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The COVID-19 pandemic led to unprecedented changes in the U.S. price of softwood lumber by more than 300% between 2020 and 2022. The increased volatility of lumber prices after the COVID-19 outbreak remains unexplained. In this paper, we examine how a calibrated random walk can induce similar price volatility through the development of a stochastic process. As a preferred approach, we employ an event model to estimate the impact of COVID-19 and other key events on the price of softwood lumber. The econometric model serves to provide evidence that the price volatility of softwood lumber is not completely random, and we can instead attribute part of the variation to recent regional and global events. We found that, while COVID-19 did result in a price jump, it was smaller than a rainfall event that restricted imports from Canada, while import duties and other trade actions had no discernible impact on U.S. lumber prices. [ABSTRACT FROM AUTHOR]

The paper proposes a novel framework based on the contract theory and Lyapunov optimization for content sharing in a wireless content delivery network (CDN) with edge caching and device-to-device (D2D) communications. The network is partitioned into a set of clusters. In a cluster, users can share contents via D2D links in coordination with the cluster head. Upon receiving the content request from any user in its cluster, the cluster head either delivers the content itself or forwards the request to another node, i.e., a base station (BS) or another user in the cluster. The content access at the BS and in each cluster is modeled as a queuing system, where arrivals represent the content requests directed to respective nodes. The objective is to assign content delivery nodes to stabilize all queues while minimizing the time-averaged network cost given incomplete information about content sharing costs of the users and unknown distribution of the network state defined by users’ locations and their cached/requested content. The proposed framework allows the users to truthfully reveal their content sharing expenditures, minimize the time-averaged network cost and stabilize the queuing system representing the CDN. Based on this framework, a distributed content access and delivery algorithm where the node assignments are made by every cluster head independently is developed. It is shown that the algorithm converges to the optimal policy with the trade-off in total queue backlog and achieves a superior performance compared with some other D2D content sharing policies. [ABSTRACT FROM AUTHOR]

In this work, we are concerned with nonparametric estimation of the distribution function when the data are possibly censored and satisfy the α -mixing condition, also called strong mixing. Among various mixing conditions used in the literature, α -mixing is reasonably weak and has many practical applications as it is fulfilled by many stochastic processes including some time series models. In practice the observed data can be complete or subject to censorship, so we deal with these different cases. More precisely, the rate of the almost complete convergence is established, under the α -mixing condition, for complete, singly censored and twice censored data. To lend further support to our theoretical results, a simulation study is carried out to illustrate the good accuracy of the studied method, for relatively small sample sizes. Finally, an application to censored dependent data is provided via the analysis of Chromium concentrations collected from two stations of the Niagara River in Canada. [ABSTRACT FROM AUTHOR]

This is a slightly expanded version of the plenary lecture the author gave at the International Congress on Mathematical Physics 2018 in Montreal, Canada. Reported are some work of the author and collaborators as well as related results of others on two kinds of dynamical systems: the first kind is deterministic (in the sense that nothing is left to chance) but is chaotic and unpredictable, and the second kind has a stochastic component in addition to a purely deterministic one. These two kinds of dynamical systems are compared and contrasted. The main points are that time series of observations from chaotic deterministic systems obey some of the same probabilistic limit laws as genuinely random stochastic processes, but random dynamical systems enjoy nicer properties and are technically more tractable. [ABSTRACT FROM AUTHOR]

Since the publication of the seminal papers by Black and Scholes and Merton on the pricing of options and corporate liabilities, their basic framework has been extended and applied to a variety of problems in finance. More recently, the same framework has been used for the valuation of interest dependent claims, and in particular for the pricing of default free bonds. These securities (generally government bonds of various types) are valued by treating them as "contingent" upon the course of one or more interest rates, along with suitable assumptions about the term structure of interest rates. Brennan and Schwartz assume that the value of a default free bond is a function solely of the instantaneous interest rate and time to maturity, and show that various types of bonds—savings bonds, retractable and extendible bonds, and callable bonds—all follow the same partial differential equation as discount bonds, the distinguishing feature being the associated boundary conditions. Taking into account the considerable theoretical work that has been done, there is relatively little published empirical research testing these models. Most of the empirical work in the area of contingent claims analysis has been on the stock options market, with the exception of Ingersoll on the pricing of dual fund shares and Brennan and Schwartz on the valuation of Canadian Federal Government coupon bonds. In this paper contingent claims analysis is applied to the valuation of retractable and extendible bonds and the resultant model is then applied to price Government of Canada bonds. [ABSTRACT FROM AUTHOR]

Summary Intensity–Duration–Frequency (IDF) curves are typically used as a standard design tool for various engineering applications, such as storm water management systems. Warming climate, however, changes the extreme precipitation quantiles represented by the IDF curves. This study attempts to construct the future IDF curves in Saskatoon, Canada, under possible climate change scenarios. For this purpose, a stochastic weather generator was used to spatially downscale the daily projections of Global Climate Models (GCMs) from coarse grid resolution to the local point scale. The stochastically downscaled daily precipitation realizations were further disaggregated to ensembles of hourly and sub-hourly (as fine as 5-min) series using a disaggregation scheme developed based on the K-nearest neighbor (K-NN) technique. This framework was applied to construct the future IDF curves in the city of Saskatoon. The sensitivity of the K-NN disaggregation model to the number of nearest neighbors (i.e. window size) was evaluated during the baseline period (1961–1990). The optimum window size was assigned based on the performance in reproducing the historical IDF curves. By using the simulated hourly and sub-hourly precipitation series and the Generalized Extreme Value (GEV) distribution, future changes in IDF curves and associated uncertainties were quantified using a large ensemble of projections obtained from eight GCMs and three representative concentration pathways – RCP2.6, RCP4.5, and RCP8.5. The constructed IDF curves were then compared with the corresponding historical ones and the IDF curves constructed using another genetic programming-based published method. The results show that the sign and the magnitude of future variations in extreme precipitation quantiles are sensitive to the selection of GCMs and/or RCPs, which seem to get intensified toward the end of the 21st century. The quantification of uncertainties suggests that GCMs are the main contributor to the uncertainty, followed by RCPs and the downscaling method. [ABSTRACT FROM AUTHOR]

