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Epidemiology is a field for evaluating the sources of illness and clinical effects in communities. Therefore, individuals are viewed globally in order to investigate the dynamics and the control of an infectious disease. However, any governmental spending on a pharmaceutical control policy in times of epidemics can lead to a state budget imbalance. For this matter, we study in this paper stochastic stability and optimization for a treatment strategy, where the infectious disease is characterized by the relapse aspect. We provided a stochastic threshold for extinction and persistence in mean. Then, we established a priori estimates of the optimal control, where we obtained sufficient and necessary conditions for the considered treatment problem of the stochastic epidemic model by applying the maximum condition on the Hamiltonian function and the Ekeland principle. We provide a characterization of stochastic optimal control and sensitivity analysis to discuss its impact on the basic reproduction number with numerical illustrations for the system to carry out our theoretical investigations.

This paper aims to incorporate a high order stochastic perturbation into a SIQR epidemic model with transient prophylaxis and lasting prophylaxis. The existence and uniqueness of the global positive solution is proven and a stochastic condition in order to study the extinction of an infectious disease is established. The existence of a stationary distribution for the stochastic epidemic model is investigated as well. Numerical simulations are conducted to support our theoretical results and an example of application with COVID-19 data from Canada is used to estimate the transmission rate and basic reproduction number while constructing a model fitting the data.

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.

Donald Andrew Dawson (Don Dawson) was born in 1937. He received a bachelor’s degree in 1958 and a master’s degree in 1959 from McGill University and a Ph.D. in 1963 from M.I.T. under the supervision of Henry P. McKean, Jr. Following an appointment at McGill University as professor for 7 years, he joined Carleton University in 1970 where he remained for the rest of his career. Among his many contributions to the theory of stochastic processes, his work leading to the creation of the Dawson–Watanabe superprocess and the analysis of its remarkable properties in describing the evolution in space and time of populations, stand out as milestones of modern probability theory. His numerous papers span the whole gamut of contemporary hot areas, notably the study of stochastic evolution equations, measure-valued processes, McKean–Vlasov limits, hierarchical structures, super-Brownian motion, as well as branching, catalytic and historical processes. He has over 200 refereed publications and 8 monographs, with an impressive number of citations, more than 7000. He is elected Fellow of the Royal Society and of the Royal Society of Canada, as well as Gold medalist of the Statistical Society of Canada and elected Fellow of the Institute of Mathematical Statistics. We realized this interview to celebrate the outstanding contribution of Don Dawson to 50 years of Stochastics at Carleton University.

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

Recently, two different copula-based approaches have been proposed to estimate the conditional quantile function of a variable Y with respect to a vector of covariates X : the first estimator is related to quantile regression weighted by the conditional copula density, while the second estimator is based on the inverse of the conditional distribution function written in terms of margins and the copula. Using empirical processes, we show that even if the two estimators look quite different, their estimation errors have the same limiting distribution. Also, we propose a bootstrap procedure for the limiting process in order to construct uniform confidence bands around the conditional quantile function.

The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula ( Nasri, 2019 ) can be used to estimate the parameters for several copula families.

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

In this paper, we consider non-stationary response variables and covariates, where the marginal distributions and the associated copula may be time-dependent. We propose estimators for the unknown parameters and we establish the limiting distribution of the estimators of the copula and the conditional copula, together with a parametric bootstrap method for constructing confidence bands around the estimator and for testing the adequacy of the model. We also consider three examples of functionals of the copula-based model under non-stationarity: conditional quantiles, conditional mean, and conditional expected shortfall. The asymptotic distribution of the estimation errors is shown to be Gaussian, and bootstrapping methods are proposed to estimate their asymptotic variances. The finite sample performance of our estimators is investigated through Monte Carlo experiments, and we show three examples of implementation of the proposed methodology.

