The valuation of financial derivatives often assumes risk neutrality with respect to the risk-neutral martingale measure,which prevents arbitrage opportunities.However,casual traders may still incur substantial losses...The valuation of financial derivatives often assumes risk neutrality with respect to the risk-neutral martingale measure,which prevents arbitrage opportunities.However,casual traders may still incur substantial losses when trading at this risk-neutral price,especially when the price has to be paid now and the payoff is only realized in the future.This study proposes a new valuation framework that provides risksensitive investors with an additional safeguard.The proposed framework embraces a worst-case perspective while exploiting the underlier’s stochastic process,representing a combination of robust optimization and stochastic programming.Notably,it aims to mitigate losses in the likelier scenarios of the underlying asset’s prices.When the underlier’s returns are independent and lognormally but not necessarily identically distributed,our approach for pricing variance and volatility swaps could be greatly simplified,benefit from parallel computing,and be solved by a two-dimensional grid search.We further derive a closed-form solution in some special stationary cases and provide experimental results to highlight the effect of risk aversion on fending off sizable trading losses.展开更多
The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained expe...The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained experimentally through tests on specimens under multiaxial loading with that calculated by the variance method. In the statistical approach criteria, several methods have been developed but we have presented only one method, namely the variance method using the equivalent stress. She assumes that the fracture plane orientation is the one on which the variance of the equivalent stress is maximum. Three types of equivalent stress are defined for this method [1]: normal stress, shear stress and combined normal and shear stress. The results obtained were compared with experimental results for multiaxial cyclic stress states, and it emerges that the variance method for the case of combined loading is conservative as it gives a better prediction of the fracture plane.展开更多
In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance c...In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.展开更多
Working toward an efficient duration and timeline for the preconstruction phase should be one of the main objectives for project owners.Failing to plan for and coordinate preconstruction decisions in order to control ...Working toward an efficient duration and timeline for the preconstruction phase should be one of the main objectives for project owners.Failing to plan for and coordinate preconstruction decisions in order to control preconstruction duration and manage time variances can lead to financial insecurities,incomplete contract documents,permitting issues,and unrealistic schedules and resource allocation during this phase.To minimize time variances and ensure a productive decision-making process,project owners should be familiar with critical elements in a project that cause variances in the preconstruction phase timeline.In this study,the impacts of eleven critical preconstruction elements on time variances were analyzed.These eleven preconstruction elements are considered critical in how they impact time variances during the preconstruction phase.They were determined to be critical based either on significantly impacting time variance during the preconstruction phase or believed to be critical from findings from previous studies,however,the findings from this study showed no significant impact on the time variances.In most previous studies focusing on the elements impacting project schedules,data were collected by surveying construction professionals.In this study,objective and quantitative data related to project preconstruction elements were used as opposed to self-reported data.Using the results of this study,project owners and stakeholders will be able to evaluate the critical preconstruction elements impacting the timing of their projects and prioritize decisions related to the critical elements early on during the preconstruction phase.展开更多
A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inve...A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.展开更多
[ Objective] The aim was to study variance type of capsule morphological characters in Platycodon grandiflorum population, and provide some theoretical basis for seeking to genetic markers which can differentiate diff...[ Objective] The aim was to study variance type of capsule morphological characters in Platycodon grandiflorum population, and provide some theoretical basis for seeking to genetic markers which can differentiate different P. grandiflorum and breeding new varieties. [ Method] According to shape morphological characters of capsule from the same population of perennial purple P. gandiflorum, seven types of distinct di- versity capsule were selected, variance analysis and multiple comparison on the length, diameter, length/diameter of the different types of capsule were carried out. [ Result] There is unicolor and bicolor, even trichrome, among main color was brown and purple. Capsule shape was main cone, furthermore, containing long roller type, spheroidicity and sphericity. [ Conclusion] P. gandiflorum capsule was divided into long form, short form and middle type from length/diameter size in perennial culture P. gandiflorum population.展开更多
An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances ...An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...展开更多
This paper is concerned with the control performance assessment based on the multivariable generalized minimum variance benchmark.An explicit expression for the feedback controller-invariant(the generalized minimum va...This paper is concerned with the control performance assessment based on the multivariable generalized minimum variance benchmark.An explicit expression for the feedback controller-invariant(the generalized minimum variance)term of the multivariable control system is obtained,which is used as a standard benchmark for the assessment of the control performance for multi input multi output(MIMO)process.The proposed approach is based on the multivariable minimum variance benchmark.In comparison with the minimum variance benchmark, the developed method is more reasonable and practical for the control performance assessment of multivariable systems.The approach is illustrated by a simulation example and an industrial application.展开更多
