Related papers: Nonparametric geostatistical risk mapping
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…
We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a…
Wavelet thresholding generally assumes independent, identically distributed normal errors when estimating functions in a nonparametric regression setting. VisuShrink and SureShrink are just two of the many common thresholding methods based…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can…
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…