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.

We 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

The conditional intensity function of a spatial point process describes how the probability that a point of the process occurs ‘at’ a particular point in its carrier space depends on the realisation of the process in the remainder of the carrier space. Provided that the point process is simple, the conditional intensity determines all of the properties of the process, in particular its likelihood function

We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity

Point 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

The 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

High-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

In this paper, using the notion of data depth, we describe two classes of affine invariant test statistics for the one-sample location problem. The tests are implemented through the idea of permutation tests. The performance of the test against some competitors is investigated with an extensive simulation study. It is observed that the tests perform well when compared to their competitors for a wide

The Higher School Certificate (HSC) is the credential awarded to secondary school students in New South Wales (NSW), Australia. This paper reviews the current moderation process of the HSC and introduces and compares a range of modern statistical methods. With a comprehensive analysis of the complete 2013–2016 HSC results, we show that the monotone spline regression with the Huber loss function consistently

We forecast the old-age dependency ratio for Australia under various pension age proposals, and estimate a pension age scheme that will provide a stable old-age dependency ratio at a specified level. Our approach involves a stochastic population forecasting method based on coherent functional data models for mortality, fertility and net migration, which we use to simulate the future age-structure of

The analysis of longitudinal income data is often made challenging for several reasons. For example, in a national Australian survey on income over time, a non-negligible proportion of responses are missing, and it is believed the missingness mechanism is non-ignorable. Also, there are a large number of reported zero incomes, some of which may be true zeros (corresponding to individuals who legitimately

Adversarial risk analysis (ARA) is an upcoming methodology that is considered to have advantages over the traditional decision-theoretic and game-theoretic approaches. ARA solutions for first-price sealed-bid (FPSB) auctions have been found but only under strong assumptions which make the model somewhat unrealistic. In this paper, we use ARA methodology to model FPSB auctions using more realistic assumptions

Various non-parametric goodness of fit tests have already been investigated in the literature. However, those tests are rarely used in the case of missing observations. We here study the goodness of fit test for missing data based on Lp distances along with Kolmogorov–Smirnov and Cramer–von-Mises distances when missingness occurs at random. The asymptotic distributions of the proposed test statistics

In this paper, we analysed classification rules under Bayesian decision theory. The setup we considered here is fairly general, which can represent all possible parametric models. The Bayes classification rule we investigated minimises the Bayes risk under general loss functions. Among the existing literatures, the 0-1 loss function appears most frequently, under which the Bayes classification rule

In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science,

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of

We suggest several constructions suitable to define the depth of set-valued observations with respect to a sample of convex sets or with respect to the distribution of a random closed convex set. With the concept of a depth, it is possible to determine if a given convex set should be regarded an outlier with respect to a sample of convex closed sets. Some of our constructions are motivated by the known

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.

In survey sampling studies, statistical inference can be constructed either using design based randomisation or super population model. Design‐based inference using judgement post‐stratified (JPS) sampling is available in the literature. This paper develops statistical inference based on super population model in a finite population setting using JPS sampling design. For a JPS sample, first a simple

For modelling the location of pyramidal cells in the human cerebral cortex, we suggest a hierarchical point process in that exhibits anisotropy in the form of cylinders extending along the z-axis. The model consists first of a generalised shot noise Cox process for the xy-coordinates, providing cylindrical clusters, and next of a Markov random field model for the z-coordinates conditioned on the xy-coordinates

It was a major breakthrough when design-based stereological methods for vertical sections were developed by Adrian Baddeley and coworkers in the 1980s. Most importantly, it was shown how to estimate in a design-based fashion surface area from observations in random vertical sections with uniform position and uniform rotation around the vertical axis. The great practical importance of these developments

Screening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three‐level rather than two‐level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, Journal of Quality Technology43, 1–15, proposed

Poverty mapping is used to facilitate efficient allocation of aid resources, with the objective of ending poverty, the first of the United Nations Sustainable Development Goals. Levels of poverty across small geographic domains within a country are estimated using a statistical model, and the resulting estimates displayed on a poverty map. Current methodology for small area estimation of poverty utilises

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool, which allows one to describe the relationships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the