This paper describes the application of the variance method for flux estimation over a mixed agricultural region in China. Eddy covariance and flux variance measurements were conducted in a near-surface layer over a n...This paper describes the application of the variance method for flux estimation over a mixed agricultural region in China. Eddy covariance and flux variance measurements were conducted in a near-surface layer over a non-uniform land surface in the central plain of China from 7 June to 20 July 2002. During this period, the mean canopy height was about 0.50 m. The study site consisted of grass （10% of area）, beans （15%）, corn （15%） and rice （60%）. Under unstable conditions, the standard deviations of temperature and water vapor density （normalized by appropriate scaling parameters）, observed by a single instrument, followed the Monin-Obukhov similarity theory. The similarity constants for heat （CT） and water vapor （Cq） were 1.09 and 1.49, respectively. In comparison with direct measurements using eddy covariance techniques, the flux variance method, on average, underestimated sensible heat flux by 21% and latent heat flux by 24%, which may be attributed to the fact that the observed slight deviations （20% or 30% at most） of the similarity ＂constants＂ may be within the expected range of variation of a single instrument from the generally-valid relations.展开更多
Peak ground acceleration(PGA) estimation is an important task in earthquake engineering practice.One of the most well-known models is the Boore-Joyner-Fumal formula,which estimates the PGA using the moment magnitude,t...Peak ground acceleration(PGA) estimation is an important task in earthquake engineering practice.One of the most well-known models is the Boore-Joyner-Fumal formula,which estimates the PGA using the moment magnitude,the site-to-fault distance and the site foundation properties.In the present study,the complexity for this formula and the homogeneity assumption for the prediction-error variance are investigated and an effi ciency-robustness balanced formula is proposed.For this purpose,a reduced-order Monte Carlo simulation algorithm for Bayesian model class selection is presented to obtain the most suitable predictive formula and prediction-error model for the seismic attenuation relationship.In this approach,each model class(a predictive formula with a prediction-error model) is evaluated according to its plausibility given the data.The one with the highest plausibility is robust since it possesses the optimal balance between the data fi tting capability and the sensitivity to noise.A database of strong ground motion records in the Tangshan region of China is obtained from the China Earthquake Data Center for the analysis.The optimal predictive formula is proposed based on this database.It is shown that the proposed formula with heterogeneous prediction-error variance is much simpler than the attenuation model suggested by Boore,Joyner and Fumal(1993).展开更多
Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased est...Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.展开更多
This paper deals with the problem of designing robust sequential covariance intersection(SCI)fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise varian...This paper deals with the problem of designing robust sequential covariance intersection(SCI)fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances.The sensor network is partitioned into clusters by the nearest neighbor rule.Using the minimax robust estimation principle,based on the worst-case conservative sensor network system with conservative upper bounds of noise variances,and applying the unbiased linear minimum variance(ULMV)optimal estimation rule,we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources,and guarantee that the actual filtering error variances have a less-conservative upper-bound.A Lyapunov equation method for robustness analysis is proposed,by which the robustness of the local and fused Kalman filters is proved.The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved.It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter.A simulation example for a tracking system verifies the robustness and robust accuracy relations.展开更多
When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem...When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.展开更多
Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of ...Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.展开更多
The current standard for measuring tumor response using X-ray, CT and MRI is based on the response evaluation criterion in solid tumors (RECIST) which, while providing simplifications over previous (WHO) 2-D methods, ...The current standard for measuring tumor response using X-ray, CT and MRI is based on the response evaluation criterion in solid tumors (RECIST) which, while providing simplifications over previous (WHO) 2-D methods, stipulate four response categories: CR (complete response), PR (partial response), PD (progressive disease), SD (stable disease) based purely on percentage changes without consideration of any measurement uncertainty. In this paper, we propose a statistical procedure for tumor response assessment based on uncertainty measures of radiologist’s measurement data. We present several variance estimation methods using time series methods and empirical Bayes methods when a small number of serial observations are available on each member of a group of subjects. We use a publically available database which contains a set of over 100 CT scan images on 23 patients with annotated RECIST measurements by two radiologist readers. We show that despite of bias in each individual reader’s measurements, statistical decisions on tumor change can be made on each individual subject. The consistency of the two readers can be established based on the intra-reader change assessments. Our proposal compares favorably with the RECIST standard protocol, raising the hope that, statistically sound decision on change analysis can be made in future based on careful variability and measurement uncertainty analysis.展开更多
