Spatio-temporal models are valuable tools for disease mapping and understanding the geographical distribution of diseases and temporal dynamics. Spatio-temporal models have been proven empirically to be very complex a...Spatio-temporal models are valuable tools for disease mapping and understanding the geographical distribution of diseases and temporal dynamics. Spatio-temporal models have been proven empirically to be very complex and this complexity has led many to oversimply and model the spatial and temporal dependencies independently. Unlike common practice, this study formulated a new spatio-temporal model in a Bayesian hierarchical framework that accounts for spatial and temporal dependencies jointly. The spatial and temporal dependencies were dynamically modelled via the matern exponential covariance function. The temporal aspect was captured by the parameters of the exponential with a first-order autoregressive structure. Inferences about the parameters were obtained via Markov Chain Monte Carlo (MCMC) techniques and the spatio-temporal maps were obtained by mapping stable posterior means from the specific location and time from the best model that includes the significant risk factors. The model formulated was fitted to both simulation data and Kenya meningitis incidence data from 2013 to 2019 along with two covariates;Gross County Product (GCP) and average rainfall. The study found that both average rainfall and GCP had a significant positive association with meningitis occurrence. Also, regarding geographical distribution, the spatio-temporal maps showed that meningitis is not evenly distributed across the country as some counties reported a high number of cases compared with other counties.展开更多
The dynamics of regional convergence include spatial and temporal dimensions. Spatial Markov chain can be used to explore how regions evolve by considering both individual regions and their geographic neighbors. Based...The dynamics of regional convergence include spatial and temporal dimensions. Spatial Markov chain can be used to explore how regions evolve by considering both individual regions and their geographic neighbors. Based on per capita GDP data set of 77 counties from 1978 to 2000, this paper attempts to investigate the spatial-temporal dynamics of regional convergence in Jiangsu. First, traditional Markov matrix for five per capita GDP classes is constructed for later comparison. Moreover, each region’s spatial lag is derived by averaging all its neighbors’ per capita GDP data. Conditioning on per capita GDP class of its spatial lag at the beginning of each year, spatial Markov transition probabilities of each region are calculated accordingly. Quantitatively, for a poor region, the probability of moving upward is 3.3% if it is surrounded by its poor neighbors, and even increases to 18.4% if it is surrounded by its rich neighbors, but it goes down to 6.2% on average if ignoring regional context. For a rich region, the probability of moving down ward is 1.2% if it is surrounded by its rich neighbors, but increases to 3.0% if it is surrounded by its poor neighbors, and averages 1.5% irrespective of regional context. Spatial analysis of regional GDP class transitions indicates those 10 upward moves of both regions and their neighbors are unexceptionally located in the southern Jiangsu, while downward moves of regions or their neighbors are almost in the northern Jiangsu. These empirical results provide a spatial explanation to the "convergence clubs" detected by traditional Markov chain.展开更多
Proper understanding of global distribution of infectious diseases is an important part of disease management and policy making. However, data are subject to complexities caused by heterogeneities across host classes ...Proper understanding of global distribution of infectious diseases is an important part of disease management and policy making. However, data are subject to complexities caused by heterogeneities across host classes and space-time epidemic processes. This paper seeks to suggest or propose Bayesian spatio-temporal model for modeling and mapping tuberculosis relative risks in space and time as well identify risks factors associated with the tuberculosis and counties in Kenya with high tuberculosis relative risks. In this paper, we used spatio-temporal Bayesian hierarchical models to study the pattern of tuberculosis relative risks in Kenya. The Markov Chain Monte Carlo method via WinBUGS and R packages were used for simulations and estimation of the parameter estimates. The best fitting model is selected using the Deviance Information Criterion proposed by Spiegelhalter and colleagues. Among the spatio-temporal models used, the Knorr-Held model with space-time interaction type III and IV fit the data well but type IV appears better than type III. Variation in tuberculosis risk is observed among Kenya counties and clustering among counties with high tuberculosis relative risks. The prevalence of HIV is identified as the determinant of TB. We found clustering and heterogeneity of TB risk among high rate counties and the overall tuberculosis risk is slightly decreasing from 2002-2009. We proposed that the Knorr-Held model with interaction type IV should be used to model and map Kenyan tuberculosis relative risks. Interaction of TB relative risk in space and time increases among rural counties that share boundaries with urban counties with high tuberculosis risk. This is due to the ability of models to borrow strength from neighboring counties, such that nearby counties have similar risk. Although the approaches are less than ideal, we hope that our study provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from tuberculosis in Kenya.展开更多
This article applies a Markov chain method to compute the probability of residential fire occurrence based on past fire history. Fitted with the fire incidence data gathered over a period of 10 years in Melbourne, Aus...This article applies a Markov chain method to compute the probability of residential fire occurrence based on past fire history. Fitted with the fire incidence data gathered over a period of 10 years in Melbourne, Australia,the spatially-integrated fire risk model predicts the likely occurrence of fire incidents using space and time as key model parameters. The mapped probabilities of fire occurrence across Melbourne show a city-centric spatial pattern where inner-city areas are relatively more vulnerable to a fire than outer suburbia. Fire risk reduces in a neighborhood when there is at least one fire in the last1 month. The results show that the time threshold of reduced fire risk after the fire occurrence is about 2 months.Fire risk increases when there is no fire in the last 1 month within the third-order neighborhood(within 5 km). A fire that occurs within this distance range, however, has no significant effect on reducing fire risk level within the neighborhood. The spatial–temporal dependencies of fire risk provide new empirical evidence useful for fire agencies to effectively plan and implement geo-targeted fire risk interventions and education programs to mitigate potential fire risk in areas where and when they are most needed.展开更多
文摘Spatio-temporal models are valuable tools for disease mapping and understanding the geographical distribution of diseases and temporal dynamics. Spatio-temporal models have been proven empirically to be very complex and this complexity has led many to oversimply and model the spatial and temporal dependencies independently. Unlike common practice, this study formulated a new spatio-temporal model in a Bayesian hierarchical framework that accounts for spatial and temporal dependencies jointly. The spatial and temporal dependencies were dynamically modelled via the matern exponential covariance function. The temporal aspect was captured by the parameters of the exponential with a first-order autoregressive structure. Inferences about the parameters were obtained via Markov Chain Monte Carlo (MCMC) techniques and the spatio-temporal maps were obtained by mapping stable posterior means from the specific location and time from the best model that includes the significant risk factors. The model formulated was fitted to both simulation data and Kenya meningitis incidence data from 2013 to 2019 along with two covariates;Gross County Product (GCP) and average rainfall. The study found that both average rainfall and GCP had a significant positive association with meningitis occurrence. Also, regarding geographical distribution, the spatio-temporal maps showed that meningitis is not evenly distributed across the country as some counties reported a high number of cases compared with other counties.