Since mid-February 2013, the ensemble Kalman filter (EnKF) in operation at the Canadian Meteorological Centre (CMC) has been using a 600 × 300 global horizontal grid and 74 vertical levels. This yields 5.4 × 107 model coordinates. The EnKF has 192 members and uses seven time levels, spaced 1 h apart, for the time interpolation in the 6-h assimilation window. It follows that over 7 × 1010 values are required to specify an ensemble of trial field trajectories. This paper focuses on numerical and computational aspects of the EnKF. In response to the increasing computational challenge posed by the ever more ambitious configurations, an ever larger fraction of the EnKF software system has gradually been parallelized over the past decade. In a strong scaling experiment, the way in which the execution time decreases as larger numbers of processes are used is investigated. In fact, using a substantial fraction of one of the CMC's computers, very short execution times are achieved. As it would thus appear that the CMC's computers can handle more demanding configurations, weak scaling experiments are also performed. Here, both the size of the problem and the number of processes are simultaneously increased. The parallel algorithm responds well to an increase in either the number of ensemble members or the number of model coordinates. A substantial increase (by an order of magnitude) in the number of assimilated observations would, however, be more problematic. Thus, to the extent that this depends on computational aspects, it appears that the meteorological quality of the Canadian operational EnKF can be further improved. [ABSTRACT FROM AUTHOR]

Abstract: A stochastic, quantitative risk assessment model was developed to evaluate the public health risks associated with consumption of ground beef and beef cuts contaminated with Escherichia coli O157:H7 in Canada. The objectives of this work were to evaluate the relative effects of pre-harvest and processing interventions on public health risks using a novel approach, and compare the baseline risks from consumption of ground beef, non-intact beef cuts, and intact beef cuts. Rather than considering efficacy of all interventions at primary production and processing as default values, the model incorporated findings from critical systematic review and meta-analysis of published literature. Public health risks, expressed as average probability of illness per serving, were reduced by 30.9%–72.1%, 44.0%–96.5%, and 95.1%–99.9%, for single pre-harvest interventions, single processing interventions excluding water spray chilling, and combinations of interventions, respectively, relative to a worst-case scenario where no pre-harvest or processing interventions were applied. Combinations of interventions applied at pre-harvest and throughout processing resulted in the greatest relative risk reductions through their effects on both prevalence and concentration of the pathogen in cattle faeces and on cattle carcasses. The use of systematic review methodology to critically assess the results of scientific studies before use of the data in risk modelling enhances the confidence in risk predictions and provides a more evidenced-based model for public health analyses. Analysis of conditions reflective of current practices in Canada indicated that risks from consumption of ground beef were approximately two to three orders of magnitude greater than those for beef cuts, suggesting that risk management measures should focus on the former product to maximize benefits to public health. Risks from consumption of non-intact beef cuts, that is, steaks or roasts that are tenderized, were an order of magnitude greater than those for intact beef cuts. The model provides a useful tool to compare relative efficacies of different intervention strategies to determine their potential impact on public health risks. This tool can be used to evaluate an essentially limitless combination of intervention scenarios and can be adapted to include interventions applied at different points along the farm-to-fork continuum as critically-reviewed data become available. [Copyright &y& Elsevier]

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi-likelihood-based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427-446; 2012 © 2012 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Modelling for marked point processes is an important problem, but has received remarkably little attention in the statistical literature. The authors developed a marked point process model that incorporates the use of functional data analysis in a joint estimation of the frequency function of the point process and the intensity of the mark, with application to data from 22 lupus patients consisting of times of flares in symptom severity combined with a quantitative assessment of the severity. The data indicate that a rapid decrease in drug dose is significantly associated with a decrease in flare frequency. Experiments with simulated data designed to model the actual data further support this conclusion. The Canadian Journal of Statistics 40: 517-529; 2012 © 2012 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Abstract: A novel statistical technique has been applied to the AG-48 seismic line from the LITHOPROBE dataset, passing through the Abitibi–Grenville Province, Canada. The method maps lateral stochastic parameters, representing von Karman heterogeneity distributions in the crust, estimated from migrated deep reflection data. Together with these parameters, viz. lateral correlation length and power-law exponent, we also compute their associated maximum-likelihood uncertainties. Combining normalised measurements of lateral correlation and their uncertainties, objective profiles of crustal fabric can be made. These profiles indicate significant spatial variations in macro-scale petrofabric. Correlation length, which carries useful information about structural scale lengths of heterogeneous bodies, is an especially robust parameter with moderate associated uncertainties. Although the general outline of the profiles conforms to the earlier tectonic interpretations (based on line-drawings), new features are visible too. The macro-scale petrofabric is seen to vary significantly within the tectonic terrains identified earlier — in depth as well as laterally. A consequence of this additional delineation is that we can explain an existing part of the AG-48 line equally well in terms of collisional deformation and in terms of the effects of a major shear zone projected onto a parallel segment of the line. [Copyright &y& Elsevier]

spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients are applied to a spectral representation of Newton's integral. In this study we utilise Molodensky's truncation coefficients in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms of Molodensky's truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data. [ABSTRACT FROM AUTHOR]

