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BNPdensity: Bayesian nonparametric mixture modelling in R
SummaryRobust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of para...
Source: Australian and New Zealand Journal of Statistics - November 18, 2021 Category: Statistics Authors: J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto ‐Barajas, I. Prünster Tags: Original Article Source Type: research

Experimental design in practice: The importance of blocking and treatment structures
SummaryExperimental design and analysis has evolved substantially over the last 100 years, driven to a large extent by the power and availability of the computer. To demonstrate this development and encourage the use of experimental design in practice, three experiments from different research areas are presented. In these examples multiple blocking factors have been employed and they show how extraneous variation can be accommodated and interpreted. The examples are used to discuss the importance of blocking and treatment structures in the conduct of designed experiments. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - November 9, 2021 Category: Statistics Authors: E.R. Williams, C.G. Forde, J. Imaki, K. Oelkers Tags: Original Article Source Type: research

Accelerating adaptation in the adaptive Metropolis –Hastings random walk algorithm
SummaryThe Metropolis –Hastings random walk algorithm remains popular with practitioners due to the wide variety of situations in which it can be successfully applied and the extreme ease with which it can be implemented. Adaptive versions of the algorithm use information from the early iterations of the Markov chain t o improve the efficiency of the proposal. The aim of this paper is to reduce the number of iterations needed to adapt the proposal to the target, which is particularly important when the likelihood is time-consuming to evaluate. First, the accelerated shaping algorithm is a generalisation of both th e adap...
Source: Australian and New Zealand Journal of Statistics - November 4, 2021 Category: Statistics Authors: Simon E.F. Spencer Tags: Original Article Source Type: research

Variable selection using penalised likelihoods for point patterns on a linear network
SummaryMotivated by the analysis of a comprehensive database of road traffic accidents, we investigate methods of variable selection for spatial point process models on a linear network. The original data may include explanatory spatial covariates, such as road curvature, and ‘mark’ variables attributed to individual accidents, such as accident severity. The treatment of mark variables is new. Variable selection is applied to the canonical covariates, which may include spatial covariate effects, mark effects and mark-covariate interactions. We approximate the likelih ood of the point process model by that of a generali...
Source: Australian and New Zealand Journal of Statistics - October 19, 2021 Category: Statistics Authors: Suman Rakshit, Greg McSwiggan, Gopalan Nair, Adrian Baddeley Tags: Original Article Source Type: research

ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density
SummaryThe simultaneous analysis of several financial time series is salient in portfolio setting and risk management. This paper proposes a novel alternating expectation conditional maximisation (AECM) algorithm to estimate the vector autoregressive moving average (VARMA) model with variance gamma (VG) error distribution in the multivariate skewed setting. We explain why the VARMA-VG model is suitable for high-frequency returns (HFRs) because VG distribution provides thick tails to capture the high kurtosis in the data and unbounded central density further captures the majority of near-zero HFRs. The distribution can also...
Source: Australian and New Zealand Journal of Statistics - October 18, 2021 Category: Statistics Authors: Thanakorn Nitithumbundit, Jennifer S.K. Chan Tags: Original Article Source Type: research

The Inverse G ‐Wishart distribution and variational message passing
SummaryMessage passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily large graphical models. The notion of a factor graph fragment allows for compartmentalisation of algebra and computer code. We show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning. (Source: Au...
Source: Australian and New Zealand Journal of Statistics - October 8, 2021 Category: Statistics Authors: Luca Maestrini, Matt P. Wand Tags: Original Article Source Type: research

Issue Information
(Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - September 6, 2021 Category: Statistics Tags: Issue Information Source Type: research

An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture ‐based clustering
SummaryWe introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto& Hennig,Journal of the American Statistical Association111, 1648 –1659) of a Gaussian mixture model allowing for observations to be classified as ‘noise’, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statisticQ that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for no...
Source: Australian and New Zealand Journal of Statistics - September 4, 2021 Category: Statistics Authors: Christian Hennig, Pietro Coretto Tags: Original Article Source Type: research

