particularly well-suited for modelling temporal dynamics. The Neural SPDE model is trained using scoring rule minimization, a recently introduced adversarial-free technique for optimizing generative models. In particular, I will discuss how to construct scoring rules for spatio-temporal data, by assembling tools from the literature on kernel functions. The effectiveness of the proposed approach will be assessed through numerical experiments using Limit Order Books data, high-frequency trading data from financial markets.

2 February 2023: Paula Moraga (KAUST) - Bayesian spatial modeling of misaligned data using INLA and SPDE

Spatially misaligned data are becoming increasingly common due to advances in data collection and management. We present a Bayesian geostatistical model for the combination of data obtained at different spatial resolutions. The model assumes that underlying all observations, there is a spatially continuous variable that can be modeled using a Gaussian random field process. The model is fitted using the integrated nested Laplace approximation (INLA) and the stochastic partial differential equation (SPDE) approaches. In order to allow the combination of spatially misaligned data, a new SPDE projection matrix for mapping the Gaussian Markov random field from the observations to the triangulation nodes is proposed. We show the performance of the new approach by means of simulation and an application of PM2.5 prediction in USA. The approach presented provides a useful tool in a wide range of situations where information at different spatial scales needs to be combined.

16 February 2023: Giorgos Vasdekis (University College London)
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23 February 2023: Myrto Limnios (University of Copenhagen)

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2 March 2023: Aldo Pacchiano (Microsoft Research)

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9 March 2023: Alex Diaz (University College London)

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16 March 2023: Oya Kalaycioglu (University College London / Bolu Abant Izzet Baysal University)

Title TBC

23 March 2023: Edwin Fong (Novonordisk)

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20 April 2023: Sofía Villar (MRC Biostatistics Unit, University of Cambridge)

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4 May 2023: Elizabeth Stuart (Johns Hopkins University)

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18 May 2023: Daniela Castro-Camilo (University of Glasgow)

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