This article presents a history of queueing theory done by Canadian researchers prior to 1980 and includes an extensive bibliography. [ABSTRACT FROM AUTHOR]

We introduce a class of multivariate seasonal time series models with periodically varying parameters, abbreviated by the acronym SPVAR. The model is suitable for multivariate data, and combines a periodic autoregressive structure and a multiplicative seasonal time series model. The stationarity conditions (in the periodic sense) and the theoretical autocovariance functions of SPVAR stochastic processes are derived. Estimation and checking stages are considered. The asymptotic normal distribution of the least squares estimators of the model parameters is established, and the asymptotic distributions of the residual autocovariance and autocorrelation matrices in the class of SPVAR time series models are obtained. In order to check model adequacy, portmanteau test statistics are considered and their asymptotic distributions are studied. A simulation study is briefly discussed to investigate the finite-sample properties of the proposed test statistics. The methodology is illustrated with a bivariate quarterly data set on travelers entering in to Canada. [ABSTRACT FROM AUTHOR]

The conventional economic evaluation technique that is currently used to evaluate the economic viability of mining operations has three important pitfalls. First, the probability distributions of key variables fed into the simulation process are in most part subjective and not based in a solid scientific ground. Second, the simulation method applied to generate metal prices paths results in unrealistic jumps and falls between the consecutive discrete time steps throughout the same simulated path. Third, the conventional technique implements a static production model in which the flexibility to alter the production policy is not applicable. These three pitfalls can impact the accuracy of evaluation results and consequently can lead to suboptimal production decisions. This paper presents an economic evaluation technique for mining projects based on the real options theory. This technique is based on generating future simulated metal price paths using the appropriate stochastic process for each metal. More important, the technique implements a flexible production model in which the production policy can be revised according to the new market information. To illustrate the difference the proposed improvements can make in the evaluations results, both the conventional and the new technique are applied to investigate the economic viability of some marginal mining zones based on data from Xstrata's Raglan mine. It has been found that the differences in the evaluation results between the two techniques range between $CAD082 million and as high as $CAD325 million depending on the size of the subzone, and for the total zone value, the difference is $CAD655 million. [ABSTRACT FROM AUTHOR]

Human life expectancy has risen in most developed countries over the last century, causing the observed demographic shifts. Babel, Bomsdorf and Schmidt (forthcoming) introduce a stochastic mortality model using panel data procedures which distinguishes between a common time effect and a common age effect of mortality evolvement. Using this mortality model, the present paper provides forecasts of future life expectancy for 17 countries divided into 12 regions: Australia, Alps, Bene, Canada, England and Wales, France, Germany, Italy, Japan, Spain, Scandinavia and the United States of America. We consider (traditional) period life expectancies as well as cohort life expectancies, the latter being a more realistic approach but less common. It turns out that a continuing increase of life expectancy is expected in all considered countries. Further, we show that the probabilistic uncertainty of forecast life expectancies is different if either period life expectancies or cohort life expectancies are considered and, moreover, the uncertainty increases substantially if the error of parameter estimation is included. [ABSTRACT FROM AUTHOR]

A major limitation of K-nearest neighbor based weather generators is that they do not produce new values but merely reshuffle the historical data to generate realistic weather sequences. In this paper, a modified approach is developed that allows nearest neighbor resampling with perturbation of the historic data. A strategy is introduced that resamples the historical data with perturbations while preserving the prominent statistical characteristics, including the interstation correlations. The approach is similar in spirit to traditional autoregressive models except that the new values are obtained by adding a random component to the individual resampled data points. An advantage of the approach is that unprecedented precipitation amounts are generated that are important for the simulation of extreme events. The approach is demonstrated through application to the Upper Thames River Basin in Ontario. Daily weather variables (maximum temperature, minimum temperature, and precipitation) were simulated at multiple stations in and around the basin. Analysis of the simulated data demonstrated the ability of the model to reproduce important statistical parameters of the observed data series while allowing perturbations to the observed data points. Additionally, no site-specific assumptions regarding the probability distribution of variables are required. [ABSTRACT FROM AUTHOR]

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Using Canadian data, the consumption-based asset pricing model is studied, defined in terms of nondurable and durable goods consumption. A two-stage estimation procedure is used, which takes account of the presence of common stochastic trends in the forcing processes. This method yields more reasonable estimates of the preference parameters than the previous studies did, and the asset-pricing equation is not rejected by the data. Moreover, the preference specification adopted in this paper allows a number of useful economic information to be obtained. The additive separability assumption and the Cobb-Douglas functional form of the utility function are ruled complements in the sense of Edgeworth and Pareto. [ABSTRACT FROM AUTHOR]

Examines the significance of temporal aggregation of multivariate processes on economics. Effects of aggregation on the characteristic properties of Canadian interest rates; Use of the stochastic process in gathering frequency data; Significance of the autoregressive integrated moving average in vector analysis and sampling.

