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At least 955 records · Page 53Linked to original sources

arXiv2023

Directional Gaussian spatial processes for South African wind data

Accurate wind pattern modelling is crucial for various applications, including renewable energy, agriculture, and climate adaptation. In this paper, we introduce the wrapped Gaussian spatial process (WGSP), as well as the projected Gaussian spatial process (PGSP) custom-tailored for South Africa's intricate wind behaviour. Unlike conventional models struggling with the circular nature of wind direction, the WGSP and PGSP adeptly incorporate circular statistics to address this challenge. Leveraging historical data sourced from meteorological stations throughout South Africa, the WGSP and PGSP significantly increase predictive accuracy while capturing the nuanced spatial dependencies inherent to wind patterns. The superiority of the PGSP model in capturing the structural characteristics of the South African wind data is evident. As opposed to the PGSP, the WGSP model is computationally less demanding, allows for the use of less informative priors, and its parameters are more easily interpretable. The implications of this study are far-reaching, offering potential benefits ranging from the optimisation of renewable energy systems to the informed decision-making in agriculture and climate adaptation strategies. The WGSP and PGSP emerge as robust and invaluable tools, facilitating precise modelling of wind patterns within the dynamic context of South Africa.

stat.AP↗

arXiv2023

edibble: An R package to encapsulate elements of experimental designs for better planning, management and workflow

I present an R package called edibble that facilitates the design of experiments by encapsulating elements of the experiment in a series of composable functions. This package is an interpretation of "the grammar of experimental designs" by Tanaka (2023) in the R programming language. The main features of the edibble package are demonstrated, illustrating how it can be used to create a wide array of experimental designs. The implemented system aims to encourage cognitive thinking for holistic planning and data management of experiments in a streamlined workflow. This workflow can increase the inherent value of experimental data by reducing potential errors or noise with careful preplanning, as well as, ensuring fit-for-purpose analysis of experimental data.

stat.CO↗

arXiv2023

Gaussian Differential Privacy on Riemannian Manifolds

We develop an advanced approach for extending Gaussian Differential Privacy (GDP) to general Riemannian manifolds. The concept of GDP stands out as a prominent privacy definition that strongly warrants extension to manifold settings, due to its central limit properties. By harnessing the power of the renowned Bishop-Gromov theorem in geometric analysis, we propose a Riemannian Gaussian distribution that integrates the Riemannian distance, allowing us to achieve GDP in Riemannian manifolds with bounded Ricci curvature. To the best of our knowledge, this work marks the first instance of extending the GDP framework to accommodate general Riemannian manifolds, encompassing curved spaces, and circumventing the reliance on tangent space summaries. We provide a simple algorithm to evaluate the privacy budget $μ$ on any one-dimensional manifold and introduce a versatile Markov Chain Monte Carlo (MCMC)-based algorithm to calculate $μ$ on any Riemannian manifold with constant curvature. Through simulations on one of the most prevalent manifolds in statistics, the unit sphere $S^d$, we demonstrate the superior utility of our Riemannian Gaussian mechanism in comparison to the previously proposed Riemannian Laplace mechanism for implementing GDP.

cs.CR↗

arXiv2023

A Bayesian Skew-heavy-tailed modelling for loss reserving

This paper focuses on modelling loss reserving to pay outstanding claims. As the amount liable on any given claim is not known until settlement, we propose a flexible model via heavy-tailed and skewed distributions to deal with outstanding liabilities. The inference relies on Markov chain Monte Carlo via Gibbs sampler with adaptive Metropolis algorithm steps allowing for fast computations and providing efficient algorithms. An illustrative example emulates a typical dataset based on a runoff triangle and investigates the properties of the proposed models. Also, a case study is considered and shows that the proposed model outperforms the usual loss reserving models well established in the literature in the presence of skewness and heavy tails.

stat.ME↗

arXiv2024

Quantifying the effectiveness of linear preconditioning in Markov chain Monte Carlo

