arXiv subjects

Andrew Parnell

Publications and source records attributed to Andrew Parnell.

31 records · Page 2Linked to original sources

arXiv2022

Review of Clustering Methods for Functional Data

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across various fields of sciences, including but not limited to biology, (bio)chemistry, engineering, environmental science, medical science, psychology, social science, etc. The phenomenal growth of the application of functional data clustering indicates the urgent need for a systematic approach to develop efficient clustering methods and scalable algorithmic implementations. On the other hand, there is abundant literature on the cluster analysis of time series, trajectory data, spatio-temporal data, etc., which are all related to functional data. Therefore, an overarching structure of existing functional data clustering methods will enable the cross-pollination of ideas across various research fields. We here conduct a comprehensive review of original clustering methods for functional data. We propose a systematic taxonomy that explores the connections and differences among the existing functional data clustering methods and relates them to the conventional multivariate clustering methods. The structure of the taxonomy is built on three main attributes of a functional data clustering method and therefore is more reliable than existing categorizations. The review aims to bridge the gap between the functional data analysis community and the clustering community and to generate new principles for functional data clustering.

stat.ME↗

arXiv2022

Vector Time Series Modelling of Turbidity in Dublin Bay

Turbidity is commonly monitored as an important water quality index. Human activities, such as dredging and dumping operations, can disrupt turbidity levels and should be monitored and analyzed for possible effects. In this paper, we model the variations of turbidity in Dublin Bay over space and time to investigate the effects of dumping and dredging while controlling for the effect of wind speed as a common atmospheric effect. We develop a novel Vector Auto-Regressive Conditional Heteroskedasticity (VARCH) approach to modelling the dynamical behaviour of turbidity over different locations and at different water depths. We use daily values of turbidity during the years 2017-2018 to fit the model. We show that the results of our fitted model are in line with the observed data and that the uncertainties, measured through Bayesian credible intervals, are well calibrated. Furthermore, we show that the daily effects of dredging and dumping on turbidity are negligible in comparison to that of wind speed.

stat.AP↗

arXiv2022

Visualizations for Bayesian Additive Regression Trees

Tree-based regression and classification has become a standard tool in modern data science. Bayesian Additive Regression Trees (BART) has in particular gained wide popularity due its flexibility in dealing with interactions and non-linear effects. BART is a Bayesian tree-based machine learning method that can be applied to both regression and classification problems and yields competitive or superior results when compared to other predictive models. As a Bayesian model, BART allows the practitioner to explore the uncertainty around predictions through the posterior distribution. In this paper, we present new visualization techniques for exploring BART models. We construct conventional plots to analyze a model's performance and stability as well as create new tree-based plots to analyze variable importance, interaction, and tree structure. We employ Value Suppressing Uncertainty Palettes (VSUP) to construct heatmaps that display variable importance and interactions jointly using color scale to represent posterior uncertainty. Our new visualizations are designed to work with the most popular BART R packages available, namely BART, dbarts, and bartMachine. Our approach is implemented in the R package bartMan (BART Model ANalysis).

stat.CO↗

arXiv2022

Bayesian Multi-Species N-Mixture Models for Unmarked Animal Communities

We propose an extension of the N-mixture model which allows for the estimation of both abundances of multiple species simultaneously and their inter-species correlations. We also propose further extensions to this multi-species N-mixture model, one of which permits us to examine data which has an excess of zero counts, and another which allows us to relax the assumption of closure inherent in N-mixture models through the incorporation of an AR term in the abundance. The inclusion of a multivariate normal distribution as prior on the random effect in the abundance facilitates the estimation of a matrix of interspecies correlations. Each model is also fitted to avian point data collected as part of the NABBS 2010-2019. Results of simulation studies reveal that these models produce accurate estimates of abundance, inter-species correlations and detection probabilities at both small and large sample sizes, in scenarios with small, large and no zero inflation. Results of model-fitting to the North American Breeding Bird Survey data reveal an increase in Bald Eagle population size in southeastern Alaska in the decade examined.Our novel multi-species N-mixture model accounts for full communities, allowing us to examine abundances of every species present in a study area and, as these species do not exist in a vacuum, allowing us to estimate correlations between species' abundances.While previous multi-species abundance models have allowed for the estimation of abundance and detection probability, ours is the first to address the estimation of both positive and negative inter-species correlations, which allows us to begin to make inferences as to the effect that these species' abundances have on one another. Our modelling approach provides a method of quantifying the strength of association between species' population sizes, and is of practical use to population and conservation ecologists.