The author proposes to treat the growth of Alberta urban areas as an absorbing Markov chain. The transition matrix is derived from the experience of all urban areas in Canada from 1901 to 1951. The matrix is tested using Alberta urban areas from 1931 to 1971 and found to have a fairly good fit. A projection is made to urban areas in Alberta in 1981. Urbanization is without a doubt the greatest social revolution in human history. From 1800 to 1950 world population increased two and a half times, while the population of urban places of 5,000 or more increased 26 times. Over the 150 years, the percentage of world population living in urban places of 5,000 or more increased from three to 30. Canada, in spite of late start as a populous area, and in spite of its early function as a colony and provider of raw materials, was always one of the most urbanized countries in the world. Projections of urban growth usually focus on the aggregate size of the urban population or on the size of individual cities. The disadvantage of the projection of aggregate urban populations is that no clue is given as to the distribution of the urban population among cities.

Discusses the stochastic properties of Canadian exchange rates as dealt with by Akgiray and Booth in `Modeling the Stochastic Behavior of Canadian Foreign exchange rates,' published in the Journal of Multinational Financial Management, Volume 1, 1993. Use of EGARCH-M model; Measurement of kurtosis; Exploration ot transmission mechanisms of innovation and volatility shocks.

Single-factor duration models of bond returns are derived from an underlying stochastic process of the term structure of interest rates. It is shown that beta in these models is a function of the parameters of the stochastic process and of implied measures of duration. Using unsmoothed Canadian monthly prices on default-free government bonds, the single-factor duration model is found to perform well from 1963 to 1986, but the hypothesis of stationarity of the duration-based bond returns model for the period cannot be accepted. Some of the underlying stochastic processes imply stationary models and some of them imply nonstationary bond return models. The models of this paper open the door to a variety of linear bond return models having a strong theoretical support based on a theory of the stochastic motion of the term structure. [ABSTRACT FROM AUTHOR]

This paper deals with theoretical and empirical aspects of firm behaviour under imperfect competition and uncertainty. It contains an analysis of the behaviour of a firm facing a stochastic demand curve for its output in the ordinary (home market), but in addition with access to a backstop (international) market. The theory is thus a variation of the theory of dumping. Since the expected volume in general differs from the volume at the expected price, a price-setting mode is not equal to a quantity mode. Cyclical dumping, in the sense of a negative correlation between domestic and foreign sales, would occur if the firm adhered to a pricing mode in the ordinary market, and was able to learn about the demand conditions in the ordinary market before it decided how much to sell in the international market. The empirical part of the paper is an illustration of how to test for different behavioural modes and cyclical dumping by applying the model to the Canadian pulp and paper industry. In the empirical exercise the domestic markets are the North American market for pulp and newsprint, while the backstop market are the corresponding European markets. One of the main results of this exercise is that the Canadian industry seems to operate under pricing behaviour for both pulp and newsprint, while cyclical dumping on the European market applies only for pulp. [ABSTRACT FROM AUTHOR]

A model of the current account using a mean-reverting Ornstein-Uhlenbeck process is developed and tested for three different measures of the current account. The results show very different adjustment patterns for the current accounts of seven large developed countries. This information can be very useful for further detailed analysis of behaviour within these individual countries. We find that with the exception of Canada and Japan all countries have a constant long-term mean which, in most cases, was not significantly different from zero The speed of adjustment to the mean was always between 0 and 1 France and Italy exhibited much more rapid adjustment patterns than did the other five countries. [ABSTRACT FROM AUTHOR]

This paper analyses the role of shocks in Canadian economic growth since 1870. It uses a nonparametric technique to evaluate the degree of persistence of an innovation in long-run GNP. It is found that a one percent shock to Canadian GNP changes the long-run forecast of this variable by approximately the same amount, which is characteristic of a random walk process. It is also shown that in important periods of Canadian economic growth, its GNP evolved as a random walk with constant drift. With the exception of the period 1929-42, no evidence of business cycles is found. These results lead to the conclusion that movements and oscillations in the GNP of Canada since 1870 have been primarily driven by the accumulation of shocks rather than by cyclical movements. [ABSTRACT FROM AUTHOR]

The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities. This was first thought to be described by a universal principle known as Zipf's law 1,2 ; however, the validity of this model has been challenged by recent empirical studies 3,4 . A theoretical model must also be able to explain the relatively frequent rises and falls of cities and civilizations 5 , but despite many attempts 6-10 these fundamental questions have not yet been satisfactorily answered. Here we introduce a stochastic equation for modelling population growth in cities, constructed from an empirical analysis of recent datasets (for Canada, France, the UK and the USA). This model reveals how rare, but large, interurban migratory shocks dominate city growth. This equation predicts a complex shape for the distribution of city populations and shows that, owing to finite-time effects, Zipf's law does not hold in general, implying a more complex organization of cities. It also predicts the existence of multiple temporal variations in the city hierarchy, in agreement with observations 5 . Our result underlines the importance of rare events in the evolution of complex systems 11 and, at a more practical level, in urban planning.

Length-biased data are frequently encountered in prevalent cohort studies. Many statistical methods have been developed to estimate the covariate effects on the survival outcomes arising from such data while properly adjusting for length-biased sampling. Among them, regression methods based on the proportional hazards model have been widely adopted. However, little work has focused on checking the proportional hazards model assumptions with length-biased data, which is essential to ensure the validity of inference. In this article, we propose a statistical tool for testing the assumed functional form of covariates and the proportional hazards assumption graphically and analytically under the setting of length-biased sampling, through a general class of multiparameter stochastic processes. The finite sample performance is examined through simulation studies, and the proposed methods are illustrated with the data from a cohort study of dementia in Canada.

