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多代理指标重建历史气候的价值AI 解读

Understanding the dynamics of climate change in its full richness requires the knowledge of long temperature time series. Although long-term, widely distributed temperature observations are not available, there are other forms of data, known as climate proxies, that can have a statistical relationship with temperatures and have been used to infer temperatures in the past before direct measurements. We propose a Bayesian hierarchical model to reconstruct past temperatures…

大型空间数据集似然估计中的协方差截尾AI 解读

Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. But calculating the likelihood can be computationally infeasible for large data sets, requiring O(n3) calculations for a data set with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approach, covariance matrixes are “tapered,” or multiplied element wise by a sparse…

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用非参数回归估计混沌系统的李雅普诺夫指数AI 解读

We discuss procedures based on nonparametric regression for estimating the dominant Lyapunov Exponent λ1 from time series data generated by a nonlinear autoregressive system with additive noise. For systems with bounded fluctuations, λ1 > 0 is the defining feature of chaos. Thus our procedures can be used to examine time series data for evidence of chaotic dynamics. We show that a consistent estimator of the partial derivatives of the autoregression function can be used to…

离散含噪数据下积分方程正则化解的收敛速率AI 解读

Given data $y_i = (Kg)(u_i) + \varepsilon_i$ where the $\varepsilon$'s are random errors, the $u$'s are known, $g$ is an unknown function in a reproducing kernel space with kernel $r$ and $K$ is a known integral operator, it is shown how to calculate convergence rates for the regularized solution of the equation as the evaluation points $\{u_i\}$ become dense in the interval of interest. These rates are shown to depend on the eigenvalue asymptotics of $KRK^\ast$, where $R$ is…

半非参数最大似然估计AI 解读

Often maximum likelihood is the method of choice for fitting an econometric model to data but cannot be used because the correct specific ation of (multivariate) density that defines the likelihood is unknown. In this situation, simply put the density equal to a Hermite series and apply standard finite dimensional maximum likelihood methods. Model parameters and nearly all aspects of the unknown density itself will be estimated consistently provided that the length of the…