arXiv subjects

Axel Gandy

Publications and source records attributed to Axel Gandy.

At least 19 recordsLinked to original sources

arXiv2026

Kernel Tests of Equivalence

We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null hypothesis may simply be a result of lack of test power, also known as the Type-II error. This motivates \emph{equivalence testing}, which aims to assess the \emph{absence} of a statistically meaningful effect under controlled error rates. However, existing equivalence tests are either limited to parametric distributions or focus only on specific moments rather than the full distribution. We address these limitations using two kernel-based statistical discrepancies: the \emph{kernel Stein discrepancy} and the \emph{Maximum Mean Discrepancy}. The null hypothesis of our proposed tests assumes the candidate distribution differs from the nominal distribution by at least a pre-defined margin, which is measured by these discrepancies. We propose two approaches for computing the critical values of the tests, one using an asymptotic normality approximation, and another based on bootstrapping. Numerical experiments are conducted to assess the performance of these tests.

stat.ML↗

arXiv2026

Focused Information Criteria for Semiparametric Linear Hazard Regression

The semiparametric linear hazard regression model introduced by McKeague and Sasieni (1994) is an extension of the linear hazard regression model developed by Aalen (1980). Methods of model selection for this type of model are still underdeveloped. In the process of fitting a semiparametric linear hazard regression model one usually starts with a given set of covariates. For each covariate one has at least the following three choices: allow it to have time-varying effect; allow it to have constant effect over time; or exclude it from the model. In this paper we discuss focused information criteria (FIC) to help with this choice. In the spirit of Claeskens and Hjort (2003, 2008), `focused' means that one is interested in one specific quantity, e.g. the probability of survival of a patient with a certain set of covariates up to a given time. The FIC involves estimating the mean squared error of the estimator of the quantity one is interested in, and the chosen model is the one minimising this estimated mean squared error. The focused model selection machinery is extended to allow for weighted versions, leading to a suitable wFIC method that aims at finding models that lead to good estimates of a given list of parameters, such as survival probabilities for a subset of patients or for a specified region of covariate vectors. In addition to developing model selection criteria, methods associated with averaging across the best models are also discussed. We illustrate these methods of model selection in a real data situation.

stat.ME↗

arXiv2025

Statistical hypothesis testing for differences between layers in dynamic multiplex networks

With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their connectivity. In this work, we introduce a hypothesis testing framework, under a latent space network model, for assessing whether the layers share a common latent representation. The method we propose extends previous literature related to the problem of pairwise testing for random graphs and enables global testing of differences between layers in multiplex graphs. While we introduce the method as a test for differences between layers, it can easily be adapted to test for differences between time points. We construct a test statistic based on a spectral embedding of an unfolded representation of the graph adjacency matrices and demonstrate its ability to detect differences across layers in the asymptotic regime where the number of nodes in each graph tends to infinity. The finite-sample properties of the test are empirically demonstrated by assessing its performance on both simulated data and a biological dataset describing the neural activity of larval Drosophila.

stat.ME↗

arXiv2024

Doubly unfolded adjacency spectral embedding of dynamic multiplex graphs

Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot product graph (DMPRDPG), which uses an inner product between layer-specific and time-specific latent representations of the nodes to obtain edge probabilities. We further introduce a computationally efficient spectral embedding method for estimation of DMPRDPG parameters, called doubly unfolded adjacency spectral embedding (DUASE). The DUASE estimates are proved to be both consistent and asymptotically normally distributed. A key strength of our method is the encoding of time-specific node representations and layer-specific effects in separate latent spaces, which allows the model to capture complex behaviors while maintaining relatively low dimensionality. The embedding method we propose can also be efficiently used for subsequent inference tasks. In particular, we highlight the use of the ISOMAP algorithm in conjunction with DUASE as a way to efficiently capture trends and global changepoints within a network, and the use of DUASE for graph clustering. Applications on real-world networks describing geopolitical interactions between countries and financial news reporting demonstrate practical uses of our method.

stat.ME↗

arXiv2023

Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

stat.ML↗

arXiv2023

A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the non-degenerate Gaussian limit to the degenerate limit, regardless of its degeneracy and depending only on a moment ratio. A surprising consequence is that a non-degenerate U-statistic in high dimensions can have a non-Gaussian limit with a larger variance and asymmetric distribution. Our bounds are valid for any finite $n$ and $d$, independent of individual eigenvalues of the underlying function, and dimension-independent under a mild assumption. As an application, we apply our theory to two popular kernel-based distribution tests, MMD and KSD, whose high-dimensional performance has been challenging to study. In a simple empirical setting, our results correctly predict how the test power at a fixed threshold scales with $d$ and the bandwidth.

