Australian & New Zealand Journal of Statistics最新文献

We introduce the relatively new concept of subtractive lack-of-fit measures in the context of robust regression, in particular in generalised linear models. We devise a fast and robust feature selection framework for regression that empirically enjoys better performance than other selection methods while remaining computationally feasible when fully exhaustive methods are not. Our method builds on the concepts of model stability, subtractive lack-of-fit measures and repeated model identification. We demonstrate how the multiple implementations add value in a robust regression type context, in particular through utilizing a combination of robust regression coefficient and scale estimates. Through resampling, we construct a robust stability matrix, which contains multiple measures of feature importance for each variable. By constructing this stability matrix and using it to rank features based on importance, we are able to reduce the candidate model space and then perform an exhaustive search on the remaining models. We also introduce two different visualisations to better convey information held within the stability matrix; a subtractive Mosaic Probability Plot and a subtractive Variable Inclusion Plot. We demonstrate how these graphics allow for a better understanding of how variable importance changes under small alterations to the underlying data. Our framework is made available in R through the RobStabR package.

This article introduces a special issue of the Australian and New Zealand Journal of Statistics, dedicated as a Festschrift for Geoff McLachlan on the occasion of his 75th birthday.

Clustering to find subgroups with common features is often a necessary first step in the statistical modelling and analysis of large and complex datasets. Although follow-up analyses often make use of complex statistical models that are appropriate for the specific application, most popular clustering approaches are either nonparametric, or based on Gaussian mixture models and their variants, often for reasons of computational efficiency. Certain characteristics in the data, such as the presence of outliers, or non-ellipsoidal cluster shapes, that are common in modern scientific datasets, often lead these methods to fail to detect the cluster components accurately. In this article, we present two efficient and robust Bayesian clustering approaches that seek to overcome these limitations—a model-based ‘tight’ clustering approach to cluster points in the presence of outliers, and a hierarchical Laplace mixture-based approach to cluster heavy-tailed and otherwise non-normal cluster components—and illustrate their power and accuracy in detecting meaningful clusters in datasets from genomics, imaging and the environmental sciences.

We develop a Bayesian non-parametric (BNP) model coupled with Markov random fields (MRFs) for risk mapping, to infer homogeneous spatial regions in terms of risks. In contrast to most existing methods, the proposed approach does not require an arbitrary commitment to a specified number of risk classes and determines their risk levels automatically. We consider settings in which the relevant information are counts and propose a so-called BNP hidden MRF (BNP-HMRF) model that is able to handle such data. The model inference is carried out using a variational Bayes expectation–maximisation algorithm and the approach is illustrated on traffic crash data in the state of Victoria, Australia. The obtained results corroborate well with the traffic safety literature. More generally, the model presented here for risk mapping offers an effective, convenient and fast way to conduct partition of spatially localised count data.

Historical data from plant breeding programs provide valuable resources to study the response of genotypes to the changing environment (i.e. genotype-by-environment interaction). Such data have been used to evaluate the pattern of genotype performance across regions or locations, but its use to evaluate the long-term pattern of genotype performance across environments (i.e. locations-by-years) has been hampered by the lack of common genotypes across years. This lack of common genotypes is due to the structure of the breeding program, especially for annual crops, where only a proportion of selected genotypes are tested in subsequent years. This has resulted in a sparse prediction of the performance of genotypes across years (i.e. a genotype-by-year table). A genomic prediction method that fitted both a relationship matrix among genotypes and a relationship matrix among environments (i.e. years) could overcome this limitation and produce a dense genotype-by-year table, thereby enabling some evaluation of long-term genotype performance. In this paper, we applied the genomic prediction model to the yield data from CIMMYT's Elite Spring Wheat Yield Trials (ESWYT) to visualise the pattern of genotype performance over 25 years.

PPGMMGA is a projection pursuit (PP) algorithm aimed at detecting and visualising clustering structures in multivariate data. The algorithm uses the negentropy as PP index obtained by fitting Gaussian mixture models (GMMs) for density estimation and, then, exploits genetic algorithms (GAs) for its optimisation. Since the PPGMMGA algorithm is a dimension reduction technique specifically introduced for visualisation purposes, cluster memberships are not explicitly provided. In this paper a modal clustering approach is proposed for estimating clusters of projected data points. In particular, a modal EM algorithm is employed to estimate the modes corresponding to the local maxima in the projection subspace of the underlying density estimated using parsimonious GMMs. Data points are then clustered according to the domain of attraction of the identified modes. Simulated and real data are discussed to illustrate the proposed method and evaluate the clustering performance.