Abstracts

 Ice model calibration using semi-continuous spatial data 

Won Chang / University of Cincinnati, USA

Rapid changes in Earth’s cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties, due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters, using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semicontinuous spatial data with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here, we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high dimensionality, we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections. 

Linking satellite data with public health: A spatial analysis of stunting prevalence and tuberculosis cases in Java Indonesia

Setia Pramana / Politeknik Statistika STIS, Indonesia

Remote sensing satellite data can provide a vast of information that can be used to identify, monitor, and track the situation on earth such as land use and cover, infrastructures, air and water quality. By combining satellite data with other data sources, such as population density, mobility patterns, survey and administrative data, we can gain a better understanding of environment and public health. The talk with focus on the use of satellite data combined with other official data to perform spatial analysis to study the impacts of several variables on the prevalence of stunting and the number of Tuberculosis cases in Java, Indonesia. Several methods used are Mixed Geographically Weighted Regression and Geographically Weighted Negative Binomial Regression. The result shows significant spatial effect, and the main variable linked to stunting and TB cases are population density, Built-Up Index, Normalized Difference Vegetation Index, and Land Surface Temperature. 

Familial inference: Tests for hypotheses on a family of centers  

Steve MacEachern / The Ohio State Universit, USA 

Many scientific disciplines face a replicability crisis.  While these crises have many drivers, we focus on one.  Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions.  The most basic tests focus on the centers of the distributions.   Such tests implicitly assume a specific center, e.g., the mean or the median.  Yet, scientific hypotheses do not always specify a particular center.  This ambiguity leaves a gap between scientific theory and statistical practice that can lead to rejection of a true null.  The gap is compounded when we consider deficiencies in the formal statistical model.  Rather than testing a single center, we propose testing a family of plausible centers, such as those induced by the Huber loss function (the Huber family).  Each center in the family generates a point null hypothesis and the resulting family of hypotheses constitutes a familial null hypothesis.  A Bayesian nonparametric procedure is devised to test the familial null.  Implementation for the Huber family is facilitated by a novel pathwise optimization routine.  Along the way, we visit the question of what it means to be the center of a distribution.  The favorable properties of the new test are demonstrated theoretically and in case studies. 

Preservation of the log concavity by Bernstein operator with an application to ageing properties of a coherent system 

German Badia / University of Zaragoza, Spain

In this paper, we provide a new proof of the preservation of the log concavity by Bernstein operator. It is based on the bivariate characterization of the likelihood ratio order. In addition, we give new conditions under which the previous property leads to preservation of ageing properties in coherent systems with independent and identically distributed components.

Correlation analysis in a two-component degrading system subject to periodic and imperfect preventive maintenance actions 

Inma Castro / University of Extremadura, Spain

Due to the rise of increasingly complex systems, research on degradation modelling does not only focus on univariate models but also it is extended to the multivariate case. Some models for multi-component systems assume that the components degrade independently. Although such as assumption allows tractable mathematical models, it remains unrealistic for system where stochastic dependence is indeed present.

This presentation is focused on the study of a system consisting of two dependent components. Several works on degradation modelling for multi-component systems with dependent components have been developed in the literature. In this work, the so called “trivariate reduction method” is used. It means that the evolution of the degradation of each component shares a common noise process. This common process represents different random factors that affect to the two components simultaneously. Assuming Wiener processes for the common noise and for the degradation of each component, it is proved that the expected degradation increases over time.

To enlarge the remaining useful life of the system, periodic preventive maintenance actions are performed. The effect of this maintenance is modelled using the so-called ARD (Arithmetic Reduction Degradation) model of infinite order. It means that the accumulated degradation of each component is reduced in a percentage fixed.

The expectation and the variance of the degradation of the two maintained components is obtained. The Pearson correlation coefficient of the degradation of the two maintained components is also assessed. Finally, if the system fails when the first component fails, the failure time distribution is also obtained. 

Discussing virtual age in reliability context 

Maxim Finkelstein / University of the Free State, South Africa

We discuss an important notion of virtual age that is widely used in reliability literature, however, often without questioning the underlying assumptions and the meaning of these assumptions as well. Our main interest is in the corresponding fundamental, underlying properties for different settings, where this notion arises. Special attention is on virtual age concepts for repairable systems with imperfect repair.  We discuss some of the well-known results in the literature (including our previous publications on the subject) from a different view-point and focus on possible justifications and comparisons of the corresponding models and approaches, where possible. We also suggest some new settings that are aligned with our general approach and focus on some misconceptions as well.