Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studie...Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.展开更多
A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which fu...A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.展开更多
Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-par...Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-parametric methods in comparison with classical ones, as well as how each isolates risk factors for child diarrhoea. This was done by fitting Logit, Poisson, and Bayesian models to 2006 Malawi Multiple Indicator Cluster Survey data. The comparison between Logit and Poisson models was done via chi-square＇s goodness-of-fit test. Confidence and Credible Intervals were used to compare Logit/Poisson and Bayesian model estimates. Modelling and inference in Bayesian method was done through MCMC techniques. The results showed agreement in significance and direction of estimates from Bayesian and Poisson/Logit models, but Poisson provided better fit than Logit model. Further, all the models identified child＇s age, breastfeeding status, region of stay and toilet-sharing status as significant factors for determining the child＇s risk. The models ruled out effects of mother＇s education, area of residence, and source of drinking water on the risk. Bayesian model separately proved significant closeness to lake/river factor. The findings imply that classical and semi-parametric models are equally helpful when estimating the child＇s risk to diarrhoea.展开更多
Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high numbe...Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against mea- sured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo （MCMC） methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identi- fiability： a basic SIR model, an influenza model with vaccination and treatment and a HIV-Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The pre- sented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.展开更多
Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weig...Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.展开更多
文摘Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.
基金Under the auspices of National Natural Science Foundation of China (No. 50609005)Chinese Postdoctoral Science Foundation (No. 2009451116)+1 种基金Postdoctoral Foundation of Heilongjiang Province (No. LBH-Z08255)Foundation of Heilongjiang Province Educational Committee (No. 11451022)
文摘A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.
文摘Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-parametric methods in comparison with classical ones, as well as how each isolates risk factors for child diarrhoea. This was done by fitting Logit, Poisson, and Bayesian models to 2006 Malawi Multiple Indicator Cluster Survey data. The comparison between Logit and Poisson models was done via chi-square＇s goodness-of-fit test. Confidence and Credible Intervals were used to compare Logit/Poisson and Bayesian model estimates. Modelling and inference in Bayesian method was done through MCMC techniques. The results showed agreement in significance and direction of estimates from Bayesian and Poisson/Logit models, but Poisson provided better fit than Logit model. Further, all the models identified child＇s age, breastfeeding status, region of stay and toilet-sharing status as significant factors for determining the child＇s risk. The models ruled out effects of mother＇s education, area of residence, and source of drinking water on the risk. Bayesian model separately proved significant closeness to lake/river factor. The findings imply that classical and semi-parametric models are equally helpful when estimating the child＇s risk to diarrhoea.
文摘Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against mea- sured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo （MCMC） methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identi- fiability： a basic SIR model, an influenza model with vaccination and treatment and a HIV-Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The pre- sented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.
基金supported by National Basic Research Program of China (Grant No. 2010CB428403)National Natural Science Foundation of China (Grant No.41075076)Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No.KZCX2-EW-QN207)
文摘Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.
