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Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…

Acquiring a substantial number of data points for training accurate machine learning (ML) models is a big challenge in scientific fields where data collection is resource-intensive. Here, we propose a novel approach for constructing a…

Bayesian probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…

Machine learning (ML) is playing an increasingly important role in scientific research. In conjunction with classical statistical approaches, ML-assisted analytical strategies have shown great promise in accelerating research findings. This…

The accuracy and precision of high-energy spallation models are key issues for the design and development of new applications and experiments. We present a method to estimate model parameters and associated uncertainties by leveraging the…

Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…

We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the…

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…

Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and…

State of the art large language models (LLMs) have shown impressive performance on a variety of benchmark tasks and are increasingly used as components in larger applications, where LLM-based predictions serve as proxies for human…

We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between…

Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix…

Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

The Potts model is frequently used to describe the behavior of image classes, since it allows to incorporate contextual information linking neighboring pixels in a simple way. Its isotropic version has only one real parameter beta, known as…

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…

Predicting the mechanical properties of polysulfone (PSF) membranes from structural descriptors remains challenging due to extreme data scarcity typical of experimental studies. To investigate this issue, this study benchmarked…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares…