# Globally intensity‐reweighted estimators for K‐ and pair correlation functions

Australian & New Zealand Journal of Statistics

Published On 2021/3

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 function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

Journal

Australian & New Zealand Journal of Statistics

Published On

2021/3

Volume

63

Issue

1

Page

93-118

## Authors

#### Jesper Møller

##### Aalborg Universitet

Position

Professor in Statistics

H-Index(all)

46

H-Index(since 2020)

23

I-10 Index(all)

0

I-10 Index(since 2020)

0

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0

Citation(since 2020)

0

Cited By

0

Research Interests

Mathematical Statistics

Probability Theory

University Profile Page

#### Rasmus Waagepetersen

##### Aalborg Universitet

Position

Professor i statistik

H-Index(all)

33

H-Index(since 2020)

20

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0

I-10 Index(since 2020)

0

Citation(all)

0

Citation(since 2020)

0

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0

Research Interests

rumlig statistik

University Profile Page

#### Thomas Shaw

##### University of Michigan

Position

PhD Candidate

H-Index(all)

5

H-Index(since 2020)

5

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0

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0

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0

Citation(since 2020)

0

Cited By

0

Research Interests

biophysics

University Profile Page

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Aalborg Universitet

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Aalborg Universitet

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Australian & New Zealand Journal of Statistics

##### Embedding latent class regression and latent class distal outcome models into cluster‐weighted latent class analysis: a detailed simulation experiment

Usually in latent class (LC) analysis, external predictors are taken to be cluster conditional probability predictors (LC models with external predictors), and/or score conditional probability predictors (LC regression models). In such cases, their distribution is not of interest. Class‐specific distribution is of interest in the distal outcome model, when the distribution of the external variables is assumed to depend on LC membership. In this paper, we consider a more general formulation, that embeds both the LC regression and the distal outcome models, as is typically done in cluster‐weighted modelling. This allows us to investigate (1) whether the distribution of the external variables differs across classes, (2) whether there are significant direct effects of the external variables on the indicators, by modelling jointly the relationship between the external and the latent variables. We show the advantages of the proposed …

*2023/9*

Tanujit Chakraborty

Indian Statistical Institute

Australian & New Zealand Journal of Statistics

##### Bayesian neural tree models for nonparametric regression

Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real‐life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical …

*2023/6*

Tugba Akkaya-Hocagil

Harvard University

Australian & New Zealand Journal of Statistics

##### Bayesian modelling of effects of prenatal alcohol exposure on child cognition based on data from multiple cohorts

High levels of prenatal alcohol exposure (PAE) result in significant cognitive deficits in children, but the exact nature of the dose‐response relationship is less well understood. To investigate this relationship, data were assembled from six longitudinal birth cohort studies examining the effects of PAE on cognitive outcomes from early school age through adolescence. Structural equation models (SEMs) are a natural approach to consider, because of the way they conceptualise multiple observed outcomes as relating to an underlying latent variable of interest, which can then be modelled as a function of exposure and other predictors of interest. However, conventional SEMs could not be fitted in this context because slightly different outcome measures were used in the six studies. In this paper we propose a multi‐group Bayesian SEM that maps the unobserved cognition variable to a broad range of observed outcomes …

*2023/9*

David Azriel

Technion - Israel Institute of Technology

Australian & New Zealand Journal of Statistics

##### The role of pairwise matching in experimental design for an incidence outcome

We consider the problem of evaluating designs for a two‐arm randomised experiment with an incidence (binary) outcome under a non‐parametric general response model. Our two main results are that the a priori pair matching design is (1) the optimal design as measured by mean squared error among all block designs which includes complete randomisation. And (2), this pair‐matching design is minimax, that is, it provides the lowest mean squared error under an adversarial response model. Theoretical results are supported by simulations and clinical trial data where we demonstrate the superior performance of pairwise matching designs under realistic conditions.

*2023/12*

Linda Haines

University of Cape Town

Australian & New Zealand Journal of Statistics

##### Exact likelihoods for N‐mixture models with time‐to‐detection data

This paper is concerned with the formulation of N$$ N $$‐mixture models for estimating the abundance and probability of detection of a species from binary response, count and time‐to‐detection data. A modelling framework, which encompasses time‐to‐first‐detection within the context of detection/non‐detection and time‐to‐each‐detection and time‐to‐first‐detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed‐form expressions for the likelihoods associated with time‐to‐detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with …

*2023/12*