This paper studies the estimation of variance and covariance compo-nents for GPS baseline network by MINQUE method.The fundamental rule forselecting variance-covariance model has been presented,and the alternative alg...This paper studies the estimation of variance and covariance compo-nents for GPS baseline network by MINQUE method.The fundamental rule forselecting variance-covariance model has been presented,and the alternative algo-rithm which simultaneouly estimates fixed variance components and scalled vari-ance components of the distance,azimuth and geodetic height difference for a GPSbaseline vector has been developed.展开更多
In order to improve the robustness and noise resistance of generalized minimum valance cothrol systems, several generalizedminimum variance control schemes are synthetically analyzed. The output variance caused by st...In order to improve the robustness and noise resistance of generalized minimum valance cothrol systems, several generalizedminimum variance control schemes are synthetically analyzed. The output variance caused by stochastic noise is decomposed to two parts. One part accords with the output variance of minboum vedance control and the other is the additional term of output variance causedby the control weighting factors. At the same time, the sensitivity function of modeling error is also deduced. A new robast design method that can minimize the sensitivity and the additional part of output variance is Presented by regulating variable parameters of contollers. The simulation results of self-tuning control show the effect of this method.展开更多
Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for t...Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.展开更多
This paper presents a new method for detection of edges in digital angiographic images. It is found that variances of local regions across edges of images are statistically different from that of those where no edge i...This paper presents a new method for detection of edges in digital angiographic images. It is found that variances of local regions across edges of images are statistically different from that of those where no edge is crossed. This difference can be utilized for the detection of edges of angiographic images. An algorithm based on local variance is proposed. As a result, the edge-detection algorithm is not sensitive to noise and low-level textures of images. A computer program based on the new algorithm has been developed and used by several hospitals.展开更多
基金supported by the Ministry of Education,Singapore,under its Academic Research Fund Tier 2 Grant MOE-T2EP20222-0003.
文摘The valuation of financial derivatives often assumes risk neutrality with respect to the risk-neutral martingale measure,which prevents arbitrage opportunities.However,casual traders may still incur substantial losses when trading at this risk-neutral price,especially when the price has to be paid now and the payoff is only realized in the future.This study proposes a new valuation framework that provides risksensitive investors with an additional safeguard.The proposed framework embraces a worst-case perspective while exploiting the underlier’s stochastic process,representing a combination of robust optimization and stochastic programming.Notably,it aims to mitigate losses in the likelier scenarios of the underlying asset’s prices.When the underlier’s returns are independent and lognormally but not necessarily identically distributed,our approach for pricing variance and volatility swaps could be greatly simplified,benefit from parallel computing,and be solved by a two-dimensional grid search.We further derive a closed-form solution in some special stationary cases and provide experimental results to highlight the effect of risk aversion on fending off sizable trading losses.
文摘The prediction of the fracture plane orientation in fatigue is a scientific topic and remains relevant for every type of material. However, in this work, we compared the orientation of the fracture plane obtained experimentally through tests on specimens under multiaxial loading with that calculated by the variance method. In the statistical approach criteria, several methods have been developed but we have presented only one method, namely the variance method using the equivalent stress. She assumes that the fracture plane orientation is the one on which the variance of the equivalent stress is maximum. Three types of equivalent stress are defined for this method [1]: normal stress, shear stress and combined normal and shear stress. The results obtained were compared with experimental results for multiaxial cyclic stress states, and it emerges that the variance method for the case of combined loading is conservative as it gives a better prediction of the fracture plane.
基金supported by the National Natural Science Foundation of China(No.42174011)。
文摘In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.
文摘Working toward an efficient duration and timeline for the preconstruction phase should be one of the main objectives for project owners.Failing to plan for and coordinate preconstruction decisions in order to control preconstruction duration and manage time variances can lead to financial insecurities,incomplete contract documents,permitting issues,and unrealistic schedules and resource allocation during this phase.To minimize time variances and ensure a productive decision-making process,project owners should be familiar with critical elements in a project that cause variances in the preconstruction phase timeline.In this study,the impacts of eleven critical preconstruction elements on time variances were analyzed.These eleven preconstruction elements are considered critical in how they impact time variances during the preconstruction phase.They were determined to be critical based either on significantly impacting time variance during the preconstruction phase or believed to be critical from findings from previous studies,however,the findings from this study showed no significant impact on the time variances.In most previous studies focusing on the elements impacting project schedules,data were collected by surveying construction professionals.In this study,objective and quantitative data related to project preconstruction elements were used as opposed to self-reported data.Using the results of this study,project owners and stakeholders will be able to evaluate the critical preconstruction elements impacting the timing of their projects and prioritize decisions related to the critical elements early on during the preconstruction phase.