Error variance estimation plays a key role in the analysis of homogeneous non‐parametric regression models. For a random design model, most methods in the literature for error variance estimation assume the independence between the predictor variable X and the error ε. In this work, we derive the optimal semi‐parametric efficiency bound for the error variance without such an independence assumption

The present paper proposes the focussed information criterion (FIC) to tackle the model selection problems pertinent to generalised linear models (GLM) for time series. As a first step towards constructing the FIC, we formally discuss the local asymptotic theory of quasi‐maximum likelihood estimation for time series GLM under potential model misspecification. The general FIC formula is derived subsequently

Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of

Panel data are collected over several time periods for the same units and hence allow for modelling both latent heterogeneity and dynamics. Since in a dynamic setup, the dependent variable also appears as an explanatory variable in later periods, missing values lead to substantial loss of information and the possibility of inefficient estimation. For linear dynamic panel models with fixed or random

Inspired by constructing large‐size cointegrated portfolios, this paper considers a vector error correction model and develops the adaptive Lasso estimator of the cointegrating vectors. The asymptotic properties of the estimators and the oracle property of the adaptive Lasso are derived. An optimisation algorithm for estimating the model parameters is proposed. The simulation study shows the effectiveness

Empirical likelihood (EL) has been extensively studied to make statistical inferences for independent and dependent observations. However, it experiences the problem of under‐coverage which causes the coverage probability of the EL‐based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we propose modified versions of different EL‐related methods

In this article, we study the statistical properties of the goodness‐of‐fit measure mpp proposed by (Eshima & Tabata 2007, Statistics & Probability Letters 77, 583–593) for generalised linear models. Focusing on the special case of Poisson regression using the canonical log link function, and assuming a random vector X of covariates, we obtain an explicit form for mpp that enables us to study its properties

Universal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions

This R package determines optimal stratification of univariate populations under stratified sampling designs using a parametric‐based method. It determines the optimum strata boundaries (OSB), optimum sample sizes (OSS) and multiple other quantities for the study variable, y, using the best‐fit probability density function of a study variable available from survey data. The method requires the parameters

Clinical work is characterised by frequent interjection of external prompts causing clinicians to switch from a primary task to deal with an incoming secondary task, a phenomenon associated with negative effects in experimental studies. This is an important yet underexplored aspect of work in safety critical settings in general, since an increase in task length due to task‐switching implies reduced

Predicting the arrival time of a transit vehicle involves not only knowledge of its current position and schedule adherence, but also traffic conditions along the remainder of the route. Road networks are dynamic and can quickly change from free‐flowing to highly congested, which impacts the arrival time of transit vehicles, particularly buses which often share the road with other vehicles, so reliable

Multivariate distributions are more and more used to model the dependence encountered in many fields. However, classical multivariate distributions can be restrictive by their nature, while Sarmanov's multivariate distribution, by joining different marginals in a flexible and tractable dependence structure, often provides a valuable alternative. In this paper, we introduce some bivariate mixed Sarmanov

In longitudinal data where the timing and frequency of the measurement of outcomes may be associated with the value of the outcome, significant bias can occur. Previous results depended on correct specification of the outcome process and a somewhat unrealistic visit process model. In practice, this will never exactly be the case, so it is important to understand to what degree the results hold when

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error

In recent years, modelling count data has become one of the most important and popular topics in time‐series analysis. At the same time, variable selection methods have become widely used in many fields as an effective statistical modelling tool. In this paper, we consider using a variable selection method to solve a modelling problem regarding the first‐order Poisson integer‐valued autoregressive

A folded type model is developed for analyzing compositional data. The proposed model, which is based upon the $\alpha$-transformation for compositional data, provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation. The model is validated

We examine the relationships between electoral socio-demographic characteristics and two-party preference in the six Australian federal elections held between 2001 to 2016. Socio-demographic information is derived from the Australian Census, which occurs every five years. Since a Census is not directly available for each election, spatio-temporal imputation is employed to estimate Census data for the

Pitman medal awarded by Statistical Society of Australia for outstanding achievement.