math.ST↗

arXiv2022

Reducing climate risk in energy system planning: a posteriori time series aggregation for models with storage

The growth in variable renewables such as solar and wind is increasing the impact of climate uncertainty in energy system planning. Addressing this ideally requires high-resolution time series spanning at least a few decades. However, solving capacity expansion planning models across such datasets often requires too much computing time or memory. To reduce computational cost, users often employ time series aggregation to compress demand and weather time series into a smaller number of time steps. Methods are usually a priori, employing information about the input time series only. Recent studies highlight the limitations of this approach, since reducing statistical error metrics on input time series does not in general lead to more accurate model outputs. Furthermore, many aggregation schemes are unsuitable for models with storage since they distort chronology. In this paper, we introduce a posteriori time series aggregation schemes for models with storage. Our methods adapt to the underlying energy system model; aggregation may differ in systems with different technologies or topologies even with the same time series inputs. Furthermore, they preserve chronology and hence allow modelling of storage technologies. We investigate a number of approaches. We find that a posteriori methods can perform better than a priori ones, primarily through a systematic identification and preservation of relevant extreme events. We hope that these tools render long demand and weather time series more manageable in capacity expansion planning studies. We make our models, data, and code publicly available.

stat.AP↗

arXiv2022

Joint Entropy Search for Multi-objective Bayesian Optimization

Many real-world problems can be phrased as a multi-objective optimization problem, where the goal is to identify the best set of compromises between the competing objectives. Multi-objective Bayesian optimization (BO) is a sample efficient strategy that can be deployed to solve these vector-valued optimization problems where access is limited to a number of noisy objective function evaluations. In this paper, we propose a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and outputs. We present several analytical approximations to the JES acquisition function and also introduce an extension to the batch setting. We showcase the effectiveness of this new approach on a range of synthetic and real-world problems in terms of the hypervolume and its weighted variants.

cs.LG↗

arXiv2022

Age-stratified epidemic model using a latent marked Hawkes process

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. [arXiv:2208.07340] considering a finite population stratified by age bands. We model the actual unobserved infections using a latent marked Hawkes process and the reported aggregated infections as random quantities driven by the underlying Hawkes process. We apply a Kernel Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous reproduction number for each age group and forecast the epidemic's future trajectory in the near future; considering the age bands and the population size does not increase the computational effort. We demonstrate the performance of the proposed inference algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK. We illustrate that taking into account the individual heterogeneity in age decreases the uncertainty of estimates and provides a real-time measurement of interventions and behavioural changes.

stat.ME↗

arXiv2022

Can a latent Hawkes process be used for epidemiological modelling?

Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for modelling the infections. Unlike other models, we model the reported cases via a probability distribution driven by the underlying Hawkes process. Modelling the infections via a Hawkes process allows us to estimate by whom an infected individual was infected. We propose a Kernel Density Particle Filter (KDPF) for inference of both latent cases and reproduction number and for predicting the new cases in the near future. The computational effort is proportional to the number of infections making it possible to use particle filter type algorithms, such as the KDPF. We demonstrate the performance of the proposed algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK, and benchmark our model to alternative approaches.

stat.ME↗

arXiv2021

Epidemia: An R Package for Semi-Mechanistic Bayesian Modelling of Infectious Diseases using Point Processes

This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an approach often termed as semi-mechanistic. Infections are propagated over time using renewal equations. This approach is inspired by self-exciting, continuous-time point processes such as the Hawkes process. A variety of inferential tasks can be performed using the package. Key epidemiological quantities, including reproduction numbers and latent infections, may be estimated within the framework. The models may be used to evaluate the determinants of changes in transmission rates, including the effects of control measures. Epidemic dynamics may be simulated either from a fitted model or a prior model; allowing for prior/posterior predictive checks, experimentation, and forecasting.

stat.CO↗

arXiv2021

Approximate Conditional Sampling for Pattern Detection in Weighted Networks

Assessing the statistical significance of network patterns is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as nodal-heterogeneity. Typically, significance is computed with reference to a null model. While there has been extensive research into such null models for unweighted graphs, little has been done for the weighted case. This article suggests a null model for weighted graphs. The model fixes node strengths exactly, and approximately fixes node degrees. A novel MCMC algorithm is proposed for sampling the model, and its stochastic stability is considered. We show empirically that the model compares favorably to alternatives, particularly when network patterns are subtle. We show how the algorithm can be used to evaluate the statistical significance of community structure.