In this paper, we propose an intuitive way to couple several dynamic time series models by inducing dependence between the so-called generalized errors of each model. This extends previous work for modelling dependance between innovations of stochastic volatility models. We consider time-independent and time-dependent copula models and we study the asymptotic behavior of some empirical processes constructed from pseudo-observations, as well as the behavior of pseudo-maximum likelihood estimators of the associated copula parameters. The results show that even if the generalized errors depend on unknown parameters, the limiting behaviour of many processes of interest do not depend on the estimation errors. One can easily perform tests of change-point on the full distribution, and the margins or the copula, as if the generalized errors were observed. For some interesting parametric models of time-dependent copulas, the same behavior is observed: one can work with the pseudo-observations, as if we were observing the generalized errors. This interesting property makes it possible to construct consistent tests of specification for the dependence models, without having to consider the dynamic time series models. An example of application with financial data is given.

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a flexible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.

The stationarity hypothesis is essential in hydrological frequency analysis and statistical inference. This assumption is often not fulfilled for large observed datasets, especially in the case of hydro-climatic variables. The Generalized Extreme Value distribution with covariates allows to model data in the presence of non-stationarity and/or dependence on covariates. Linear and non-linear dependence structures have been proposed with the corresponding fitting approach. The objective of the present study is to develop the GEV model with B-Spline in a Bayesian framework. A Markov Chain Monte Carlo (MCMC) algorithm has been developed to estimate quantiles and their posterior distributions. The methods are tested and illustrated using simulated data and applied to meteorological data. Results indicate the better performance of the proposed Bayesian method for rainfall quantile estimation according to BIAS and RMSE criteria especially for high return period events.

The high precipitation variability over North Africa presents a major challenge for the population and the infrastructure in the region. The last decades have seen many flood events caused by extreme precipitation in this area. There is a strong need to identify the most relevant atmospheric predictors to model these extreme events. In the present work, the effect of 14 different predictors calculated from NCEP–NCAR reanalysis, with daily to seasonal time steps, on the maximum annual precipitation (MAP) is evaluated at six coastal stations located in North Africa (Larache, Tangier, Melilla, Algiers, Tunis, and Gabès). The generalized extreme value (GEV) B-spline model was used to detect this influence. This model considers all continuous dependence forms (linear, quadratic, etc.) between the covariates and the variable of interest, thus providing a very flexible framework to evaluate the covariate effects on the GEV model parameters. Results show that no single set of covariates is valid for all stations. Overall, a strong dependence between the NCEP–NCAR predictors and MAP is detected, particularly with predictors describing large-scale circulation (geopotential height) or moisture (humidity). This study can therefore provide insights for developing extreme precipitation downscaling models that are tailored for North African conditions.

American (Anguilla rostrata) and European (Anguilla anguilla) eel populations are declining since the 1980s, and contamination is thought to play a role. To determine the influence of organic (organochlorinated pesticides (OCPs), polybrominated diphenyl ethers (PBDEs), polychlorinated biphenyls (PCBs)) and inorganic (Zn, As, Cd, Cu, Pb, Cr, Ni, Ag, Se, Hg) contaminants on wild yellow eels liver and muscle metabolic capacities, enzymatic assays were performed. In A. rostrata liver, G6PDH moderate negative correlations with Ag, Pb, and As suggest impacts on lipid metabolism, and correlations between Cd and age (positive) and between Cd and relative condition factor (Kn; negative) indicate impacts on older eels health. Anguilla anguilla liver proteins, pyruvate kinase (PK), and lactate dehydrogenase (LDH) were positively linked to Zn, Pb, and Cu, suggesting effects on glycolytic and anaerobic capacities. In A. anguilla muscle, absence of correlation between age and lipids plus strong positive correlations between age and OCPs, PBDEs, PCBs, and Hg suggest lipid storage impairment in older contaminated eels. Overall, our study indicates contamination impacts on both species’ metabolic capacities, but the broader range of contaminants found in A. anguilla brings greater impacts compared with A. rostrata.