Tests of independence and randomness for arbitrary data using copula-based covariances

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using M\"obius transforms. We find the asymptotic distributions of the statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald's type combinations of these statistics to assess the finite sample performance

On factor copula-based mixed regression models

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and the effect of a common latent variable pertaining to a cluster is modelled with a factor copula. We show how to estimate the parameters of the copula and the parameters of the margins, and we find the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of an application is given using COVID-19 vaccination hesitancy from several countries. Computations are based on R package CopulaGAMM

Assessing the Impact of Mutations and Horizontal Gene Transfer on the AMR Control: A Mathematical Model

Antimicrobial resistance (AMR) poses a significant threat to public health by increasing mortality, extending hospital stays, and increasing healthcare costs. It affects people of all ages and affects health services, veterinary medicine, and agriculture, making it a pressing global issue. Mathematical models are required to predict the behaviour of AMR and to develop control measures to eliminate resistant bacteria or reduce their prevalence. This study presents a simple deterministic mathematical model in which sensitive and resistant bacteria interact in the environment, and mobile genetic elements (MGEs) are functions that depend on resistant bacteria. We analyze the qualitative properties of the model and propose an optimal control problem in which avoiding mutations and horizontal gene transfer (HGT) are the primary control strategies. We also provide a case study of the resistance and multidrug resistance (MDR) percentages of Escherichia coli to gentamicin and amoxicillin in some European countries using data from the European Antimicrobial Resistance Surveillance Network (EARS-Net). Our theoretical results and numerical experiments indicate that controlling the spread of resistance in southern European regions through the supply of amoxicillin is challenging. However, the host immune system is also critical for controlling AMR.Comment: 1

Forecast of streamflows to the Arctic Ocean by a Bayesian neural network model with snowcover and climate inputs

Increasing water flowing into the Arctic Ocean affects oceanic freshwater balance, which may lead to the thermohaline circulation collapse and unpredictable climatic conditions if freshwater inputs continue to increase. Despite the crucial role of ocean inflow in the climate system, less is known about its predictability, variability, and connectivity to cryospheric and climatic patterns on different time scales. In this study, multi-scale variation modes were decomposed from observed daily and monthly snowcover and river flows to improve the predictability of Arctic Ocean inflows from the Mackenzie River Basin in Canada. Two multi-linear regression and Bayesian neural network models were used with different combinations of remotely sensed snowcover, in-situ inflow observations, and climatic teleconnection patterns as predictors. The results showed that daily and monthly ocean inflows are associated positively with decadal snowcover fluctuations and negatively with interannual snowcover fluctuations. Interannual snowcover and antecedent flow oscillations have a more important role in describing the variability of ocean inflows than seasonal snowmelt and large-scale climatic teleconnection. Both models forecasted inflows seven months in advance with a Nash–Sutcliffe efficiency score of ≈0.8. The proposed methodology can be used to assess the variability of the freshwater input to northern oceans, affecting thermohaline and atmospheric circulations

Identifiability and inference for copula-based semiparametric models for random vectors with arbitrary marginal distributions

In this paper, we study the identifiability and the estimation of the parameters of a copula-based multivariate model when the margins are unknown and are arbitrary, meaning that they can be continuous, discrete, or mixtures of continuous and discrete. When at least one margin is not continuous, the range of values determining the copula is not the entire unit square and this situation could lead to identifiability issues that are discussed here. Next, we propose estimation methods when the margins are unknown and arbitrary, using pseudo log-likelihood adapted to the case of discontinuities. In view of applications to large data sets, we also propose a pairwise composite pseudo log-likelihood. These methodologies can also be easily modified to cover the case of parametric margins. One of the main theoretical result is an extension to arbitrary distributions of known convergence results of rank-based statistics when the margins are continuous. As a by-product, under smoothness assumptions, we obtain that the asymptotic distribution of the estimation errors of our estimators are Gaussian. Finally, numerical experiments are presented to assess the finite sample performance of the estimators, and the usefulness of the proposed methodologies is illustrated with a copula-based regression model for hydrological data. The proposed estimation is implemented in the R package CopulaInference, together with a function for checking identifiability.Comment: 5 figure

Forecast of streamflows to the Arctic Ocean by a Bayesian neural network model with snowcover and climate inputs

Abstract Increasing water flowing into the Arctic Ocean affects oceanic freshwater balance, which may lead to the thermohaline circulation collapse and unpredictable climatic conditions if freshwater inputs continue to increase. Despite the crucial role of ocean inflow in the climate system, less is known about its predictability, variability, and connectivity to cryospheric and climatic patterns on different time scales. In this study, multi-scale variation modes were decomposed from observed daily and monthly snowcover and river flows to improve the predictability of Arctic Ocean inflows from the Mackenzie River Basin in Canada. Two multi-linear regression and Bayesian neural network models were used with different combinations of remotely sensed snowcover, in-situ inflow observations, and climatic teleconnection patterns as predictors. The results showed that daily and monthly ocean inflows are associated positively with decadal snowcover fluctuations and negatively with interannual snowcover fluctuations. Interannual snowcover and antecedent flow oscillations have a more important role in describing the variability of ocean inflows than seasonal snowmelt and large-scale climatic teleconnection. Both models forecasted inflows seven months in advance with a Nash–Sutcliffe efficiency score of ≈0.8. The proposed methodology can be used to assess the variability of the freshwater input to northern oceans, affecting thermohaline and atmospheric circulations