In clinical studies with time-to-event outcomes, the restricted mean survival time (RMST) has attracted substantial attention as a summary measurement for its straightforward clinical interpretation. When the data are subject to length-biased sampling, which is frequently encountered in observational cohort studies, existing methods to estimate the RMST are not applicable. In this article, we consider nonparametric and semiparametric regression methods to estimate the RMST under the setting of length-biased sampling. To assess the covariate effects on the RMST, a semiparametric regression model that directly relates the covariates and the RMST is assumed. Based on the model, we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias. Stochastic process theories are used to establish the asymptotic properties of the proposed estimators. We investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in Canada., (© 2017, The International Biometric Society.)

Environmental heterogeneity can combine with evolutionary responses to create very dynamic and often locally independent populations across a landscape. Such complexity creates difficulties for managers trying to conserve populations across large areas. This study develops, applies, and tests the use of stochastic life history modeling and Monte Carlo simulation to assess management scenarios related to the realities of regional fisheries management and conservation. We apply this approach to the management of recreational brook trout (Salvelinus fontinalis) fishing; an activity that can severely impact species balance, abundance, and the size structure of fish communities. Specifically, the model incorporates population-specific life-history information (e.g., growth rate, reproductive effort, and survival) to allow forecasts of the impact of various management strategies and/or changes to environmental conditions on a population's ecological characteristics (e.g., size structure, abundance, and probability of persistence). Sampling was carried out in 16 water bodies spread across four sites in Atlantic Canada. Each water body was sampled in 2005 and reassessed in 2008. This sampling had two primary objectives: (1) define a significant proportion of life-history variation of brook trout in Atlantic Canada, and (2) to test the precision and accuracy of model predictions of population responses to experimental exploitation and management changes. The model successfully predicted population responses to changes in adult survival in 12 of 13 populations having sufficient data for validation testing, while also proving to be a useful tool when engaging stakeholders regarding management options and their associated risk. We suggest that such models are cost-effective and have great potential for informing proactive management of jurisdictions with numerous and diverse populations.

The effective management of a cancer treatment facility for radiation therapy depends mainly on optimizing the use of the linear accelerators. In this project, we schedule patients on these machines taking into account their priority for treatment, the maximum waiting time before the first treatment, and the treatment duration. We collaborate with the Centre Intégré de Cancérologie de Laval to determine the best scheduling policy. Furthermore, we integrate the uncertainty related to the arrival of patients at the center. We develop a hybrid method combining stochastic optimization and online optimization to better meet the needs of central planning. We use information on the future arrivals of patients to provide an accurate picture of the expected utilization of resources. Results based on real data show that our method outperforms the policies typically used in treatment centers.

An optimal design approach for groundwater remediation is developed through incorporating numerical simulation, health risk assessment, uncertainty analysis and nonlinear optimization within a general framework. Stochastic analysis and goal programming are introduced into the framework to handle uncertainties in real-world groundwater remediation systems. Carcinogenic risks associated with remediation actions are further evaluated at four confidence levels. The differences between ideal and predicted constraints are minimized by goal programming. The approach is then applied to a contaminated site in western Canada for creating a set of optimal remediation strategies. Results from the case study indicate that factors including environmental standards, health risks and technical requirements mutually affected and restricted themselves. Stochastic uncertainty existed in the entire process of remediation optimization, which should to be taken into consideration in groundwater remediation design., (Copyright © 2014 Elsevier B.V. All rights reserved.)

While many of the measurement approaches in health inequality measurement assume the existence of a ratio-scale variable, most of the health information available in population surveys is given in the form of categorical variables. Therefore, the well-known inequality indices may not always be readily applicable to measure health inequality as it may result in the arbitrariness of the health concentration index's value. In this paper, we address this problem by changing the dimension in which the categorical information is used. We therefore exploit the multi-dimensionality of this information, define a new ratio-scale health status variable and develop positional stochastic dominance conditions that can be implemented in a context of categorical variables. We also propose a parametric class of population health and socioeconomic health inequality indices. Finally we provide a twofold empirical illustration using the Joint Canada/United States Surveys of Health 2004 and the National Health Interview Survey 2010., (Copyright © 2013 Elsevier B.V. All rights reserved.)

