Gareth Peters

University of California, Santa Barbara | UCSB · Department of Statistics and Applied Probability

In this study an exploration of insurance risk transfer is undertaken for the cyber insurance industry in the United States of America, based on the leading industry dataset of cyber events provided by Advisen. We seek to address two core unresolved questions. First, what factors are the most significant covariates that may explain the frequency an...

The ability to test for statistical causality in linear and nonlinear contexts, in stationary or non-stationary settings, and to identify whether statistical causality influences trend of volatility forms a particularly important class of problems to explore in multi-modal and multivariate processes. In this paper, we develop novel testing framewor...

Effective symbol detection, channel estimation and decoding of channel codes require an accurate characterization of the noise probability distribution. In many systems, notably the internet of things, noise is largely in the form of interference, arising from a massive number of simultaneous transmissions from uncoordinated devices. Obtaining the...

In this study we examine the nature of losses from cyber related events across different risk categories and business sectors. Using a leading industry dataset of cyber events, we evaluate the relationship between the frequency and severity of individual cyber-related events and the number of affected records. We find that the frequency of reported...

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 parameters uncertainty. We demonstrate how to q...

This paper establishes a new framework for assessing multimodal statistical causality between cryptocurrency market (cryptomarket) sentiment and cryptocurrency price processes. In order to achieve this we present an efficient algorithm for multimodal statistical causality analysis based on Multiple-Output Gaussian Processes. Signals from different...

We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the quantile processes satisfy first- and second-order stochastic dominance. The introduced valuation principle reli...

Recent technological advances have made possible the obtention of vast amounts of market data and strong computing power for advanced models which would not have been practicable for use in real market settings before. In this manuscript we devise a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansions coupled with sto...

In this study an exploration of insurance risk transfer is undertaken for the cyber insurance industry in the United States of America, based on the leading industry dataset of cyber events provided by Advisen. We seek to address two core unresolved questions. First, what factors are the most significant covariates that may explain the frequency an...

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...

The score test is a computationally efficient method for determining whether marks have a significant impact on the intensity of a Hawkes process. This paper provides theoretical justification for use of this test. It is shown that the score statistic has an asymptotic chi-squared distribution under the null hypothesis that marks do not impact the...

Statistical analysis of speech is an emerging area of machine learning. In this paper, we tackle the biometric challenge of Automatic Speaker Verification (ASV) of differentiating between samples generated by two distinct populations of utterances, those of an authentic human voice and those generated by a synthetic one. Solving such an issue throu...

Mobile crowd sensing is a widely used sensing paradigm allowing applications on mobile smart devices to routinely obtain spatially distributed data on a range of user attributes: location, temperature, video and audio. Such data then typically forms the input to application specific machine learning tasks to achieve objectives such as improving use...

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 the Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support var...

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 mo...

Understanding core statistical properties and data features in mortality data are fundamental to the development of machine learning methods for demographic and actuarial applications of mortality projection. The study of statistical features in such data forms the basis for classification, regression and forecasting tasks. In particular, the under...

The cyber risk insurance market is at a nascent stage of its development, even as the magnitude of cyber losses is significant and the rate of cyber risk events is increasing. Existing cyber risk insurance products as well as academic studies have been focusing on classifying cyber risk events and developing models of these events, but little atten...

Mortality projection and forecasting of life expectancy are two important aspects of the study of demography and life insurance modelling. We demonstrate in this work the existence of long memory in mortality data. Furthermore, models incorporating long memory structure provide a new approach to enhance mortality forecasts in terms of accuracy and...

Interference is an important limitation in many communication systems. It has been shown in many situations that the popular Gaussian approximation is not adequate and interference exhibits an impulsive behavior. This paper surveys the different statistical models proposed for such an interference, that can generally be unified using the class of s...

Classification of IoT devices into different types is of paramount importance, from multiple perspectives, including security and privacy aspects. Recent works have explored machine learning techniques for fingerprinting (or classifying) IoT devices, with promising results. However, existing works have assumed that the features used for building th...

Climate change could have both positive and negative effects on the energy consumption of buildings. Today, it is not clear what the extent of these effects could be at multiple spatial scales including building sectors, cities, and climate zones. More importantly, the uncertainty of mathematical models used to estimate these effects is not well un...

We propose a novel generalisation to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalised multiple-degree-of-freedom structures, which provides a more flexible approach to modelling groups of marginal tail dependence in...

We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion is adopted, with which we first calculate the distribution and the survival functions for the maximum of a homogeneous OU-process in a si...

There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence in stochastic processes. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. In this work, we propose a class of new method...

While several tests for serial correlation in financial markets have been proposed and applied successfully in the literature, such tests provide rather limited information to construct predictive econometric models. This manuscript addresses this gap by providing a model-free definition of signed path dependence based on how the sign of cumulative...

Real-time heatwave risk management with fine-grained spatial resolution is important for analysis of urban heat island (UHI) effects and local heatwaves. This study analyzed the spatio-temporal behavior of ground temperatures and developed methods for modeling them. The developed models consider two higher-order stochastic spatial properties (skewn...

Spatial regression of random fields based on potentially biased sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each sensor is, the performance can be negatively affected if the collected information is not fused appropriately...

The statistical quantification of temperature processes for the analysis of urban heat island (UHI) effects and local heat-waves is an increasingly important application domain in smart city dynamic modelling. This leads to the increased importance of real-time heatwave risk management on a fine-grained spatial resolution. This study attempts to an...

A blockchain architecture and solution is proposed to audit processing under exchange regulation for trading activity of exchanges. A particular focus is made on dark pools and periodic auctions. An architecture of the solution is described conceptually and an implementation of the proposed solution is made in .NET framework in C# via a RESTful API...

We consider the source–destination location privacy problem for routing in wireless networks. Previous routing schemes mainly provided privacy protection by minimizing the average detection probability of traffic analysis attempts. However, they do not seek to provide strict privacy guarantees of the vulnerable source–destination pairs, which could...

We investigate how vector auto‐regressive models can be used to study the soybean crush spread. By crush spread we mean a time series marking the difference between a weighted combination of the value of soymeal and soyoil to the value of the original soybeans. Commodity industry practitioners often use fixed prescribed values for these weights, wh...

We develop extensions that introduce regression structure to the multi-factor stochastic models of commodity futures price term structure dynamics. We demonstrate the accuracy with which these models can be calibrated to oil futures data and how they improve on existing models both in model fit and in model interpretation. We found leading observab...

The existence of long memory in mortality data improves the understandings of features of mortality data and provides a new approach for establishing mortality models. The findings of long-memory phenomena in mortality data motivate us to develop new mortality models by extending the Lee–Carter (LC) model to death counts and incorporating long-memo...

This paper focuses on the development of a new class of diffusion processes that allows for direct and dynamic modelling of quantile diffusions. We constructed quantile diffusion processes by transforming each marginal of a given univariate diffusion process under a composite map consisting of a distribution function and quantile function, which in...

Spatial regression of random fields based on unreliable sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each sensor is, the performance can be negatively affected if the collected information is not fused appropriately. For exam...

We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and exhibit complex dependence structures can be constructed. To this end we develop a model where a latent process of...

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chi-squared. These asymptotic results are derived using exis...

Ground-motion prediction equations (GMPEs), also called groundmotion models and attenuation relationships, are empirical models widely used in probabilistic seismic hazard analysis (PSHA). They estimate the conditional distribution of ground shaking at a site given an earthquake of a certain magnitude occurring at a nearby location. In the past dec...

We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion is adopted, with which we are able to calculate the distribution and the survival functions for the maxima of a homogeneous OU-process in...