arXiv subjects

Janet Van Niekerk

Publications and source records attributed to Janet Van Niekerk.

6 recordsLinked to original sources

arXiv2026

Penalizing complexity priors for Bayesian inference of circular models

Advancements in computational power and methodologies have enabled research on massive datasets. However, tools for analyzing data with directional or periodic characteristics, such as wind directions and customers' arrival time in 24-hour clock, remain underdeveloped. While statisticians have proposed circular distributions for such analyses, significant challenges persist in constructing circular statistical models, particularly in the context of Bayesian methods. These challenges stem from limited theoretical development and a lack of historical studies on prior selection for circular distribution parameters. In this article, we propose a framework for selecting hyperpriors that contracts to a simpler model in circular scenarios, especially when there is insufficient information to guide prior selection. We introduce well-examined Penalized Complexity (PC) priors for the most widely used circular distributions. Comprehensive comparisons with existing hyperpriors in the literature are conducted through simulation studies and a practical case study. Finally, we discuss the contributions and implications of our work, providing a foundation for further advancements in constructing Bayesian circular statistical models.

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arXiv2026

A Bayesian regression framework for circular models with INLA

Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we introduce a new approach to rectify this issue, leading to well-defined regression models for circular responses when the data are concentrated. Our approach extends naturally to joint regression models where we can have several circular and non-circular responses, and allow us to handle a mix of linear covariates, circular covariates and various random effects. Our formulation aligns naturally with the integrated nested Laplace approximation (INLA), which provides fast and accurate Bayesian inference. We illustrate our approach through several simulated and real examples.

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arXiv2025

Leave-group-out cross-validation for latent Gaussian models

Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations, LOOCV has since been extended to other cases such as hierarchical models. However, it focuses primarily on short-range prediction and may not fully capture long-range prediction scenarios. For structured hierarchical models, particularly those involving multiple random effects, the concepts of short- and long-range predictions become less clear, which can complicate the interpretation of LOOCV results. In this paper, we propose a complementary cross-validation framework specifcally tailored for longer-range prediction in latent Gaussian models, including those with structured random effects. Our approach differs from LOOCV by excluding a carefully constructed set from the training set, which better emulates longer-range prediction conditions. Furthermore, we achieve computational effciency by adjusting the full joint posterior for this modifed cross-validation, thus eliminating the need for model reftting. This method is implemented in the R-INLA package (www.r-inla.org) and can be adapted to a variety of inferential frameworks.

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arXiv2023

INLA+ -- Approximate Bayesian inference for non-sparse models using HPC

The integrated nested Laplace approximations (INLA) method has become a widely utilized tool for researchers and practitioners seeking to perform approximate Bayesian inference across various fields of application. To address the growing demand for incorporating more complex models and enhancing the method's capabilities, this paper introduces a novel framework that leverages dense matrices for performing approximate Bayesian inference based on INLA across multiple computing nodes using HPC. When dealing with non-sparse precision or covariance matrices, this new approach scales better compared to the current INLA method, capitalizing on the computational power offered by multiprocessors in shared and distributed memory architectures available in contemporary computing resources and specialized dense matrix algebra. To validate the efficacy of this approach, we conduct a simulation study then apply it to analyze cancer mortality data in Spain, employing a three-way spatio-temporal interaction model.

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arXiv2021

Smart Gradient -- An Adaptive Technique for Improving Gradient Estimation

Computing the gradient of a function provides fundamental information about its behavior. This information is essential for several applications and algorithms across various fields. One common application that require gradients are optimization techniques such as stochastic gradient descent, Newton's method and trust region methods. However, these methods usually requires a numerical computation of the gradient at every iteration of the method which is prone to numerical errors. We propose a simple limited-memory technique for improving the accuracy of a numerically computed gradient in this gradient-based optimization framework by exploiting (1) a coordinate transformation of the gradient and (2) the history of previously taken descent directions. The method is verified empirically by extensive experimentation on both test functions and on real data applications. The proposed method is implemented in the R package smartGrad and in C++.

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arXiv2019

Joint models as latent Gaussian models - not reinventing the wheel

Joint models have received increasing attention during recent years with extensions into various directions; numerous hazard functions, different association structures, linear and non-linear longitudinal trajectories amongst others. Many of these resulted in new R packages and new formulations of the joint model. However, a joint model with a linear bivariate Gaussian association structure is still a latent Gaussian model (LGM) and thus can be implemented using most existing packages for LGM's. In this paper, we will show that these joint models can be implemented from a LGM viewpoint using the R-INLA package. As a particular example, we will focus on the joint model with a non-linear longitudinal trajectory, recently developed and termed the partially linear joint model. Instead of the usual spline approach, we argue for using a Bayesian smoothing spline framework for the joint model that is stable with respect to knot selection and hence less cumbersome for practitioners.

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