stat.ME↗

arXiv2022

A Bayesian Hierarchical Time Series Model for Reconstructing Hydroclimate from Multiple Proxies

We propose a Bayesian hierarchical model which produces probabilistic reconstructions of hydroclimatic variability in Queensland Australia. The model provides a standardised approach to hydroclimate reconstruction using multiple palaeoclimate proxy records derived from natural archives such as speleothems, ice cores and tree rings. The method combines time-series modelling with inverse prediction to quantify the relationships between a given hydroclimate index and relevant proxies over an instrumental period and subsequently reconstruct the hydroclimate back through time. We present case studies for Brisbane and Fitzroy catchments focusing on two hydroclimate indices, the Rainfall Index (RFI) and the Standardised Precipitation-Evapotranspiration Index (SPEI). The probabilistic nature of the reconstructions allows us to estimate the probability that a hydroclimate index in any reconstruction year was lower (higher) than the minimum (maximum) value observed over the instrumental period. In Brisbane, the RFI is unlikely (probabilities < 20%) to have exhibited extremes beyond the minimum/maximum values observed between 1889 and 2017. However, in Fitzroy there are several years during the reconstruction period where the RFI is likely (> 50% probability) to have exhibited behaviour beyond the minimum/maximum of what has been observed. For SPEI, the probability of observing such extremes since the end of the instrumental period in 1889 doesn't exceed 50% in any reconstruction year in Brisbane or Fitzroy.

stat.AP↗

arXiv2021

Visualizing Variable Importance and Variable Interaction Effects in Machine Learning Models

Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these model summaries. We construct heatmap and graph-based displays showing variable importance and interaction jointly, which are carefully designed to highlight important aspects of the fit. We describe a new matrix-type layout showing all single and bivariate partial dependence plots, and an alternative layout based on graph Eulerians focusing on key subsets. Our new visualizations are model-agnostic and are applicable to regression and classification supervised learning settings. They enhance interpretation even in situations where the number of variables is large. Our R package vivid (variable importance and variable interaction displays) provides an implementation.

stat.CO↗

arXiv2020

Real-Time Anomaly Detection for Advanced Manufacturing: Improving on Twitter's State of the Art

The detection of anomalies in real time is paramount to maintain performance and efficiency across a wide range of applications including web services and smart manufacturing. This paper presents a novel algorithm to detect anomalies in streaming time series data via statistical learning. We adapt the generalised extreme studentised deviate test [1] to streaming data by using a sliding window approach. This is made computationally feasible by recursive updates of the Grubbs test statistic [2]. Moreover, a priority queue [3] is employed to reduce memory requirements, where subsets of the required data streaming window are maintained in the algorithm rather than the full list. Our method is statistically principled. It is suitable for streaming data and it outperforms the AnomalyDetection software package, recently released by Twitter Inc. (Twitter) [4] and used by multiple teams at Twitter as their state of the art on a daily basis [5]. The methodology is demonstrated using an example of unlabelled data from the Twitter AnomalyDetection GitHub repository and using a real manufacturing example with labelled anomalies.

eess.SP↗

arXiv2020

Generalizing Gain Penalization for Feature Selection in Tree-based Models

We develop a new approach for feature selection via gain penalization in tree-based models. First, we show that previous methods do not perform sufficient regularization and often exhibit sub-optimal out-of-sample performance, especially when correlated features are present. Instead, we develop a new gain penalization idea that exhibits a general local-global regularization for tree-based models. The new method allows for more flexibility in the choice of feature-specific importance weights. We validate our method on both simulated and real data and implement itas an extension of the popular R package ranger.

stat.ML↗

arXiv2018

An Evaluation of Methods for Real-Time Anomaly Detection using Force Measurements from the Turning Process

We examined the use of three conventional anomaly detection methods and assess their potential for on-line tool wear monitoring. Through efficient data processing and transformation of the algorithm proposed here, in a real-time environment, these methods were tested for fast evaluation of cutting tools on CNC machines. The three-dimensional force data streams we used were extracted from a turning experiment of 21 runs for which a tool was run until it generally satisfied an end-of-life criterion. Our real-time anomaly detection algorithm was scored and optimised according to how precisely it can predict the progressive wear of the tool flank. Most of our tool wear predictions were accurate and reliable as illustrated in our off-line simulation results. Particularly when the multivariate analysis was applied, the algorithm we develop was found to be very robust across different scenarios and against parameter changes. It shall be reasonably easy to apply our approach elsewhere for real-time tool wear analytics.

