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We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…

Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…

Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input…

The spatial structure of fluctuations in spatially inhomogeneous processes can be modeled in terms of Gibbs random fields. A local low energy estimator (LLEE) is proposed for the interpolation (prediction) of such processes at points where…

The four-dimensional nonlinear model is extended to include the inter-channel stimulated Raman scattering, enabling accurate prediction of dual-polarization four-dimensional modulation formats and probabilistically shaped constellations in…

To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…

The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

The problem of distributed identification of linear stochastic system with unknown coefficients over time-varying networks is considered. For estimating the unknown coefficients, each agent in the network can only access the input and the…

Regression for spatially dependent outcomes poses many challenges, for inference and for computation. Non-spatial models and traditional spatial mixed-effects models each have their advantages and disadvantages, making it difficult for…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Autonomous robots are increasingly deployed to estimate spatiotemporal fields (e.g., wind, temperature, gas concentration) that vary across space and time. We consider environments divided into non-overlapping regions with distinct spatial…

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…

In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the…

The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform…

We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…

The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…