Episodic high-risk sexual behavior is common and can have a profound effect on HIV transmission. In a model of HIV transmission among men who have sex with men (MSM), changing the frequency, duration and contact rates of high-risk episodes can take endemic prevalence from zero to 50% and more than double transmissions during acute HIV infection (AHI). Undirected test and treat could be inefficient in the presence of strong episodic risk effects. Partner services approaches that use a variety of control options will be likely to have better effects under these conditions, but the question remains: What data will reveal if a population is experiencing episodic risk effects? HIV sequence data from Montreal reveals genetic clusters whose size distribution stabilizes over time and reflects the size distribution of acute infection outbreaks (AIOs). Surveillance provides complementary behavioral data. In order to use both types of data efficiently, it is essential to examine aspects of models that affect both the episodic risk effects and the shape of transmission trees. As a demonstration, we use a deterministic compartmental model of episodic risk to explore the determinants of the fraction of transmissions during acute HIV infection (AHI) at the endemic equilibrium. We use a corresponding individual-based model to observe AIO size distributions and patterns of transmission within AIO. Episodic risk parameters determining whether AHI transmission trees had longer chains, more clustered transmissions from single individuals, or different mixes of these were explored. Encouragingly for parameter estimation, AIO size distributions reflected the frequency of transmissions from acute infection across divergent parameter sets. Our results show that episodic risk dynamics influence both the size and duration of acute infection outbreaks, thus providing a possible link between genetic cluster size distributions and episodic risk dynamics., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Aging in a given individual can be characterized by the number of deficits (symptoms, signs, laboratory abnormalities, disabilities) that they accumulate. The number of accumulated deficits, more than their nature, well characterizes health status in individuals - the proportion of deficits present in an individual to deficits considered is known as a frailty index. While on average deficits accumulate with age, individual trajectories in the number of deficits is highly dynamic. Transitions in the number of deficits over a fixed time interval can be represented by the Poisson law, with the Poisson mean dependent on the deficit numbers at baseline. Here we present an extension of the model to make possible predictions for any given time period. Using data from the Canadian National Population Health Survey of people aged 55 and over (n=4330), followed during 7cycles being the baseline and 6cycles of follow-up every 2years, we found that the transition in the number of deficits during any time period can be approximated using a time dependent Poisson distribution with the Poisson mean tending to decelerate over time, according to square-root-of-time kinetics characteristic for stochastic processes (e.g. diffusion, Brownian motion ) while the probability of death shows a pattern of time acceleration with a high degree of precision, "explaining" over 98% of variance. The model predicts a variety of changes in health status including the possibility of health improvement indicating the repair/remodeling abilities of the organism. The model is valuable for estimating how changes in health can influence mortality across the life course from late middle age., (Copyright © 2012. Published by Elsevier Inc.)

Ecosystems driven by wildfire regimes are characterized by fire size distributions resembling power laws. Existing models produce power laws, but their predicted exponents are too high and fail to capture the exponent's variation with geographic region. Here we present a minimal model of fire dynamics that describes fire spread as a stochastic birth-death process, analogous to stochastic population growth or disease spread and incorporating memory effects from previous fires. The model reproduces multiple regional patterns in fire regimes and allows us to classify different regions in terms of their proximity to a critical threshold. Transitions across this critical threshold imply abrupt and pronounced increases in average fire size. The model predicts that large regions in Canada are currently close to this transition and might be driven beyond the threshold in the future. We illustrate this point by analyzing the time series for large fires (>199 ha) from the Canadian Boreal Plains, found to have shifted from a subcritical regime to a critical regime in the recent past. By contrast to its predecessor, the model also suggests that a critical transition, and not self-organized criticality, underlies forest fire dynamics, with implications for other ecological systems exhibiting power-law-like patterns, in particular for their sensitivity to environmental change and control efforts.

This paper uses sequential stochastic dominance procedures to compare the joint distribution of health and income across space and time. It is the first application of which we are aware of methods to compare multidimensional distributions of income and health using procedures that are robust to aggregation techniques. The paper's approach is more general than comparisons of health gradients and does not require the estimation of health equivalent incomes. We illustrate the approach by contrasting Canada and the US using comparable data. Canada dominates the US over the bottom part of the bi-dimensional distribution of health and income, though not generally over the uni-dimensional distributions of health or income. The paper also finds that welfare for both Canadians and Americans has not unambiguously improved during the last decade over the joint distribution of income and health, in spite of the fact that the uni-dimensional distributions of income have clearly improved during that period., (Copyright © 2010 Elsevier B.V. All rights reserved.)

The polar bear (Ursus maritimus) depends on sea ice for feeding, breeding, and movement. Significant reductions in Arctic sea ice are forecast to continue because of climate warming. We evaluated the impacts of climate change on polar bears in the southern Beaufort Sea by means of a demographic analysis, combining deterministic, stochastic, environment-dependent matrix population models with forecasts of future sea ice conditions from IPCC general circulation models (GCMs). The matrix population models classified individuals by age and breeding status; mothers and dependent cubs were treated as units. Parameter estimates were obtained from a capture-recapture study conducted from 2001 to 2006. Candidate statistical models allowed vital rates to vary with time and as functions of a sea ice covariate. Model averaging was used to produce the vital rate estimates, and a parametric bootstrap procedure was used to quantify model selection and parameter estimation uncertainty. Deterministic models projected population growth in years with more extensive ice coverage (2001-2003) and population decline in years with less ice coverage (2004-2005). LTRE (life table response experiment) analysis showed that the reduction in lambda in years with low sea ice was due primarily to reduced adult female survival, and secondarily to reduced breeding. A stochastic model with two environmental states, good and poor sea ice conditions, projected a declining stochastic growth rate, log lambdas, as the frequency of poor ice years increased. The observed frequency of poor ice years since 1979 would imply log lambdas approximately - 0.01, which agrees with available (albeit crude) observations of population size. The stochastic model was linked to a set of 10 GCMs compiled by the IPCC; the models were chosen for their ability to reproduce historical observations of sea ice and were forced with "business as usual" (A1B) greenhouse gas emissions. The resulting stochastic population projections showed drastic declines in the polar bear population by the end of the 21st century. These projections were instrumental in the decision to list the polar bear as a threatened species under the U.S. Endangered Species Act.

White-nose syndrome (WNS) is an emerging disease affecting hibernating bats in eastern North America that causes mass mortality and precipitous population declines in winter hibernacula. First discovered in 2006 in New York State, WNS is spreading rapidly across eastern North America and currently affects seven species. Mortality associated with WNS is causing a regional population collapse and is predicted to lead to regional extinction of the little brown myotis (Myotis lucifugus), previously one of the most common bat species in North America. Novel diseases can have serious impacts on naïve wildlife populations, which in turn can have substantial impacts on ecosystem integrity.

