Bayesian empirical likelihood for ridge and lasso regressions

Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest is only considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.

Qualitative–Quantitative Warning Modeling of Energy Consumption Processes in Inland Waterway Freight Transport on River Sections for Environmental Management

The article concerns the assessment of the energy consumption of inland waterway freight transport on river sections in the context of environmental management. The research question was: Does the choice of the route determine the total energy consumption of inland waterway transport and therefore affect the potential of cargo transport of this mode? The article aims to indicate the directions of energy consumption by inland waterway freight transport depending on the route selection, the volume of transport, and the length of the route. The study was carried out on nine sections of the Odra River in Poland during the years 2015–2020. Statistical and econometric techniques were used, i.e., ANOVA, generalized linear models, Eta coefficients, Lasso and Ridge regularization, and X-average control charts (Six Sigma tool). Based on early warning models, river sections were identified that favor the rationalization of energy consumption in terms of the network. The sensitivity of the energy consumption of inland waterway transport to changes in the average distance and in the volume of transport was examined. With the use of Six Sigma tools, the instability of the energy consumption processes of inland waterway transport was identified, paying attention to the source of the mismatch, which was the increase in the average transport distance in the sections, where energy consumption increased due to the operational and navigation conditions of these sections.

Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data

Bayesian empirical likelihood (BEL) models are becoming increasingly popular as an attractive alternative to fully parametric models. However, they have only recently been applied to spatial data analysis for small area estimation. This study considers the development of spatial BEL models using two popular conditional autoregressive (CAR) priors, namely BYM and Leroux priors. The performance of the proposed models is compared with their parametric counterparts and with existing spatial BEL models using independent Gaussian priors and generalised Moran basis priors. The models are applied to two benchmark spatial datasets, simulation study and COVID-19 data. The results indicate promising opportunities for these models to capture new insights into spatial data. Specifically, the spatial BEL models outperform the parametric spatial models when the underlying distributional assumptions of data appear to be violated.