We study linear preconditioning in Markov chain Monte Carlo. We consider the class of well-conditioned distributions, for which several mixing time bounds depend on the condition number $κ$. First we show that well-conditioned distributions exist for which $κ$ can be arbitrarily large and yet no linear preconditioner can reduce it. We then impose two sets of extra assumptions under which a linear preconditioner can significantly reduce $κ$. For the random walk Metropolis we further provide upper and lower bounds on the spectral gap with tight $1/κ$ dependence. This allows us to give conditions under which linear preconditioning can provably increase the gap. We then study popular preconditioners such as the covariance, its diagonal approximation, the hessian at the mode, and the QR decomposition. We show conditions under which each of these reduce $κ$ to near its minimum. We also show that the diagonal approach can in fact \textit{increase} the condition number. This is of interest as diagonal preconditioning is the default choice in well-known software packages. We conclude with a numerical study comparing preconditioners in different models, and showing how proper preconditioning can greatly reduce compute time in Hamiltonian Monte Carlo.

stat.CO↗

arXiv2024

On the Uplink and Downlink EMF Exposure and Coverage in Dense Cellular Networks: A Stochastic Geometry Approach

Existing studies analyzing electromagnetic field (EMFE) in wireless networks have primarily considered downlink communications. In the uplink, the EMFE caused by the user's smartphone is usually the only considered source of radiation, thereby ignoring contributions caused by other active neighboring devices. In addition, the network coverage and EMFE are typically analyzed independently for both the uplink and downlink, while a joint analysis would be necessary to fully understand the network performance and answer various questions related to optimal network deployment. This paper bridges these gaps by presenting an enhanced stochastic geometry framework that includes the above aspects. The proposed topology features base stations modeled via a homogeneous Poisson point process. The users active during a same time slot are distributed according to a mixture of a Matérn cluster process and a Gauss-Poisson process, featuring groups of users possibly carrying several equipments. In this paper, we derive the marginal and meta distributions of the downlink and uplink EMFE and we characterize the uplink to downlink EMFE ratio. Moreover, we derive joint probability metrics considering the uplink and downlink coverage and EMFE. These metrics are evaluated in four scenarios considering BS, cluster and/or intracluster densifications. Our numerical results highlight the existence of optimal node densities maximizing these joint probabilities.

cs.NI↗

arXiv2023

Applying Pre-Trained Deep-Learning Model on Wrist Angel Data -- An Analysis Plan

We aim to investigate if we can improve predictions of stress caused by OCD symptoms using pre-trained models, and present our statistical analysis plan in this paper. With the methods presented in this plan, we aim to avoid bias from data knowledge and thereby strengthen our hypotheses and findings. The Wrist Angel study, which this statistical analysis plan concerns, contains data from nine participants, between 8 and 17 years old, diagnosed with obsessive-compulsive disorder (OCD). The data was obtained by an Empatica E4 wristband, which the participants wore during waking hours for 8 weeks. The purpose of the study is to assess the feasibility of predicting the in-the-wild OCD events captured during this period. In our analysis, we aim to investigate if we can improve predictions of stress caused by OCD symptoms, and to do this we have created a pre-trained model, trained on four open-source data for stress prediction. We intend to apply this pre-trained model to the Wrist Angel data by fine-tuning, thereby utilizing transfer learning. The pre-trained model is a convolutional neural network that uses blood volume pulse, heart rate, electrodermal activity, and skin temperature as time series windows to predict OCD events. Furthermore, using accelerometer data, another model filters physical activity to further improve performance, given that physical activity is physiologically similar to stress. By evaluating various ways of applying our model (fine-tuned, non-fine-tuned, pre-trained, non-pre-trained, and with or without activity classification), we contextualize the problem such that it can be assessed if transfer learning is a viable strategy in this domain.

stat.AP↗

arXiv2023

Better Foundations for Subjective Probability

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents.

