Graph Regression Model for Spatial and Temporal Environmental Data-Case of Carbon Dioxide Emissions in the United States.

We develop a new model for spatio-temporal data. More specifically, a graph penalty function is incorporated in the cost function in order to estimate the unknown parameters of a spatio-temporal mixed-effect model based on a generalized linear model. This model allows for more flexible and general regression relationships than classical linear ones through the use of generalized linear models (GLMs) and also captures the inherent structural dependencies or relationships of the data through this regularization based on the graph Laplacian. We use a publicly available dataset from the National Centers for Environmental Information (NCEI) in the United States of America and perform statistical inferences of future CO2 emissions in 59 counties. We empirically show how the proposed method outperforms widely used methods, such as the ordinary least squares (OLS) and ridge regression for this challenging problem.

Cyber loss model risk translates to premium mispricing and risk sensitivity.

In this paper we focus on model risk and risk sensitivity when addressing the insurability of cyber risk. The standard statistical approaches to assessment of insurability and potential mispricing are enhanced in several aspects involving consideration of model risk. Model risk can arise from model uncertainty and parameter uncertainty. We demonstrate how to quantify the effect of model risk in this analysis by incorporating various robust estimators for key model parameters that apply in both marginal and joint cyber risk loss process modelling. Through this analysis we are able to address the question that, to the best of our knowledge, no other study has investigated in the context of cyber risk: is model risk present in cyber risk data, and how does is it translate into premium mispricing? We believe our findings should complement existing studies seeking to explore the insurability of cyber losses.

Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction.

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we study both the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators, the multi-point Maximum A-Posteriori (MAP) estimators, an efficient class of multi-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators, and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening.

In this work we seek to enhance the frameworks practitioners in asset management and wealth management may adopt to asses how different screening rules may influence the diversification benefits of portfolios. The problem arises naturally in the area of Environmental, Social, and Governance (ESG) based investing practices as practitioners often need to select subsets of the total available assets based on some ESG screening rule. Once a screening rule is identified, one constructs a dynamic portfolio which is usually compared with another dynamic portfolio to check if it satisfies or outperforms the risk and return profile set by the company. Our study proposes a novel method that tackles the problem of comparing diversification benefits of portfolios constructed under different screening rules. Each screening rule produces a sequence of graphs, where the nodes are assets and edges are partial correlations. To compare the diversification benefits of screening rules, we propose to compare the obtained graph sequences. The method proposed is based on a machine learning hypothesis testing framework called the kernel two-sample test whose objective is to determine whether the graphs come from the same distribution. If they come from the same distribution, then the risk and return profiles should be the same. The fact that the sample data points are graphs means that one needs to use graph testing frameworks. The problem is natural for kernel two-sample testing as one can use so-called graph kernels to work with samples of graphs. The null hypothesis of the two-sample graph kernel test is that the graph sequences were generated from the same distribution, while the alternative is that the distributions are different. A failure to reject the null hypothesis would indicate that ESG screening does not affect diversification while rejection would indicate that ESG screening does have an effect. The article describes the graph kernel two-sample testing framework, and further provides a brief overview of different graph kernels. We then demonstrate the power of the graph two-sample testing framework under different realistic scenarios. Finally, the proposed methodology is applied to data within the SnP500 to demonstrate the workflow one can use in asset management to test for structural differences in diversification of portfolios under different ESG screening rules.

Adaptive Markov chain Monte Carlo forward projection for statistical analysis in epidemic modelling of human papillomavirus.

