Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的...Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的独立抽样和随机游走抽样的Metropolis-Hastings(M-H)算法,利用可读性较强的Matlab程序来实现两种抽样算法,并给出了详细的程序实施过程,分析了两种抽样的优缺点。模拟分析结果表明:独立抽样M-H算法比较容易实施,但是要求建议分布和后验分布的吻合度较高,否则计算效率低下,而且模拟效果不理想;随机游走抽样的M-H算法不需要建议分布接近后验分布,模拟效果也比较好,因此,克服了独立抽样算法的不足,适用范围更广。展开更多
针对不规则区域面积测算中定位精度和面积计算精度两方面不足,提出一种定位精度高、面积误差小的面积测算新方法。其采用一种组合定位方法精确定位,即将差分GPS测量系统(DGPS)与马尔可夫链蒙特卡罗(Markov chain Monte Carol,MCMC)粒子...针对不规则区域面积测算中定位精度和面积计算精度两方面不足,提出一种定位精度高、面积误差小的面积测算新方法。其采用一种组合定位方法精确定位,即将差分GPS测量系统(DGPS)与马尔可夫链蒙特卡罗(Markov chain Monte Carol,MCMC)粒子滤波相结合,再配合复化Newton-cotes算法,拟合边界曲线并准确求得区域面积。将MCMC粒子滤波应用于DGPS定位数据处理,其既可处理非高斯分布噪声,又解决粒子滤波(PF)的粒子退化问题,提高定位精度。将复化Newton-cotes算法应用于面积计算,其既避免高次插值的舍入误差,又将面积区间进一步细分,提高面积计算精度。实验结果表明,该新方法定位精度更高,面积误差更小。展开更多
Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of ...Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.展开更多
This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters an...This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.展开更多
文摘Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的独立抽样和随机游走抽样的Metropolis-Hastings(M-H)算法,利用可读性较强的Matlab程序来实现两种抽样算法,并给出了详细的程序实施过程,分析了两种抽样的优缺点。模拟分析结果表明:独立抽样M-H算法比较容易实施,但是要求建议分布和后验分布的吻合度较高,否则计算效率低下,而且模拟效果不理想;随机游走抽样的M-H算法不需要建议分布接近后验分布,模拟效果也比较好,因此,克服了独立抽样算法的不足,适用范围更广。
文摘针对不规则区域面积测算中定位精度和面积计算精度两方面不足,提出一种定位精度高、面积误差小的面积测算新方法。其采用一种组合定位方法精确定位,即将差分GPS测量系统(DGPS)与马尔可夫链蒙特卡罗(Markov chain Monte Carol,MCMC)粒子滤波相结合,再配合复化Newton-cotes算法,拟合边界曲线并准确求得区域面积。将MCMC粒子滤波应用于DGPS定位数据处理,其既可处理非高斯分布噪声,又解决粒子滤波(PF)的粒子退化问题,提高定位精度。将复化Newton-cotes算法应用于面积计算,其既避免高次插值的舍入误差,又将面积区间进一步细分,提高面积计算精度。实验结果表明,该新方法定位精度更高,面积误差更小。
文摘Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.
文摘This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.