stat.OT↗

arXiv2026

Quantiles on global non-positive curvature spaces

This paper develops a notion of geometric quantiles on Hadamard spaces, also known as global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function at quantiles on Hadamard manifolds, we investigate asymptotic properties of sample quantiles on Hadamard manifolds, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space and, in particular, an explicit formula for the gradient of the quantile loss function, along with experiments using simulated and real single-cell RNA sequencing data.

math.ST↗

arXiv2023

Bayesian and minimax estimators of loss

We study the problem of loss estimation that involves for an observable $X \sim f_θ$ the choice of a first-stage estimator $\hatγ$ of $γ(θ)$, incurred loss $L=L(θ, \hatγ)$, and the choice of a second-stage estimator $\hat{L}$ of $L$. We consider both: (i) a sequential version where the first-stage estimate and loss are fixed and optimization is performed at the second-stage level, and (ii) a simultaneous version with a Rukhin-type loss function designed for the evaluation of $(\hatγ, \hat{L})$ as an estimator of $(γ, L)$. We explore various Bayesian solutions and provide minimax estimators for both situations (i) and (ii). The analysis is carried out for several probability models, including multivariate normal models $N_d(θ, σ^2 I_d)$ with both known and unknown $σ^2$, Gamma, univariate and multivariate Poisson, and negative binomial models, and relates to different choices of the first-stage and second-stage losses. The minimax findings are achieved by identifying least favourable of sequence of priors and depend critically on particular Bayesian solution properties, namely situations where the second-stage estimator $\hat{L}(x)$ is constant as a function of $x$.

math.ST↗

arXiv2023

Revisiting the effect of greediness on the efficacy of exchange algorithms for generating exact optimal experimental designs

Coordinate exchange (CEXCH) is a popular algorithm for generating exact optimal experimental designs. The authors of CEXCH advocated for a highly greedy implementation - one that exchanges and optimizes single element coordinates of the design matrix. We revisit the effect of greediness on CEXCHs efficacy for generating highly efficient designs. We implement the single-element CEXCH (most greedy), a design-row (medium greedy) optimization exchange, and particle swarm optimization (PSO; least greedy) on 21 exact response surface design scenarios, under the $D$- and $I-$criterion, which have well-known optimal designs that have been reproduced by several researchers. We found essentially no difference in performance of the most greedy CEXCH and the medium greedy CEXCH. PSO did exhibit better efficacy for generating $D$-optimal designs, and for most $I$-optimal designs than CEXCH, but not to a strong degree under our parametrization. This work suggests that further investigation of the greediness dimension and its effect on CEXCH efficacy on a wider suite of models and criterion is warranted.

stat.ME↗

arXiv2025

The many routes to the ubiquitous Bradley-Terry model

The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and explain a variety of motivations for its use. Some are based on principles or on maximising an objective function; others are derived from well-known statistical models, or stylised game scenarios. They include both examples well-known in the literature as well as what are believed to be novel presentations.

math.ST↗

arXiv2024

Facilitating the Integration of Ethical Reasoning into Quantitative Courses: Stakeholder Analysis, Ethical Practice Standards, and Case Studies

Case studies are typically used to teach 'ethics', but in quantitative courses it can seem distracting, for both instructor and learner, to introduce a case analysis. Moreover, case analyses are typically focused on issues relating to people: obtaining consent, dealing with research team members, and/or potential institutional policy violations. While relevant to some research, not all students in quantitative courses plan to become researchers, and ethical practice is an essential topic for students of of mathematics, statistics, data science, and computing regardless of whether or not the learner intends to do research. Ethical reasoning is a way of thinking that requires the individual to assess what they know about a potential ethical problem (their prerequisite knowledge), and in some cases, how behaviors they observe, are directed to perform, or have performed, diverge from what they know to be ethical behavior. Ethical reasoning is a learnable, improvable set of knowledge, skills, and abilities that enable learners to recognize what they do and do not know about what constitutes 'ethical practice' of a discipline, and in some cases, to contemplate alternative decisions about how to first recognize, and then proceed past, or respond to, such divergences. A stakeholder analysis is part of prerequisite knowledge, and can be used whether there is or is not an actual case or situation to react to. In courses with mainly quantitative content, a stakeholder analysis is a useful tool for instruction and assessment. It can be used to both integrate authentic ethical content and encourage careful quantitative thought. It is a mistake to treat 'training in ethical practice' and 'training in responsible conduct of research' as the same thing. This paper discusses how to introduce ethical reasoning, stakeholder analysis, and ethical practice standards authentically in quantitative courses.

