arXiv subjects

Gordon J. Ross

Publications and source records attributed to Gordon J. Ross.

11 recordsLinked to original sources

arXiv2026

Sequential Bayesian Monitoring for Recoverable and Drifting Processes

In many Phase II statistical process control (SPC) problems, the main concern is not whether a monitored process has ever changed, but whether it is currently operating at an acceptable level. This distinction is especially important when monitoring continues after a signal, or when corrective action may restore the process. We develop Bayesian monitoring procedures for this formulation of the Phase II task. For recoverable processes that may alternate between in-control and out-of-control states, we derive recursions for the posterior probability that the process is presently in control. For sequential tracking problems in which a latent parameter evolves over time, we monitor the posterior probability that the parameter lies inside an acceptable region of behavior. The methods are studied through calibrated time-between-failure experiments, Gaussian and Binomial tracking examples, and a held-out multivariate data illustration using white wine quality measurements.

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arXiv2026

Bayesian Modelling of Nonstationary Extreme Values Using a Nonparametric Hawkes Process

Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach this task by developing a Bayesian point process model for extreme events, which uses a self-exciting Hawkes process to model the rate at which extremes occur. The Hawkes process has a structure which allows events to occur in clusters, making it realistic for many types of data. We use a flexible Bayesian nonparametric approach based on the Dirichlet process to learn the temporal excitation pattern from the data. Further, we build on Extreme Value Theory by using a Generalised Pareto Distribution (GPD) to model the magnitudes of the extremes, with a hierarchical mark model allowing these magnitudes to vary across Hawkes-induced clusters. A hierarchical specification of the model results in partial pooling, allowing for more accurate GPD estimation even in clusters with only a small number of observations. We develop an MCMC algorithm to sample from the resulting hierarchical model. A simulation study confirms that the two flexible components improve prediction when the corresponding features are present in the data-generating mechanism, and across four real data sets the nonparametric Hawkes model with hierarchical GPD marks gives the best held-out predictive performance among the model variants considered.

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arXiv2026

dirichletprocess: An R Package for Fitting Complex Bayesian Nonparametric Models

The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead, the user can utilise our pre-built models or specify their own models whilst allowing the dirichletprocess package to handle the Markov chain Monte Carlo sampling. Our Dirichlet process objects can act as building blocks for a variety of statistical models including: density estimation, clustering and prior distributions in hierarchical models.

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arXiv2026

Nonparametric Detection of Multiple Location-Scale Change Points via Wild Binary Segmentation

Change point methods are used to divide a sequence of observations into segments with different behaviour. Often, the distributional form of the observations is unknown, but the changes of interest are likely to involve shifts in location, scale, or both. We consider the problem of detecting multiple change points in a sequence without specifying a parametric model for the data. We propose the WBS-Lepage procedure, a nonparametric method which combines wild binary segmentation with a rank-based Lepage statistic. The statistic is formed from Mann--Whitney and Mood components, which are respectively sensitive to changes in location and scale. Since it depends on the observations only through their ranks, its null distribution is distribution-free. This allows finite-sample thresholds to be calibrated by Monte Carlo simulation, providing direct control over the probability of falsely detecting change points when none exist. We compare WBS-Lepage with existing nonparametric change point methods, including penalised likelihood and binary-segmentation-based competitors. The proposed method performs competitively for location changes and is particularly effective for detecting changes in scale. We illustrate the procedure on a stylometric analysis of changes in an author's writing style and provide an implementation of our method in the accompanying R package npwbs.

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arXiv2023

Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition

Product cannibalisation in the marketplace refers to the decrease in the sales of one product due to competition from another product. We examine this phenomenon in a wholesale data set provided by an international company. We use a multivariate Hawkes process where each product is represented by a dimension, with cross-inhibition effects that model product cannibalisation. To implement the Hawkes process with inhibition we resolve challenges regarding the integration of the intensity function and introduce a new, stronger conditions for stability as existing conditions are unnecessarily strict under inhibition. We conduct our analysis in a Bayesian framework, for which we design a dimension-independent prior on the cross-inhibition based on a reparametrisation.

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arXiv2021

ABC Learning of Hawkes Processes with Missing or Noisy Event Times

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such distortion can severely bias the learning of the Hawkes process parameters. To circumvent this, we propose modeling the distortion function explicitly. This leads to a model with an intractable likelihood function which makes it difficult to deploy standard parameter estimation techniques. As such, we develop the ABC-Hawkes algorithm which is a novel approach to estimation based on Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo. This allows the parameters of the Hawkes process to be learned in settings where conventional methods induce substantial bias or are inapplicable. The proposed approach is shown to perform well on both real and simulated data.

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arXiv2020

Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.

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arXiv2015

Dynamic Multi-Factor Clustering of Financial Networks

We investigate the tendency for financial instruments to form clusters when there are multiple factors influencing the correlation structure. Specifically, we consider a stock portfolio which contains companies from different industrial sectors, located in several different countries. Both sector membership and geography combine to create a complex clustering structure where companies seem to first be divided based on sector, with geographical subclusters emerging within each industrial sector. We argue that standard techniques for detecting overlapping clusters and communities are not able to capture this type of structure, and show how robust regression techniques can instead be used to remove the influence of both sector and geography from the correlation matrix separately. Our analysis reveals that prior to the 2008 financial crisis, companies did not tend to form clusters based on geography. This changed immediately following the crisis, with geography becoming a more important determinant of clustering.

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arXiv2012

Sequential Monitoring of a Bernoulli Sequence when the Pre-change Parameter is Unknown

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world situations: 1) the pre-change value of the Bernoulli parameter is known in advance, 2) computational efficiency is not paramount, and 3) enough observations occur between change points to allow asymptotic approximations to be used. We develop a novel change detection method based on Fisher's Exact Test which does not make any of these assumptions. We show that our method can be implemented in a computationally efficient manner, and is hence suited to sequential monitoring where new observations are constantly being received over time. We assess our method's performance empirically via using simulated data, and find that it is comparable to the optimal CUSUM scheme which assumes both pre- and post-change values of the parameter to be known.

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arXiv2012

Exponentially Weighted Moving Average Charts for Detecting Concept Drift

Classifying streaming data requires the development of methods which are computationally efficient and able to cope with changes in the underlying distribution of the stream, a phenomenon known in the literature as concept drift. We propose a new method for detecting concept drift which uses an Exponentially Weighted Moving Average (EWMA) chart to monitor the misclassification rate of an streaming classifier. Our approach is modular and can hence be run in parallel with any underlying classifier to provide an additional layer of concept drift detection. Moreover our method is computationally efficient with overhead O(1) and works in a fully online manner with no need to store data points in memory. Unlike many existing approaches to concept drift detection, our method allows the rate of false positive detections to be controlled and kept constant over time.

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arXiv2012

Modeling Financial Volatility in the Presence of Abrupt Changes

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive days, creating temporal clusters. The GARCH model, which treats volatility as a drift process, is commonly used to capture this behavior. However research suggests that volatility is often better described by a structural break model, where the volatility undergoes abrupt jumps in addition to drift. Most efforts to integrate these jumps into the GARCH methodology have resulted in models which are either very computationally demanding, or which make problematic assumptions about the distribution of the instruments, often assuming that they are Gaussian. We present a new approach which uses ideas from nonparametric statistics to identify structural break points without making such distributional assumptions, and then models drift separately within each identified regime. Using our method, we investigate the volatility of several major stock indexes, and find that our approach can potentially give an improved fit compared to more commonly used techniques.

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