Fishery management policies need to be based on historical summaries of stock status which are well correlated with the size of the group of individuals who will be affected by any harvest. This paper is motivated by the problem of managing stocks of Atlantic salmon, which can be accurately monitored during the riverine stages of their life-history, but which spend a lengthy period at sea before returning to spawn. We begin by formulating a minimal stochastic model of stock-recruitment driven population dynamics, which linearises to a standard ARMA form. We investigate the relation between maturity dispersion and the auto-covariance of stock fluctuations driven by process noise in the recruitment process and/or random variability in survival from recruitment to spawning. We demonstrate that significant reductions in fluctuation intensity and/or increases in long-run average yield can be achieved by controlling harvesting in response to the value of a historical summary focussed on lags at which the uncontrolled population dynamics produce strong correlations. We apply our minimal model to two well-characterised Atlantic salmon populations, and find poor agreement between predicted and observed stock fluctuation ACF. Re-examination of the ancilliary data available for one of our two exemplary systems leads us to propose an extended model which also linearises to ARMA form, and which predicts a fluctuation ACF more closely in agreement with that observed, and could thus form a satisfactory vehicle for policy discussion.

A new stochastic optimization model under modeling uncertainty (SOMUM) and parameter certainty is applied to a practical site located in western Canada. Various groundwater remediation strategies under different significance levels are obtained from the SOMUM model. The impact of modeling uncertainty (proxy-simulator residuals) on optimal remediation strategies is compared to that of parameter uncertainty (arising from physical properties). The results show that the increased remediation cost for mitigating modeling-uncertainty impact would be higher than those from models where the coefficient of variance of input parameters approximates to 40%. This provides new evidence that the modeling uncertainty in proxy-simulator residuals can hardly be ignored; there is thus a need of investigating and mitigating the impact of such uncertainties on groundwater remediation design. This work would be helpful for lowering the risk of system failure due to potential environmental-standard violation when determining optimal groundwater remediation strategies., (2009 Elsevier B.V. All rights reserved.)

Nonindigenous species have caused significant impacts to North American forests despite past and present international phytosanitary efforts. Though broadly acknowledged, the risks of pest invasions are difficult to quantify as they involve interactions between many factors that operate across a range of spatial and temporal scales: the transmission of invading organisms via various pathways, their spread and establishment in new environments. Our study presents a stochastic simulation approach to quantify these risks and associated uncertainties through time in a unified fashion. We outline this approach with an example of a forest pest recently detected in North America, Sirex noctilio Fabricius. We simulate new potential entries of S. noctilio as a stochastic process, based on recent volumes of marine shipments of commodities from countries where S. noctilio is established, as well as the broad dynamics of foreign marine imports. The results are then linked with a spatial model that simulates the spread of S. noctilio within the geographical distribution of its hosts (pines) while incorporating existing knowledge about its behavior in North American landscapes. Through replications, this approach yields a spatial representation of S. noctilio risks and uncertainties in a single integrated product. The approach should also be appealing to decisionmakers, since it accounts for projected flows of commodities that may serve as conduits for pest entry. Our 30-year forecasts indicate high establishment probability in Ontario, Quebec, and the northeastern United States, but further southward expansion of S. noctilio is uncertain, ultimately depending on the impact of recent international treatment standards for wood packing materials.

Background: Exercise improves cognition and lessens the risk of death in older adults. Cognition and mortality are each also affected by biological sex, which might modify the effect of exercise. We investigated how sex mediates the impact of exercise on mortality and 5-year changes in cognition., Methods: In the Canadian Study of Health and Aging (n = 8,403, 60.7% women), cognitive states were defined as errors in the Modified Mini-Mental State Examination. Improvement and declines were modeled using a 4-parameter truncated Poisson distribution., Results: Men and women showed similar levels of improvement or stabilization (34.1%, 95% CI = 32.1-35.9 in women and 30.2%, 95% CI = 28.2-32.4 in men). In unadjusted analysis, more men died (34%, 95% CI = 32.3-36.3) than did women (30.3%, 95% CI = 28.4-32.2). Higher education was beneficial for cognitive function in both sexes, but did not impact survival when other factors were considered. The effect of exercise differed by sex: women had a survival advantage compared with men, but men most benefited in cognitive functioning., Conclusions: Exercise is strongly associated with cognitive improvement and stabilization in men, and with better survival in women. In contrast to conventional approaches, our model allows us to analyze how different risk factors affect cognition to any degree, and simultaneously to assess their impact on survival., ((c) 2009 S. Karger AG, Basel.)

Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The introduction of extensive transportation data sets is therefore an important step in order to develop epidemic models endowed with realism., Methods: We develop a general stochastic meta-population model that incorporates actual travel and census data among 3 100 urban areas in 220 countries. The model allows probabilistic predictions on the likelihood of country outbreaks and their magnitude. The level of predictability offered by the model can be quantitatively analyzed and related to the appearance of robust epidemic pathways that represent the most probable routes for the spread of the disease., Results: In order to assess the predictive power of the model, the case study of the global spread of SARS is considered. The disease parameter values and initial conditions used in the model are evaluated from empirical data for Hong Kong. The outbreak likelihood for specific countries is evaluated along with the emerging epidemic pathways. Simulation results are in agreement with the empirical data of the SARS worldwide epidemic., Conclusion: The presented computational approach shows that the integration of long-range mobility and demographic data provides epidemic models with a predictive power that can be consistently tested and theoretically motivated. This computational strategy can be therefore considered as a general tool in the analysis and forecast of the global spreading of emerging diseases and in the definition of containment policies aimed at reducing the effects of potentially catastrophic outbreaks.