An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture ?based clustering
SummaryWe introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto& Hennig,Journal of the American Statistical Association111, 1648 1659) of a Gaussian mixture model allowing for observations to be classified as noise, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statisticQ that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for non-Gaus...
Source: Australian and New Zealand Journal of Statistics - September 3, 2021 Category: Statistics Authors: Christian Hennig, Pietro Coretto Tags: Original Article Source Type: research

Issue Information
(Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 22, 2021 Category: Statistics Tags: Issue Information Source Type: research

Anna Karenina and the two envelopes problem
SummaryThe Anna Karenina principle is named after the opening sentence in the eponymous novel: Happy families are all alike; every unhappy family is unhappy in its own way. The two envelopes problem (TEP) is a much-studied paradox in probability theory, mathematical economics, logic and philosophy. Time and again a new analysis is published in which an author claims finally to explain what actually goes wrong in this paradox. Each author (the present author included) emphasises what is new in their approach and concludes that earlier approaches did not get to the root of the matter. We observe that though a logical argumen...
Source: Australian and New Zealand Journal of Statistics - July 22, 2021 Category: Statistics Authors: R. D. Gill Tags: Original Article Source Type: research

What is the effective sample size of a spatial point process?
SummaryPoint process models are a natural approach for modelling data that arise as point events. In the case of Poisson counts, these may be fitted easily as a weighted Poisson regression. Point processes lack the notion of sample size. This is problematic for model selection, because various classical criteria such as the Bayesian information criterion (BIC) are a function of the sample size,n, and are derived in an asymptotic framework wheren tends to infinity. In this paper, we develop an asymptotic result for Poisson point process models in which the observed number of point events,m, plays the role that sample size d...
Source: Australian and New Zealand Journal of Statistics - July 22, 2021 Category: Statistics Authors: Ian W. Renner, David I. Warton, Francis K.C. Hui Tags: Original Article Source Type: research

Dependent radius marks of Laguerre tessellations: a case study
SummaryWe study a particular marked three-dimensional point process sample that represents a Laguerre tessellation. It comes from a polycrystalline sample of aluminium alloy material. The ‘points’ are the cell generators while the ‘marks’ are radius marks that control the size and shape of the tessellation cells. Our statistical mark correlation analyses show that the marks of the sample are in clear and plausible spatial correlation: the marks of generators close together te nd to be small and similar and the form of the correlation functions does not justify geostatistical marking. We show that a simplified model...
Source: Australian and New Zealand Journal of Statistics - July 22, 2021 Category: Statistics Authors: Dietrich Stoyan, Viktor Bene š, Filip Seitl Tags: Original Article Source Type: research

A Festschrift for Adrian Baddeley
This article introduces a special issue of the Australian and New Zealand Journal of Statistics, being a Festschrift for Adrian Baddeley on the occasion of his 65th birthday. (Source: Australian and New Zealand Journal of Statistics)
Source: Australian and New Zealand Journal of Statistics - July 22, 2021 Category: Statistics Authors: Martin L. Hazelton, R. Turner Tags: Original Article Source Type: research

Modelling temporal genetic and spatio ‐temporal residual effects for high‐throughput phenotyping data
SummaryHigh-throughput phenomics data are being collected in both the laboratory and the field. The data are often collected at many time points and there may be spatial variation in the laboratory or field that impacts on the growth of the plants, and that may influence the traits of interest. Modelling the genetic effects is of primary interest in such studies, but these effects might be biased if non-genetic effects present in the experiment are ignored. With data that are collected both in time and space, there may be a need to jointly model these multi-dimensional non-genetic effects. Thus both modelling of genetic ef...
Source: Australian and New Zealand Journal of Statistics - July 21, 2021 Category: Statistics Authors: A. P. Verbyla, J. De Faveri, D. M. Deery, G. J. Rebetzke Tags: Original Article Source Type: research