stat.ME↗

arXiv2020

Semi-Mechanistic Bayesian Modeling of COVID-19 with Renewal Processes

We propose a general Bayesian approach to modeling epidemics such as COVID-19. The approach grew out of specific analyses conducted during the pandemic, in particular an analysis concerning the effects of non-pharmaceutical interventions (NPIs) in reducing COVID-19 transmission in 11 European countries. The model parameterizes the time varying reproduction number $R_t$ through a regression framework in which covariates can e.g be governmental interventions or changes in mobility patterns. This allows a joint fit across regions and partial pooling to share strength. This innovation was critical to our timely estimates of the impact of lockdown and other NPIs in the European epidemics, whose validity was borne out by the subsequent course of the epidemic. Our framework provides a fully generative model for latent infections and observations deriving from them, including deaths, cases, hospitalizations, ICU admissions and seroprevalence surveys. One issue surrounding our model's use during the COVID-19 pandemic is the confounded nature of NPIs and mobility. We use our framework to explore this issue. We have open sourced an R package epidemia implementing our approach in Stan. Versions of the model are used by New York State, Tennessee and Scotland to estimate the current situation and make policy decisions.

stat.AP↗

arXiv2020

Importance subsampling for power system planning under multi-year demand and weather uncertainty

This paper introduces a generalised version of importance subsampling for time series reduction/aggregation in optimisation-based power system planning models. Recent studies indicate that reliably determining optimal electricity (investment) strategy under climate variability requires the consideration of multiple years of demand and weather data. However, solving planning models over long simulation lengths is typically computationally unfeasible, and established time series reduction approaches induce significant errors. The importance subsampling method reliably estimates long-term planning model outputs at greatly reduced computational cost, allowing the consideration of multi-decadal samples. The key innovation is a systematic identification and preservation of relevant extreme events in modeling subsamples. Simulation studies on generation and transmission expansion planning models illustrate the method's enhanced performance over established "representative days" clustering approaches. The models, data and sample code are made available as open-source software.

stat.AP↗

arXiv2020

Inference of COVID-19 epidemiological distributions from Brazilian hospital data

Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informa\c{c}\~ao de Vigil\^ancia Epidemiol\'ogica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.

q-bio.PE↗

arXiv2020

On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective

Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious disease can be difficult to justify from first principles. It has been shown from the seminal work of Bellman and Harris that the renewal equation arises as the expectation of an age-dependent branching process. In this paper we provide a detailed derivation of the original Bellman Harris process. We introduce generalisations, that allow for time-varying reproduction numbers and the accounting of exogenous events, such as importations. We show how inference on the renewal equation is easy to accomplish within a Bayesian hierarchical framework. Using off the shelf MCMC packages, we fit to South Korea COVID-19 case data to estimate reproduction numbers and importations. Our derivation provides the mathematical fundamentals and assumptions underpinning the use of the renewal equation for modelling outbreaks.

q-bio.PE↗

arXiv2020

BART-based inference for Poisson processes

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.

math.ST↗

arXiv2020

Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update

Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, wide-scale social distancing including local and national lockdowns. In this technical update, we extend a semi-mechanistic Bayesian hierarchical model that infers the impact of these interventions and estimates the number of infections over time. Our methods assume that changes in the reproductive number - a measure of transmission - are an immediate response to these interventions being implemented rather than broader gradual changes in behaviour. Our model estimates these changes by calculating backwards from temporal data on observed to estimate the number of infections and rate of transmission that occurred several weeks prior, allowing for a probabilistic time lag between infection and death. In this update we extend our original model [Flaxman, Mishra, Gandy et al 2020, Report #13, Imperial College London] to include (a) population saturation effects, (b) prior uncertainty on the infection fatality ratio, (c) a more balanced prior on intervention effects and (d) partial pooling of the lockdown intervention covariate. We also (e) included another 3 countries (Greece, the Netherlands and Portugal). The model code is available at https://github.com/ImperialCollegeLondon/covid19model/ We are now reporting the results of our updated model online at https://mrc-ide.github.io/covid19estimates/ We estimated parameters jointly for all M=14 countries in a single hierarchical model. Inference is performed in the probabilistic programming language Stan using an adaptive Hamiltonian Monte Carlo (HMC) sampler.

stat.AP↗