arXiv subjects

Axel Gandy

Publications and source records attributed to Axel Gandy.

At least 37 records · Page 2Linked to original sources

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 Informação de Vigilância Epidemiológica 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.

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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.

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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↗

arXiv2019

Implementing Monte Carlo Tests with P-value Buckets

Software packages usually report the results of statistical tests using p-values. Users often interpret these by comparing them to standard thresholds, e.g. 0.1%, 1% and 5%, which is sometimes reinforced by a star rating (***, **, *). We consider an arbitrary statistical test whose p-value p is not available explicitly, but can be approximated by Monte Carlo samples, e.g. by bootstrap or permutation tests. The standard implementation of such tests usually draws a fixed number of samples to approximate p. However, the probability that the exact and the approximated p-value lie on different sides of a threshold (the resampling risk) can be high, particularly for p-values close to a threshold. We present a method to overcome this. We consider a finite set of user-specified intervals which cover [0,1] and which can be overlapping. We call these p-value buckets. We present algorithms that, with arbitrarily high probability, return a p-value bucket containing p. We prove that for both a bounded resampling risk and a finite runtime, overlapping buckets need to be employed, and that our methods both bound the resampling risk and guarantee a finite runtime for such overlapping buckets. To interpret decisions with overlapping buckets, we propose an extension of the star rating system. We demonstrate that our methods are suitable for use in standard software, including for low p-value thresholds occurring in multiple testing settings, and that they can be computationally more efficient than standard implementations.

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arXiv2019

A simple method for implementing Monte Carlo tests

We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

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arXiv2019

Joint analysis of clinical risk factors and 4D cardiac motion for survival prediction using a hybrid deep learning network

In this work, a novel approach is proposed for joint analysis of high dimensional time-resolved cardiac motion features obtained from segmented cardiac MRI and low dimensional clinical risk factors to improve survival prediction in heart failure. Different methods are evaluated to find the optimal way to insert conventional covariates into deep prediction networks. Correlation analysis between autoencoder latent codes and covariate features is used to examine how these predictors interact. We believe that similar approaches could also be used to introduce knowledge of genetic variants to such survival networks to improve outcome prediction by jointly analysing cardiac motion traits with inheritable risk factors.

q-bio.QM↗

arXiv2019

Importance subsampling: improving power system planning under climate-based uncertainty

Recent studies indicate that the effects of inter-annual climate-based variability in power system planning are significant and that long samples of demand & weather data (spanning multiple decades) should be considered. At the same time, modelling renewable generation such as solar and wind requires high temporal resolution to capture fluctuations in output levels. In many realistic power system models, using long samples at high temporal resolution is computationally unfeasible. This paper introduces a novel subsampling approach, referred to as "importance subsampling", allowing the use of multiple decades of demand & weather data in power system planning models at reduced computational cost. The methodology can be applied in a wide class of optimisation-based power system simulations. A test case is performed on a model of the United Kingdom created using the open-source modelling framework Calliope and 36 years of hourly demand and wind data. Standard data reduction approaches such as using individual years or clustering into representative days lead to significant errors in estimates of optimal system design. Furthermore, the resultant power systems lead to supply capacity shortages, raising questions of generation capacity adequacy. In contrast, "importance subsampling" leads to accurate estimates of optimal system design at greatly reduced computational cost, with resultant power systems able to meet demand across all 36 years of demand & weather scenarios.

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arXiv2018

State-Dependent Kernel Selection for Conditional Sampling of Graphs

This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the presence or absence of an arbitrary number of edges. The resulting conditional distributions provide the basis for exact tests. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency degrades in sparse graphs. MCMC methods usually require explicit computation of a Markov basis to navigate the complex state space; this is computationally intensive even for small graphs. We use state-dependent kernel selection to develop new MCMC samplers. These do not require a Markov basis, and are efficient both in sparse and dense graphs. The key idea is to intelligently select a Markov kernel on the basis of the current state of the chain. We apply our methods to testing hypotheses on a real network and contingency table. The algorithms appear orders of magnitude more efficient than existing methods in the test cases considered.

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arXiv2018

Tree-based Particle Smoothing Algorithms in a Hidden Markov Model

We provide a new strategy built on the divide-and-conquer approach by Lindsten et al. (2017) to investigate the smoothing problem in a hidden Markov model. We employ this approach to decompose a hidden Markov model into sub-models with intermediate target distributions based on an auxiliary tree structure and produce independent samples from the sub-models at the leaf nodes towards the original model of interest at the root. We review the target distribution in the sub-models suggested by Lindsten et al. and propose two new classes of target distributions, which are the estimates of the (joint) filtering distributions and the (joint) smoothing distributions. The first proposed type is straightforwardly constructible by running a filtering algorithm in advance. The algorithm using the second type of target distributions has an advantage of roughly retaining the marginals of all random variables invariant at all levels of the tree at the cost of approximating the marginal smoothing distributions in advance. We further propose the constructions of these target distributions using pre-generated Monte Carlo samples. We show empirically the algorithms with the proposed intermediate target distributions give stable and comparable results as the conventional smoothing methods in a linear Gaussian model and a non-linear model.