stat.OT↗

arXiv2024

ceylon: An R package for plotting the maps of Sri Lanka

The rapid evolution in the fields of computer science, data science, and artificial intelligence has significantly transformed the utilisation of data for decision-making. Data visualisation plays a critical role in any work that involves data. Visualising data on maps is frequently encountered in many fields. Visualising data on maps not only transforms raw data into visually comprehensible representations but also converts complex spatial information into simple, understandable form. Locating the data files necessary for map creation can be a challenging task. Establishing a centralised repository can alleviate the challenging task of finding shape files, allowing users to efficiently discover geographic data. The ceylon R package is designed to make simple feature data related to Sri Lanka's administrative boundaries and rivers and streams accessible for a diverse range of R users. With straightforward functionalities, this package allows users to quickly plot and explore administrative boundaries and rivers and streams in Sri Lanka.

stat.OT↗

arXiv2024

Quotient geometry of bounded or fixed rank correlation matrices

This paper studies the quotient geometry of bounded or fixed-rank correlation matrices. We establish a bijection between the set of bounded-rank correlation matrices and a quotient set of a spherical product manifold by an orthogonal group. We show that it forms an orbit space, whose stratification is determined by the rank of the matrices, and the principal stratum has a compatible Riemannian quotient manifold structure. We show that any minimizing geodesic in the orbit space has constant rank on the interior of the segment. We also develop efficient Riemannian optimization algorithms for computing the distance and weighted the Frechet mean in the orbit space. Moreover, we examine geometric properties of the quotient manifold, including horizontal and vertical spaces, Riemannian metric, injectivity radius, exponential and logarithmic map, curvature, gradient and Hessian. Finally, we apply our approach to a functional connectivity study using the Autism Brain Imaging Data Exchange.

math.MG↗

arXiv2024

Introduction to probability and statistics: a computational framework of randomness

This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary probability and theory of distributions, the material progresses towards conceptual and advances in prediction and generalization in statistical models and large sample theory. We also pay special attention to unified derivation approach and one-shot proof of each and every probabilistic concept. Our presentation of intuitive and computation framework of conditional distribution and probability are strongly influenced by unified patterns of linear models for regression and for classification. The text ends with a future note on the unified approximation of the linear models, the generalized linear models and the discovery models to neural networks and a summarized ML system.

math.HO↗

arXiv2024

Asymptotic Normality of the Conditional Value-at-Risk based Pickands Estimator

The Pickands estimator for the extreme value index is beneficial due to its universal consistency, location, and scale invariance, which sets it apart from other types of estimators. However, similar to many extreme value index estimators, it is marked by poor asymptotic efficiency. Chen (2021) introduces a Conditional Value-at-Risk (CVaR)-based Pickands estimator, establishes its consistency, and demonstrates through simulations that this estimator significantly reduces mean squared error while preserving its location and scale invariance. The initial focus of this paper is on demonstrating the weak convergence of the empirical CVaR in functional space. Subsequently, based on the established weak convergence, the paper presents the asymptotic normality of the CVaR-based Pickands estimator. It further supports these theoretical findings with empirical evidence obtained through simulation studies.

math.ST↗

arXiv2024

Graph fission and cross-validation

We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge set in a way that splits the original graph's information amongst them in any desired proportion. Our proposal builds on data fission/thinning, a method that uses external randomization to create independent copies of an unstructured dataset. We extend this idea to the graph setting where there may be latent structure between observations. We demonstrate the utility of this framework via two applications: inference after structural trend estimation on graphs and a model selection procedure we term "graph cross-validation".

stat.ME↗