基金Under the auspices ofthe National Natural Science Foundation of China (No .40301038)
文摘The dynamics of regional convergence include spatial and temporal dimensions. Spatial Markov chain can be used to explore how regions evolve by considering both individual regions and their geographic neighbors. Based on per capita GDP data set of 77 counties from 1978 to 2000, this paper attempts to investigate the spatial-temporal dynamics of regional convergence in Jiangsu. First, traditional Markov matrix for five per capita GDP classes is constructed for later comparison. Moreover, each region’s spatial lag is derived by averaging all its neighbors’ per capita GDP data. Conditioning on per capita GDP class of its spatial lag at the beginning of each year, spatial Markov transition probabilities of each region are calculated accordingly. Quantitatively, for a poor region, the probability of moving upward is 3.3% if it is surrounded by its poor neighbors, and even increases to 18.4% if it is surrounded by its rich neighbors, but it goes down to 6.2% on average if ignoring regional context. For a rich region, the probability of moving down ward is 1.2% if it is surrounded by its rich neighbors, but increases to 3.0% if it is surrounded by its poor neighbors, and averages 1.5% irrespective of regional context. Spatial analysis of regional GDP class transitions indicates those 10 upward moves of both regions and their neighbors are unexceptionally located in the southern Jiangsu, while downward moves of regions or their neighbors are almost in the northern Jiangsu. These empirical results provide a spatial explanation to the "convergence clubs" detected by traditional Markov chain.
文摘Proper understanding of global distribution of infectious diseases is an important part of disease management and policy making. However, data are subject to complexities caused by heterogeneities across host classes and space-time epidemic processes. This paper seeks to suggest or propose Bayesian spatio-temporal model for modeling and mapping tuberculosis relative risks in space and time as well identify risks factors associated with the tuberculosis and counties in Kenya with high tuberculosis relative risks. In this paper, we used spatio-temporal Bayesian hierarchical models to study the pattern of tuberculosis relative risks in Kenya. The Markov Chain Monte Carlo method via WinBUGS and R packages were used for simulations and estimation of the parameter estimates. The best fitting model is selected using the Deviance Information Criterion proposed by Spiegelhalter and colleagues. Among the spatio-temporal models used, the Knorr-Held model with space-time interaction type III and IV fit the data well but type IV appears better than type III. Variation in tuberculosis risk is observed among Kenya counties and clustering among counties with high tuberculosis relative risks. The prevalence of HIV is identified as the determinant of TB. We found clustering and heterogeneity of TB risk among high rate counties and the overall tuberculosis risk is slightly decreasing from 2002-2009. We proposed that the Knorr-Held model with interaction type IV should be used to model and map Kenyan tuberculosis relative risks. Interaction of TB relative risk in space and time increases among rural counties that share boundaries with urban counties with high tuberculosis risk. This is due to the ability of models to borrow strength from neighboring counties, such that nearby counties have similar risk. Although the approaches are less than ideal, we hope that our study provide a useful stepping stone in the development of spatial and spatio-temporal methodology for the statistical analysis of risk from tuberculosis in Kenya.
文摘This article applies a Markov chain method to compute the probability of residential fire occurrence based on past fire history. Fitted with the fire incidence data gathered over a period of 10 years in Melbourne, Australia,the spatially-integrated fire risk model predicts the likely occurrence of fire incidents using space and time as key model parameters. The mapped probabilities of fire occurrence across Melbourne show a city-centric spatial pattern where inner-city areas are relatively more vulnerable to a fire than outer suburbia. Fire risk reduces in a neighborhood when there is at least one fire in the last1 month. The results show that the time threshold of reduced fire risk after the fire occurrence is about 2 months.Fire risk increases when there is no fire in the last 1 month within the third-order neighborhood(within 5 km). A fire that occurs within this distance range, however, has no significant effect on reducing fire risk level within the neighborhood. The spatial–temporal dependencies of fire risk provide new empirical evidence useful for fire agencies to effectively plan and implement geo-targeted fire risk interventions and education programs to mitigate potential fire risk in areas where and when they are most needed.