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arXiv2018

QuickMMCTest - Quick Multiple Monte Carlo Testing

Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation tests or bootstrap tests. This article presents a simple algorithm based on Thompson Sampling to test multiple hypotheses. It works with arbitrary multiple testing procedures, in particular with step-up and step-down procedures. Its main feature is to sequentially allocate Monte Carlo effort, generating more Monte Carlo samples for tests whose decisions are so far less certain. A simulation study demonstrates that for a low computational effort, the new approach yields a higher power and a higher degree of reproducibility of its results than previously suggested methods.

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arXiv2017

A latent trawl process model for extreme values

This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for extreme values is constructed by embedding a trawl process in a hierarchical framework, which ensures that the marginal distribution is generalised Pareto, as expected from classical extreme value theory. We also consider a modified version of this model that works with a wider class of generalised Pareto distributions, and has the advantage of separating marginal and temporal dependence properties. The model is illustrated by applications to environmental time series, and it is shown that the model offers considerable flexibility in capturing the dependence structure of extreme value data.

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arXiv2016

The chopthin algorithm for resampling

Resampling is a standard step in particle filters and more generally sequential Monte Carlo methods. We present an algorithm, called chopthin, for resampling weighted particles. In contrast to standard resampling methods the algorithm does not produce a set of equally weighted particles; instead it merely enforces an upper bound on the ratio between the weights. Simulation studies show that the chopthin algorithm consistently outperforms standard resampling methods. The algorithms chops up particles with large weight and thins out particles with low weight, hence its name. It implicitly guarantees a lower bound on the effective sample size. The algorithm can be implemented efficiently, making it practically useful. We show that the expected computational effort is linear in the number of particles. Implementations for C++, R (on CRAN), Python and Matlab are available.

stat.CO↗

arXiv2016

A Framework for Monte Carlo based Multiple Testing

We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p-values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non-rejections as the ones obtained if the p-values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions which guarantee that the rejections and non-rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p-values. Our framework is applicable to a general class of step-up and step-down procedures which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini-Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset.

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arXiv2015

A Lévy-driven rainfall model with applications to futures pricing

We propose a parsimonious stochastic model for characterising the distributional and temporal properties of rainfall. The model is based on an integrated Ornstein-Uhlenbeck process driven by the Hougaard Lévy process. We derive properties of this process and propose an extended model which generalises the Ornstein-Uhlenbeck process to the class of continuous-time ARMA (CARMA) processes. The model is illustrated by fitting it to empirical rainfall data on both daily and hourly time scales. It is shown that the model is sufficiently flexible to capture important features of the rainfall process across locations and time scales. Finally we study an application to the pricing of rainfall derivatives which introduces the market price of risk via the Esscher transform. We first give a result specifying the risk-neutral expectation of a general moving average process. Then we illustrate the pricing method by calculating futures prices based on empirical daily rainfall data, where the rainfall process is specified by our model.

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arXiv2014

RMCMC: A System for Updating Bayesian Models

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted samples stored in a database. The stored samples are maintained such that the accuracy of the estimates and quality of the samples is satisfactory. This maintenance involves varying the number of samples in the database and updating their weights. New samples are generated, when required, by a Markov chain Monte Carlo algorithm. The system is demonstrated using a football league model that is used to predict the end of season table. Correctness of the estimates and their accuracy is shown in a simulation using a linear Gaussian model.

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arXiv2014

MMCTest - A Safe Algorithm for Implementing Multiple Monte Carlo Tests

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest, a sequential algorithm which gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p-values. The method can be used with a class of multiple testing procedures which includes the Benjamini & Hochberg False Discovery Rate (FDR) procedure and the Bonferroni correction controlling the Familywise Error Rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses which can already be decided as being rejected or non-rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non-rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.

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arXiv2013

An algorithm to compute the power of Monte Carlo tests with guaranteed precision

This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that achieves this aim for almost any Monte Carlo test. Previous research has focused on obtaining as accurate a result as possible for a fixed computational effort, without providing a guaranteed precision in the above sense. The algorithm we propose does not have a fixed effort and runs until a confidence interval with a user-specified length and coverage probability can be constructed. We show that the expected effort required by the algorithm is finite in most cases of practical interest, including situations where the distribution of the p-value is absolutely continuous or discrete with finite support. The algorithm is implemented in the R-package simctest, available on CRAN.

stat.CO↗

arXiv2012

Optimality of Non-Restarting CUSUM charts

We show optimality, in a well-defined sense, using cumulative sum (CUSUM) charts for detecting changes in distributions. We consider a setting with multiple changes between two known distributions. This result advocates the use of non-restarting CUSUM charts with an upper boundary. Typically, after signalling, a CUSUM chart is restarted by setting it to some value below the threshold. A non-restarting CUSUM chart is not reset after signalling; thus is able to signal continuously. Imposing an upper boundary prevents the CUSUM chart rising too high, which facilitates detection in our setting. We discuss, via simulations, how the choice of the upper boundary changes the signals made by the non-restarting CUSUM charts.

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