This paper presents a methodology for quantifying the effectiveness of water-trading under uncertainty, by developing an optimization model based on the interval-parameter two-stage stochastic program (TSP) technique. In the study, the effectiveness of a water-trading program is measured by the water volume that can be released through trading from a statistical point of view. The methodology can also deal with recourse water allocation problems generated by randomness in water availability and, at the same time, tackle uncertainties expressed as intervals in the trading system. The developed methodology was tested with a hypothetical water-trading program in an agricultural system in the Swift Current Creek watershed, Canada. Study results indicate that the methodology can effectively measure the effectiveness of a trading program through estimating the water volume being released through trading in a long-term view. A sensitivity analysis was also conducted to analyze the effects of different trading costs on the trading program. It shows that the trading efforts would become ineffective when the trading costs are too high. The case study also demonstrates that the trading program is more effective in a dry season when total water availability is in shortage.

Background: The highly pathogenic H5N1 avian influenza virus, which is now widespread in Southeast Asia and which diffused recently in some areas of the Balkans region and Western Europe, has raised a public alert toward the potential occurrence of a new severe influenza pandemic. Here we study the worldwide spread of a pandemic and its possible containment at a global level taking into account all available information on air travel., Methods and Findings: We studied a metapopulation stochastic epidemic model on a global scale that considers airline travel flow data among urban areas. We provided a temporal and spatial evolution of the pandemic with a sensitivity analysis of different levels of infectiousness of the virus and initial outbreak conditions (both geographical and seasonal). For each spreading scenario we provided the timeline and the geographical impact of the pandemic in 3,100 urban areas, located in 220 different countries. We compared the baseline cases with different containment strategies, including travel restrictions and the therapeutic use of antiviral (AV) drugs. We investigated the effect of the use of AV drugs in the event that therapeutic protocols can be carried out with maximal coverage for the populations in all countries. In view of the wide diversity of AV stockpiles in different regions of the world, we also studied scenarios in which only a limited number of countries are prepared (i.e., have considerable AV supplies). In particular, we compared different plans in which, on the one hand, only prepared and wealthy countries benefit from large AV resources, with, on the other hand, cooperative containment scenarios in which countries with large AV stockpiles make a small portion of their supplies available worldwide., Conclusions: We show that the inclusion of air transportation is crucial in the assessment of the occurrence probability of global outbreaks. The large-scale therapeutic usage of AV drugs in all hit countries would be able to mitigate a pandemic effect with a reproductive rate as high as 1.9 during the first year; with AV supply use sufficient to treat approximately 2% to 6% of the population, in conjunction with efficient case detection and timely drug distribution. For highly contagious viruses (i.e., a reproductive rate as high as 2.3), even the unrealistic use of supplies corresponding to the treatment of approximately 20% of the population leaves 30%-50% of the population infected. In the case of limited AV supplies and pandemics with a reproductive rate as high as 1.9, we demonstrate that the more cooperative the strategy, the more effective are the containment results in all regions of the world, including those countries that made part of their resources available for global use.

This study estimated the health burden and costs associated with gastroenteritis in the City of Hamilton (Ontario, Canada). The number of cases, number of different resource units used, and cost per resource unit were represented by probability distributions and point estimates. These were subsequently integrated in a stochastic model to estimate the overall burden and cost in the population and to depict the uncertainty of the estimates. The estimated mean annual cost per capita was Can dollar 115. The estimated mean annual cost per case was Can dollar 1,089 and was similar to other published figures. Gastroenteritis represented a significant burden in the study population, with costs high enough to justify prevention efforts. These results, currently the most accurate available estimates for a Canadian population, can inform future economic evaluations to determine the most cost effective measures for reducing the burden and cost of gastroenteritis in the community.

Severe acute respiratory syndrome (SARS) has been the first severe contagious disease to emerge in the 21st century. The available epidemic curves for SARS show marked differences between the affected regions with respect to the total number of cases and epidemic duration, even for those regions in which outbreaks started almost simultaneously and similar control measures were implemented at the same time. The authors developed a likelihood-based estimation procedure that infers the temporal pattern of effective reproduction numbers from an observed epidemic curve. Precise estimates for the effective reproduction numbers were obtained by applying this estimation procedure to available data for SARS outbreaks that occurred in Hong Kong, Vietnam, Singapore, and Canada in 2003. The effective reproduction numbers revealed that epidemics in the various affected regions were characterized by markedly similar disease transmission potentials and similar levels of effectiveness of control measures. In controlling SARS outbreaks, timely alerts have been essential: Delaying the institution of control measures by 1 week would have nearly tripled the epidemic size and would have increased the expected epidemic duration by 4 weeks.

The use of probabilistic analysis as a means for analyzing uncertainty within economic analysis has grown in popularity in recent years as it has been recognized as the most complete method for propagating uncertainty with respect to input parameters in terms of uncertainty about outcomes of interest. The World Health Organization (WHO) in a series of recent reports and publications have recognized the role of probabilistic analysis in what they term generalized cost-effectiveness analysis. However, there are fundamental problems with the analysis and the interpretation of such analysis as proposed by WHO. This study highlights three specific points for concern and offers constructive criticism by recommending more appropriate approaches.