cs.LG↗

arXiv2018

Statistical modeling of rates and trends in Holocene relative sea level

Characterizing the spatio-temporal variability of relative sea level (RSL) and estimating local, regional, and global RSL trends requires statistical analysis of RSL data. Formal statistical treatments, needed to account for the spatially and temporally sparse distribution of data and for geochronological and elevational uncertainties, have advanced considerably over the last decade. Time-series models have adopted more flexible and physically-informed specifications with more rigorous quantification of uncertainties. Spatio-temporal models have evolved from simple regional averaging to frameworks that more richly represent the correlation structure of RSL across space and time. More complex statistical approaches enable rigorous quantification of spatial and temporal variability, the combination of geographically disparate data, and the separation of the RSL field into various components associated with different driving processes. We review the range of statistical modeling and analysis choices used in the literature, reformulating them for ease of comparison in a common hierarchical statistical framework. The hierarchical framework separates each model into different levels, clearly partitioning measurement and inferential uncertainty from process variability. Placing models in a hierarchical framework enables us to highlight both the similarities and differences among modeling and analysis choices. We illustrate the implications of some modeling and analysis choices currently used in the literature by comparing the results of their application to common datasets within a hierarchical framework. In light of the complex patterns of spatial and temporal variability exhibited by RSL, we recommend non-parametric approaches for modeling temporal and spatio-temporal RSL.

stat.AP↗

arXiv2018

A general framework for modelling zero inflation

We propose a new framework for the modelling of count data exhibiting zero inflation (ZI). The main part of this framework includes a new and more general parameterisation for ZI models which naturally includes both over- and under-inflation. It further sheds new theoretical light on modelling and inference and permits a simpler alternative, which we term as multiplicative, in contrast to the dominant mixture and hurdle models. Our approach gives the statistician access to new types of ZI of which mixture and hurdle are special cases. We outline a simple parameterised modelling approach which can help to infer both ZI type and degree and provide an underlying treatment that shows that current ZI models are themselves typically within the exponential family, thus permitting much simpler theory, computation and classical inference. We outline some possibilities for a natural Bayesian framework for inference; and a rich basis for work on correlated ZI counts. The present paper is an incomplete report on the underlying theory. A later version will include computational issues and provide further examples.

stat.ME↗

arXiv2017

Contrasting Prediction Methods for Early Warning Systems at Undergraduate Level

In this study, we investigate prediction methods for an early warning system for a large STEM undergraduate course. Recent studies have provided evidence in favour of adopting early warning systems as a means of identifying at-risk students. Many of these early warning systems rely on data from students' engagement with Learning Management Systems (LMSs). Our study examines eight prediction methods, and investigates the optimal time in a course to apply an early warning system. We present findings from a statistics university course which has a large proportion of resources on the LMS Blackboard and weekly continuous assessment. We identify weeks 5-6 of our course (half way through the semester) as an optimal time to implement an early warning system, as it allows time for the students to make changes to their study patterns whilst retaining reasonable prediction accuracy. Using detailed (fine-grained) variables, clustering and our final prediction method of BART (Bayesian Additive Regressive Trees) we are able to predict students' final grade by week 6 based on mean absolute error (MAE) to 6.5 percentage points. We provide our R code for implementation of the prediction methods used in a GitHub repository.

math.HO↗

arXiv2016

Prediction of tool-wear in turning of medical grade cobalt chromium molybdenum alloy (ASTM F75) using non-parametric Bayesian models

We present a novel approach to estimating the effect of control parameters on tool wear rates and related changes in the three force components in turning of medical grade Co-Cr-Mo (ASTM F75) alloy. Co-Cr-Mo is known to be a difficult to cut material which, due to a combination of mechanical and physical properties, is used for the critical structural components of implantable medical prosthetics. We run a designed experiment which enables us to estimate tool wear from feed rate and cutting speed, and constrain them using a Bayesian hierarchical Gaussian Process model which enables prediction of tool wear rates for untried experimental settings. The predicted tool wear rates are non-linear and, using our models, we can identify experimental settings which optimise the life of the tool. This approach has potential in the future for realtime application of data analytics to machining processes.

stat.AP↗