The Markov chain is well studied and widely applied in many areas.For some Markov chains,it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is ...The Markov chain is well studied and widely applied in many areas.For some Markov chains,it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is time-consuming for computation.In this paper,we propose an approximation method for Markov chains by applying the copula theory.For this purpose,we first discuss the checkerboard copula-based Markov chain,which is the Markov chain generated by the family of checkerboard copulas.This Markov chain has some appealing properties,such as self-similarity in copulas and having explicit forms of finite-dimensional distributions.Then we prove that each Markov chain can be approximated by a sequence of checkerboard copula-based Markov chains,and the error bounds of the approximate distributions are provided.Employing the checkerboard copula-based approximation method,we propose a sufficient condition for the geometric β-mixing of copula-based Markov chains.This condition allows copulas of Markov chains to be asymmetric.Finally,by applying the approximation method,analytical recurrence formulas are also derived for computing approximate distributions of both the first passage time and the occupation time of a Markov chain,and numerical results are listed to show the approximation errors.展开更多
A new stop frequency model was developed to predict the daily number of maintenance activity stops made by individual household heads during a typical weekday. This new model was based on the modification of a convent...A new stop frequency model was developed to predict the daily number of maintenance activity stops made by individual household heads during a typical weekday. This new model was based on the modification of a conventional multivariate ordered probit(MOP) model by maintaining the probit assumption for the marginal distributions while introducing nonnormal dependence among the error terms using copula functions. Therefore, the copulabased MOP model would relieve the restriction of imposing joint normality on the error terms in the conventional MOP model. The new MOP model would not only account for the intrahousehold interactions in stop-making decisions, but also allow the best functional form to be determined for representing dependencies among household heads. Using the New York Metropolitan Transportation Council’s 2010/2011 regional household travel survey data, the copula-based MOP model was employed to examine stop-making behavior for individual household heads residing in New York City and its adjacent counties in Mid-Hudson Valley and New Jersey. Empirical results provided useful insights into the observed effects of sociodemographics, land use density, transportation service, and work schedule together with potential unobserved common effects on the inter-relatedness of spousal stop-making decisions at the household level. The results show that the MOP model with a Clayton copula structure provides the best data fits and there is a very strong positive dependence among error terms of stop-making equations. Furthermore, the dependence among the maintenance activity propensities of household heads is asymmetric, with a stronger tendency of household heads to simultaneously have low maintenance activity levels than to simultaneously have high maintenance activity levels.展开更多
The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifie...The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifies the influence of heat and drought on their likelihood using a copula-based Bayesian probability framework.The wildfires were characterized by burned area(BA)and intensity(fire radiative power,FRP).The criteria establishing the presence of“hot drought”conditions were identified using the 5-day Standardized Temperature Index(STI)and 75-day Standardized Precipitation Index(SPI),respectively.The wildfire outbreak began on 7 January 2025 and burned for more than six days,with the total burned area exceeding 245 km^(2) and the cumulative FRP exceeding 41060 MW.Based on satellite-derived active fire observations from 2001 to 2025,we estimate that such large and intense wildfires during LA’s rainy season represent a once-in-a-67-year event.The wildfires were largely driven by the combination of hot and dry conditions,which dried out soils and vegetation that had proliferated due to above-average precipitation in previous winter seasons,thereby providing abundant fuel.Our seasonal analysis reveals that extreme drought increased the probability of wildfires matching the 2025 intensity and BA by 54%and 75%,respectively.Hot drought further amplified these probabilities by 149%(intensity)and 210%(BA).These findings suggest an elevated risk of large wildfires under hot drought conditions,contributing to their expansion into the non-traditional fire season.展开更多
基金supported by the National Key R&D Program of China(Grant No.2018YFA0703900)National Natural Science Foundation of China(Grant No.11671021)+1 种基金supported by National Natural Science Foundation of China(Grant Nos.11761051and 11561047)the Natural Science Foundation of Jiangxi Province(Grant Nos.20181BAB211003 and 20192BAB211006)。
文摘The Markov chain is well studied and widely applied in many areas.For some Markov chains,it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is time-consuming for computation.In this paper,we propose an approximation method for Markov chains by applying the copula theory.For this purpose,we first discuss the checkerboard copula-based Markov chain,which is the Markov chain generated by the family of checkerboard copulas.This Markov chain has some appealing properties,such as self-similarity in copulas and having explicit forms of finite-dimensional distributions.Then we prove that each Markov chain can be approximated by a sequence of checkerboard copula-based Markov chains,and the error bounds of the approximate distributions are provided.Employing the checkerboard copula-based approximation method,we propose a sufficient condition for the geometric β-mixing of copula-based Markov chains.This condition allows copulas of Markov chains to be asymmetric.Finally,by applying the approximation method,analytical recurrence formulas are also derived for computing approximate distributions of both the first passage time and the occupation time of a Markov chain,and numerical results are listed to show the approximation errors.
文摘A new stop frequency model was developed to predict the daily number of maintenance activity stops made by individual household heads during a typical weekday. This new model was based on the modification of a conventional multivariate ordered probit(MOP) model by maintaining the probit assumption for the marginal distributions while introducing nonnormal dependence among the error terms using copula functions. Therefore, the copulabased MOP model would relieve the restriction of imposing joint normality on the error terms in the conventional MOP model. The new MOP model would not only account for the intrahousehold interactions in stop-making decisions, but also allow the best functional form to be determined for representing dependencies among household heads. Using the New York Metropolitan Transportation Council’s 2010/2011 regional household travel survey data, the copula-based MOP model was employed to examine stop-making behavior for individual household heads residing in New York City and its adjacent counties in Mid-Hudson Valley and New Jersey. Empirical results provided useful insights into the observed effects of sociodemographics, land use density, transportation service, and work schedule together with potential unobserved common effects on the inter-relatedness of spousal stop-making decisions at the household level. The results show that the MOP model with a Clayton copula structure provides the best data fits and there is a very strong positive dependence among error terms of stop-making equations. Furthermore, the dependence among the maintenance activity propensities of household heads is asymmetric, with a stronger tendency of household heads to simultaneously have low maintenance activity levels than to simultaneously have high maintenance activity levels.
基金supported by the National Natural Science Foundation of China(Grant Nos.42471034,42330604)the Qing Lan Projectsupport from the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(EarthLab).
文摘The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifies the influence of heat and drought on their likelihood using a copula-based Bayesian probability framework.The wildfires were characterized by burned area(BA)and intensity(fire radiative power,FRP).The criteria establishing the presence of“hot drought”conditions were identified using the 5-day Standardized Temperature Index(STI)and 75-day Standardized Precipitation Index(SPI),respectively.The wildfire outbreak began on 7 January 2025 and burned for more than six days,with the total burned area exceeding 245 km^(2) and the cumulative FRP exceeding 41060 MW.Based on satellite-derived active fire observations from 2001 to 2025,we estimate that such large and intense wildfires during LA’s rainy season represent a once-in-a-67-year event.The wildfires were largely driven by the combination of hot and dry conditions,which dried out soils and vegetation that had proliferated due to above-average precipitation in previous winter seasons,thereby providing abundant fuel.Our seasonal analysis reveals that extreme drought increased the probability of wildfires matching the 2025 intensity and BA by 54%and 75%,respectively.Hot drought further amplified these probabilities by 149%(intensity)and 210%(BA).These findings suggest an elevated risk of large wildfires under hot drought conditions,contributing to their expansion into the non-traditional fire season.
