ISM Symposium on Environmental Statistics 2020

We propose a new distribution for analysing palaeomagnetic directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. We also develop a general regression model framework that allows both the mean direction and the shape parameters of the error distribution to depend on covariates. To illustrate, we analyse palaeomagnetic directional data from the GEOMAGIA50.v3 database. We predict the mean direction at various geological time points and show that there is significant heteroscedasticity present. It is envisaged that the regression structures and error distribution proposed here will also prove useful when covariate information is available with (i) other types of directional response data; and (ii) square-root transformed compositional data of general dimension. This is joint work with Andrew T. A. Wood.

Circular data, comprising of angular observations, arise in various disciplines including environmental sciences. In this talk, we propose a mixed-effects model in which responses are circular variables and covariates are multiple circular and linear variables. The random effects and random errors of the proposed model are assumed to have the von Mises distributions. A measure of intraclass circular correlation and a predictor for an unobserved random effect are studied. Preliminary estimators for the parameters of the model are presented, and their performance is compared with that of the maximum likelihood estimators in a simulation study. A numerical example investigating the factors impacting the orientation taken by a sand hopper when released is presented. This is joint work with Louis-Paul Rivest of Universite Laval, Canada.

In this talk, I will introduce a multi-resolution spatial method, which uses a special class of basis functions extracted from thin-plate splines. The functions are ordered in terms of their degrees of smoothness with higher-order functions corresponding to larger-scale features and lower-order ones corresponding to smaller-scale details, leading to a parsimonious representation of a spatial process with the number of basis functions playing the role of spatial resolution. Some applications of this method will be introduced, including spatial prediction of fine particulate matter (PM2.5) based on data from small internet-of-things sensing devices, called AirBoxes, and independence test between two spatial random fields using a dimension-reduced canonical correlation analysis method.

Repeating earthquake sequences on the plate subduction zone represent the slip-rate histories around their fault patches. So they are useful resources for monitoring precursory aseismic slip of major earthquakes on plate boundaries. Repeating earthquakes are often modeled by renewal processes, point processes whose recurrence intervals are independent and identically distributed. However, their repeating intervals are greatly influenced by larger seismic events or aseismic slow slip, and hence we need to model such non-stationary behavior of repeating earthquakes. In this study, we propose a non-stationary space-time model for repeating earthquakes based on the renewal process. We use the empirical relation between magnitudes and slip sizes of repeating earthquakes to estimate the slip-rate histories in repeating sequences. The proposed model can estimate spatio-temporal variation in slip rate with smoothness restriction adjusted to optimize its Bayesian likelihood. We apply the proposed model to the large catalog of repeating earthquakes on subduction zone of Pacific Plate in the northeastern Japan and estimate slip-rate history of the plate boundary. From this analysis, we discuss the characteristic changes in slip rate before and after the major earthquakes in that area.

We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior which does not satisfy any structural restrictions. In the second step, the posterior samples are transformed to satisfy the structural restriction through a post-processing function. The conceptually straightforward procedure of the post-processed posterior makes its computation efficient and can render interval estimators of any functional of co-variance matrices. We also show that it has nearly optimal minimax rates for banded and bandable covariances among all possible pairs of priors and post-processing functions. The advantages of the post-processed posterior are demonstrated by a simulation study and a real data analysis.

For estimating the generalized (four-parameter) beta distributions, Nagatsuka-Balakrishnan-Kamakura transformation is applied to the shape parameter, combined with Hall and Wang's empirical Bayesian likelihood to the location-scale parameter. With this procedure and a smoothing, a new estimator of parameters is proposed. Some non-normal limit distributions of the estimators of the location-scale parameter are discussed, and the performance of the proposed estimator is evaluated and applied to a historical dataset of tsunami magnitude scales.

We derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result yields very simple asymptotic approximations to and estimators of the prediction mean squared error of EBLUPs, and then asymptotic prediction intervals for the unobserved random effects. We provide a detailed theoretical and empirical comparison with the well-known analytical prediction mean squared error approximations and estimators proposed by Kackar and Harville (1984) and Prasad and Rao (1990). We show that our simple estimator of the predictor mean squared errors of EBLUPs works very well in practice when both the number of clusters and the cluster sizes are sufficiently large.

This study develops a spatial additive modeling (AMM) approach estimating spatial and non-spatial effects from large samples, such as millions of observations. The Moran-coefficient-based approach is applied to model spatial effects flexibly. The proposed approach pre-conditions large matrices whose size grows with respect to the sample size N before the model estimation; thus, the computational complexity for the estimation is independent of the sample size. Furthermore, the pre-conditioning is done through a block-wise procedure that makes the memory consumption independent of N. Eventually, the spatial AMM is memory-free and fast even for millions of observations. The developed approach is compared to alternatives through Monte Carlo simulation experiments. The result confirms the accuracy and computational efficiency of the developed approach. The developed approaches are implemented in an R package spmoran.

Managing extreme event risk in finance and insurance is vital in our modern society. It is known that the statistically justifiable modeling and prediction of rare events are challenging because the historical data on extreme events are inherently scarce. In order to prevent or prepare for unfavorable scenarios, the approaches based on Extreme Value Theory (EVT) have been devised. In the literature on financial risk management, McNeil and Frey (2000, J. Empir. Finance) introduced the GARCH-EVT approach. It is a two-step procedure consisting of GARCH filtering and Peaks-Over-Thresholds method. It should be noted that one drawback of this methodology is that the correction of bias is not thoroughly considered. In this research, we propose a new way, as far as we aware, to estimate conditional Value-at-Risk considering both bias correction and volatility background based on standard GARCH-EVT approach. We illustrate the use of our approach in NASDAQ Index data.

A priori, tree crowns and wood pellet biochar do not have much in common, except that the branching patterns of the former and the networks made of pores in the latter have a structural complexity that can be explored by fractal analysis. In this talk, I will explain how macro- and micro-CT scanning technology (CT: computed tomography) can respectively be used to collect images and data to study these two types of structures. Statistical analysis is based on fractal geometry concepts and multi-fractal tools called “singularity spectrum” and “Rényi entropy spectrum”. The relevant statistical procedures and some newly developed software will be presented, and their application allows researchers to identify which structure, from tree crowns or biochar pore networks, is mono-fractal and which one is multi-fractal. This is joint work with Liwen Han (McGill University, Canada), Franziska Srocke (McGill University, Canada; University of Edinburgh, UK,), Ondrej Masek (University of Edinburgh, UK), and Donald Smith (McGill University, Canada).