A Bayesian statistical model and estimation methodology based on forward projection adaptive Markov chain Monte Carlo is developed in order to perform the calibration of a high-dimensional nonlinear system of ordinary differential equations representing an epidemic model for human papillomavirus types 6 and 11 (HPV-6, HPV-11). The model is compartmental and involves stratification by age, gender and sexual-activity group. Developing this model and a means to calibrate it efficiently is relevant because HPV is a very multi-typed and common sexually transmitted infection with more than 100 types currently known. The two types studied in this paper, types 6 and 11, are causing about 90% of anogenital warts. We extend the development of a sexual mixing matrix on the basis of a formulation first suggested by Garnett and Anderson, frequently used to model sexually transmitted infections. In particular, we consider a stochastic mixing matrix framework that allows us to jointly estimate unknown attributes and parameters of the mixing matrix along with the parameters involved in the calibration of the HPV epidemic model. This matrix describes the sexual interactions between members of the population under study and relies on several quantities that are a priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters as well as unknown sexual mixing matrix parameters related to assortativity. Finally, we explore the ability of an extension to the class of adaptive Markov chain Monte Carlo algorithms to incorporate a forward projection strategy for the ordinary differential equation state trajectories. Efficient exploration of the Bayesian posterior distribution developed for the ordinary differential equation parameters provides a challenge for any Markov chain sampling methodology, hence the interest in adaptive Markov chain methods. We conclude with simulation studies on synthetic and recent actual data.

Correction: Statistical modelling for precision agriculture: A case study in optimal environmental schedules for Agaricus Bisporus production via variable domain functional regression.

[This corrects the article DOI: 10.1371/journal.pone.0181921.].

Ataxic speech disorders and Parkinson's disease diagnostics via stochastic embedding of empirical mode decomposition.

Medical diagnostic methods that utilise modalities of patient symptoms such as speech are increasingly being used for initial diagnostic purposes and monitoring disease state progression. Speech disorders are particularly prevalent in neurological degenerative diseases such as Parkinson's disease, the focus of the study undertaken in this work. We will demonstrate state-of-the-art statistical time-series methods that combine elements of statistical time series modelling and signal processing with modern machine learning methods based on Gaussian process models to develop methods to accurately detect a core symptom of speech disorder in individuals who have Parkinson's disease. We will show that the proposed methods out-perform standard best practices of speech diagnostics in detecting ataxic speech disorders, and we will focus the study, particularly on a detailed analysis of a well regarded Parkinson's data speech study publicly available making all our results reproducible. The methodology developed is based on a specialised technique not widely adopted in medical statistics that found great success in other domains such as signal processing, seismology, speech analysis and ecology. In this work, we will present this method from a statistical perspective and generalise it to a stochastic model, which will be used to design a test for speech disorders when applied to speech time series signals. As such, this work is making contributions both of a practical and statistical methodological nature.

Modeling extreme risks in ecology.

Extreme risks in ecology are typified by circumstances in which data are sporadic or unavailable, understanding is poor, and decisions are urgently needed. Expert judgments are pervasive and disagreements among experts are commonplace. We outline approaches to evaluating extreme risks in ecology that rely on stochastic simulation, with a particular focus on methods to evaluate the likelihood of extinction and quasi-extinction of threatened species, and the likelihood of establishment and spread of invasive pests. We evaluate the importance of assumptions in these assessments and the potential of some new approaches to account for these uncertainties, including hierarchical estimation procedures and generalized extreme value distributions. We conclude by examining the treatment of consequences in extreme risk analysis in ecology and how expert judgment may better be harnessed to evaluate extreme risks.

Infection rate models for COVID-19: Model risk and public health news sentiment exposure adjustments.