This paper considers modelling of a non‐stationary bivariate integer‐valued autoregressive process of order 1 (BINAR(1)) where the cross‐dependence between the counting series is formed through the relationship of the current series with the previous‐lagged count series observations while the pair of innovations is independent and marginally Poisson. In addition, this paper proposes a generalised quasi‐likelihood

In outcome‐dependent sampling, the continuous or binary outcome variable in a regression model is available in advance to guide selection of a sample on which explanatory variables are then measured. Selection probabilities may either be a smooth function of the outcome variable or be based on a stratification of the outcome. In many cases, only data from the final sample is accessible to the analyst

A generalised regression estimation procedure is proposed that can lead to much improved estimation of population characteristics, such as quantiles, variances and coefficients of variation. The method involves conditioning on the discrepancy between an estimate of an auxiliary parameter and its known population value. The key distributional assumption is joint asymptotic normality of the estimates

Negative binomial (NB) regression is the most common full‐likelihood method for analysing count data exhibiting overdispersion with respect to the Poisson distribution. Usually most practitioners are content to fit one of two NB variants, however other important variants exist. It is demonstrated here that the VGAMR package can fit them all under a common statistical framework founded upon a generalised

Data from large surveys are often supplemented with sampling weights that are designed to reflect unequal probabilities of response and selection inherent in complex survey sampling methods. We propose two methods for Bayesian estimation of parametric models in a setting where the survey data and the weights are available, but where information on how the weights were constructed is unavailable. The

The score test statistic computed using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood-ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular

The origins of Rachel Fewster’s tenure in The Department of Statistics at the University of Auckland can be traced back to the 1997 meeting of the Australasian Region of the International Biometrics Society, held at Paradise Cove in South Australia. It was there that some newly converted Bayesians (Renate Meyer and Russell Millar) met a keen young PhD student from the University of St Andrews. She

This paper discusses a semiparametric single-index model. The link function is allowed to be unbounded and has unbounded support that fill the gap in the literature. The link function is treated as a point in an infinitely many dimensional function space which enables us to derive the estimates for the index parameter and the link function simultaneously. This approach is different from the profile

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either

Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper, we review techniques exploiting the graph structure for exact inference, borrowed from optimisation and computer science. They are built on the principle

We present an application study which exemplifies a cutting edge statistical approach for detecting climate regime shifts. The algorithm uses Bayesian computational techniques that make time-efficient analysis of large volumes of climate data possible. Output includes probabilistic estimates of the number and duration of regimes, the number and probability distribution of hidden states, and the probability

Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of

We discuss posterior sampling for two distinct multivariate generalizations of the univariate ARIMA model with fractional integration. The existing approach to Bayesian estimation, introduced by Ravishanker and Ray (1997), claims to provide a posterior-sampling algorithm for fractionally integrated vector autoregressive moving averages (FIVARMAs). We show that this algorithm produces posterior draws

This paper is motivated by our attempt to answer an empirical question: how is private health insurance take-up in Australia affected by the income threshold at which the Medicare Levy Surcharge (MLS) kicks in? We propose a new difference de-convolution kernel estimator for the location and size of regression discontinuities. We also propose a bootstrapping procedure for estimating confidence bands

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have measurements on all interacting chemical species in the process, observed continuously in time. However, in practice, measurements are taken only at a relatively few time-points

Robustness against design breakdown following observation loss is investigated for Partially Balanced Incomplete Block Designs with two associate classes (PBIBD(2)s). New results are obtained which add to the body of knowledge on PBIBD(2)s. In particular, using an approach based on the E-value of a design, all PBIBD(2)s with triangular and Latin square association schemes are established as having

Expectation propagation is a general approach to deterministic approximate Bayesian inference for graphical models, although its literature is confined mostly to machine learning applications. We investigate the utility of expectation propagation in generalised, linear, and mixed model settings. We show that, even though the algebra and computations are complicated, the notion of message passing on

Consistency and optimality of block bootstrap schemes for distribution and variance estimation of smooth functionals of dependent data have been thoroughly investigated by Hall, Horowitz & Jing (1995), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri (2006), regarding strong consistency for distribution and variance estimation