亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Recent methods in modeling spatial extreme events have focused on utilizing parametric max-stable processes and their underlying dependence structure. In this work, we provide a unified approach for analyzing spatial extremes with little available data by estimating the distribution of model parameters or the spatial dependence directly. By employing recent developments in generative neural networks we predict a full sample-based distribution, allowing for direct assessment of uncertainty regarding model parameters or other parameter dependent functionals. We validate our method by fitting several simulated max-stable processes, showing a high accuracy of the approach, regarding parameter estimation, as well as uncertainty quantification. Additional robustness checks highlight the generalization and extrapolation capabilities of the model, while an application to precipitation extremes across Western Germany demonstrates the usability of our approach in real-world scenarios.

We present a Bayesian method for multivariate changepoint detection that allows for simultaneous inference on the location of a changepoint and the coefficients of a logistic regression model for distinguishing pre-changepoint data from post-changepoint data. In contrast to many methods for multivariate changepoint detection, the proposed method is applicable to data of mixed type and avoids strict assumptions regarding the distribution of the data and the nature of the change. The regression coefficients provide an interpretable description of a potentially complex change. For posterior inference, the model admits a simple Gibbs sampling algorithm based on P\'olya-gamma data augmentation. We establish conditions under which the proposed method is guaranteed to recover the true underlying changepoint. As a testing ground for our method, we consider the problem of detecting topological changes in time series of images. We demonstrate that our proposed method $\mathtt{bclr}$, combined with a topological feature embedding, performs well on both simulated and real image data. The method also successfully recovers the location and nature of changes in more traditional changepoint tasks.

In the literature on spatial point processes, there is an emerging challenge in studying marked point processes with points being labelled by functions. In this paper, we focus on point processes living on linear networks and, from distinct points of view, propose several marked summary characteristics that are of great use in studying the average association and dispersion of the function-valued marks. Through a simulation study, we evaluate the performance of our proposed marked summary characteristics, both when marks are independent and when some sort of spatial dependence is evident among them. Finally, we employ our proposed mark summary characteristics to study the spatial structure of urban cycling profiles in Vancouver, Canada.

This paper investigates the application of mini-batch gradient descent to semiflows. Given a loss function, we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow. We prove that, under suitable assumptions on the gradient flow, the mini-batch descent flow trajectory closely approximates the original gradient flow trajectory on average. Additionally, we propose a randomized minimizing movement scheme that also approximates the gradient flow of the loss function. We illustrate the versatility of this approach across various problems, including constrained optimization, sparse inversion, and domain decomposition. Finally, we validate our results with several numerical examples.

In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the concentration of the chemotactic agent. By controlling the concentration of the chemical substrates, this study can guide the optimal growth of cells. The novelty of this work lies on the direct and dual models that remain in a weak setting, which is uncommon in the recent literature for solving optimal control systems. Moreover, it is known that the adjoint problems offer a powerful approach to quantifying the uncertainty associated with model inputs. However, these systems typically lack closed-form solutions, making it challenging to obtain weak solutions. For that, the well-posedness of the direct problem is first well guaranteed. Then, the existence of an optimal control and the first-order optimality conditions are established. Finally, weak solutions for the adjoint system to the non-linear degenerate direct model, are introduced and investigated.

A new approach based on censoring and moment criterion is introduced for parameter estimation of count distributions when the probability generating function is available even though a closed form of the probability mass function and/or finite moments do not exist.

Bayesian design can be used for efficient data collection over time when the process can be described by the solution to an ordinary differential equation (ODE). Typically, Bayesian designs in such settings are obtained by maximising the expected value of a utility function that is derived from the joint probability distribution of the parameters and the response, given prior information about an appropriate ODE. However, in practice, appropriately defining such information \textit{a priori} can be difficult due to incomplete knowledge about the mechanisms that govern how the process evolves over time. In this paper, we propose a method for finding Bayesian designs based on a flexible class of ODEs. Specifically, we consider the inclusion of spline terms into ODEs to provide flexibility in modelling how the process changes over time. We then propose to leverage this flexibility to form designs that are efficient even when the prior information is misspecified. Our approach is motivated by a sampling problem in agriculture where the goal is to provide a better understanding of fruit growth where prior information is based on studies conducted overseas, and therefore is potentially misspecified.

Characterized by an outer integral connected to an inner integral through a nonlinear function, nested integration is a challenging problem in various fields, such as engineering and mathematical finance. The available numerical methods for nested integration based on Monte Carlo (MC) methods can be prohibitively expensive owing to the error propagating from the inner to the outer integral. Attempts to enhance the efficiency of these approximations using the quasi-MC (QMC) or randomized QMC (rQMC) method have focused on either the inner or outer integral approximation. This work introduces a novel nested rQMC method that simultaneously addresses the approximation of the inner and outer integrals. The method leverages the unique nested integral structure to offer a more efficient approximation mechanism. Incorporating Owen's scrambling techniques, we address integrands exhibiting infinite variation in the Hardy--Krause sense, enabling theoretically sound error estimates. As the primary contribution, we derive asymptotic error bounds for the bias and variance of our estimator, along with the regularity conditions under which these bounds can be attained. Moreover, we derive a truncation scheme for applications in the context of expected information gain estimation and indicate how to use importance sampling to remedy the measure concentration arising in the inner integral. We verify the estimator quality through numerical experiments by comparing the computational efficiency of the nested rQMC method against standard nested MC estimation for two case studies: one in thermomechanics and the other in pharmacokinetics. These examples highlight the computational savings and enhanced applicability of the proposed approach.

Discrete choice models with non-monotonic response functions are important in many areas of application, especially political sciences and marketing. This paper describes a novel unfolding model for binary data that allows for heavy-tailed shocks to the underlying utilities. One of our key contributions is a Markov chain Monte Carlo algorithm that requires little or no parameter tuning, fully explores the support of the posterior distribution, and can be used to fit various extensions of our core model that involve (Bayesian) hypothesis testing on the latent construct. Our empirical evaluations of the model and the associated algorithm suggest that they provide better complexity-adjusted fit to voting data from the United States House of Representatives.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.