During the COVID-19 pandemic, governments globally had to impose severe contact restriction measures and social mobility limitations in order to limit the exposure of the population to COVID-19. These public health policy decisions were informed by statistical models for infection rates in national populations. In this work, we are interested in modelling the temporal evolution of national-level infection counts for the United Kingdom (UK-Wales, England, Scotland), Germany (GM), Italy (IT), Spain (SP), Japan (JP), Australia (AU) and the United States (US). We model the national-level infection counts for the period January 2020 to January 2021, thus covering both the pre- and post-vaccine roll-out periods, in order to better understand the most reliable model structure for the COVID-19 epidemic growth curve. We achieve this by exploring a variety of stochastic population growth models and comparing their calibration, with respect to in-sample fitting and out-of-sample forecasting, both with and without exposure adjustment, to the most widely used and reported growth model, the Gompertz population model, often referred to in the public health policy discourse during the COVID-19 pandemic. Model risk as we explore it in this work manifests in the inability to adequately capture the behaviour of the disease progression growth rate curve. Therefore, our concept of model risk is formed relative to the standard reference Gompertz model used by decision-makers, and then we can characterise model risk mathematically as having two components: the dispersion of the observation distribution, and the structure of the intensity function over time for cumulative counts of new infections daily (i.e. the force of infection) attributed directly to the COVID-19 pandemic. We also explore how to incorporate in these population models the effect that governmental interventions have had on the number of infected cases. This is achieved through the development of an exposure adjustment to the force of infection comprised of a purpose-built sentiment index, which we construct from various authoritative public health news reporting. The news reporting media we employed were the New York Times, the Guardian, the Telegraph, Reuters global blog, as well as national and international health authorities: the European Centre for Disease Prevention and Control, the United Nations Economic Commission for Europe, the United States Centres for Disease Control and Prevention, and the World Health Organisation. We find that exposure adjustments that incorporate sentiment are better able to calibrate to early stages of infection spread in all countries under study.

Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance.

We derive explicit solutions to the problem of completing a partially specified correlation matrix. Our results apply to several block structures for the unspecified entries that arise in insurance and risk management, where an insurance company with many lines of business is required to satisfy certain capital requirements but may have incomplete knowledge of the underlying correlation matrix. Among the many possible completions, we focus on the one with maximal determinant. This has attractive properties and we argue that it is suitable for use in the insurance application. Our explicit formulae enable easy solution of practical problems and are useful for testing more general algorithms for the maximal determinant correlation matrix completion problem.

Statistical modelling for precision agriculture: A case study in optimal environmental schedules for Agaricus Bisporus production via variable domain functional regression.

Quantifying the effects of environmental factors over the duration of the growing process on Agaricus Bisporus (button mushroom) yields has been difficult, as common functional data analysis approaches require fixed length functional data. The data available from commercial growers, however, is of variable duration, due to commercial considerations. We employ a recently proposed regression technique termed Variable-Domain Functional Regression in order to be able to accommodate these irregular-length datasets. In this way, we are able to quantify the contribution of covariates such as temperature, humidity and water spraying volumes across the growing process, and for different lengths of growing processes. Our results indicate that optimal oxygen and temperature levels vary across the growing cycle and we propose environmental schedules for these covariates to optimise overall yields.

Herd immunity effect of the HPV vaccination program in Australia under different assumptions regarding natural immunity against re-infection.

Deterministic dynamic compartmental transmission models (DDCTMs) of human papillomavirus (HPV) transmission have been used in a number of studies to estimate the potential impact of HPV vaccination programs. In most cases, the models were built under the assumption that an individual who cleared HPV infection develops (life-long) natural immunity against re-infection with the same HPV type (this is known as SIR scenario). This assumption was also made by two Australian modelling studies evaluating the impact of the National HPV Vaccination Program to assist in the health-economic assessment of male vaccination. An alternative view denying natural immunity after clearance (SIS scenario) was only presented in one study, although neither scenario has been supported by strong evidence. Some recent findings, however, provide arguments in favour of SIS. We developed HPV transmission models implementing life-time (SIR), limited, and non-existent (SIS) natural immunity. For each model we estimated the herd immunity effect of the ongoing Australian HPV vaccination program and its extension to cover males. Given the Australian setting, we aimed to clarify the extent to which the choice of model structure would influence estimation of this effect. A statistically robust and efficient calibration methodology was applied to ensure credibility of our results. We observed that for non-SIR models the herd immunity effect measured in relative reductions in HPV prevalence in the unvaccinated population was much more pronounced than for the SIR model. For example, with vaccine efficacy of 95% for females and 90% for males, the reductions for HPV-16 were 3% in females and 28% in males for the SIR model, and at least 30% (females) and 60% (males) for non-SIR models. The magnitude of these differences implies that evaluations of the impact of vaccination programs using DDCTMs should incorporate several model structures until our understanding of natural immunity is improved.