文摘A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.
文摘[ Objective] The aim was to study variance type of capsule morphological characters in Platycodon grandiflorum population, and provide some theoretical basis for seeking to genetic markers which can differentiate different P. grandiflorum and breeding new varieties. [ Method] According to shape morphological characters of capsule from the same population of perennial purple P. gandiflorum, seven types of distinct di- versity capsule were selected, variance analysis and multiple comparison on the length, diameter, length/diameter of the different types of capsule were carried out. [ Result] There is unicolor and bicolor, even trichrome, among main color was brown and purple. Capsule shape was main cone, furthermore, containing long roller type, spheroidicity and sphericity. [ Conclusion] P. gandiflorum capsule was divided into long form, short form and middle type from length/diameter size in perennial culture P. gandiflorum population.
基金National Basic Research Program of China (JW132006093)
文摘An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...
基金Supported by the National High Technology Research and Development Program of China(2008AA042902)the National Basic Research Program of China(2007CB714006)the Graduate Creative Research Program of Zhejiang Province (YK2008024)
文摘This paper is concerned with the control performance assessment based on the multivariable generalized minimum variance benchmark.An explicit expression for the feedback controller-invariant(the generalized minimum variance)term of the multivariable control system is obtained,which is used as a standard benchmark for the assessment of the control performance for multi input multi output(MIMO)process.The proposed approach is based on the multivariable minimum variance benchmark.In comparison with the minimum variance benchmark, the developed method is more reasonable and practical for the control performance assessment of multivariable systems.The approach is illustrated by a simulation example and an industrial application.
文摘This paper describes the application of the variance method for flux estimation over a mixed agricultural region in China. Eddy covariance and flux variance measurements were conducted in a near-surface layer over a non-uniform land surface in the central plain of China from 7 June to 20 July 2002. During this period, the mean canopy height was about 0.50 m. The study site consisted of grass （10% of area）, beans （15%）, corn （15%） and rice （60%）. Under unstable conditions, the standard deviations of temperature and water vapor density （normalized by appropriate scaling parameters）, observed by a single instrument, followed the Monin-Obukhov similarity theory. The similarity constants for heat （CT） and water vapor （Cq） were 1.09 and 1.49, respectively. In comparison with direct measurements using eddy covariance techniques, the flux variance method, on average, underestimated sensible heat flux by 21% and latent heat flux by 24%, which may be attributed to the fact that the observed slight deviations （20% or 30% at most） of the similarity ＂constants＂ may be within the expected range of variation of a single instrument from the generally-valid relations.
基金Research Committee of University of Macao under Research Grant No.MYRG081(Y1-L2)-FST13-YKVthe Science and Technology Development Fund of the Macao SAR government under Grant No.012/2013/A1
文摘Peak ground acceleration(PGA) estimation is an important task in earthquake engineering practice.One of the most well-known models is the Boore-Joyner-Fumal formula,which estimates the PGA using the moment magnitude,the site-to-fault distance and the site foundation properties.In the present study,the complexity for this formula and the homogeneity assumption for the prediction-error variance are investigated and an effi ciency-robustness balanced formula is proposed.For this purpose,a reduced-order Monte Carlo simulation algorithm for Bayesian model class selection is presented to obtain the most suitable predictive formula and prediction-error model for the seismic attenuation relationship.In this approach,each model class(a predictive formula with a prediction-error model) is evaluated according to its plausibility given the data.The one with the highest plausibility is robust since it possesses the optimal balance between the data fi tting capability and the sensitivity to noise.A database of strong ground motion records in the Tangshan region of China is obtained from the China Earthquake Data Center for the analysis.The optimal predictive formula is proposed based on this database.It is shown that the proposed formula with heterogeneous prediction-error variance is much simpler than the attenuation model suggested by Boore,Joyner and Fumal(1993).
文摘Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.
基金Supported by National Natural Science Foundation of China(60874063)Innovation and Scientific Research Foundation of Graduate Student of Heilongjiang Province(YJSCX2012-263HLJ)
文摘This paper deals with the problem of designing robust sequential covariance intersection(SCI)fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances.The sensor network is partitioned into clusters by the nearest neighbor rule.Using the minimax robust estimation principle,based on the worst-case conservative sensor network system with conservative upper bounds of noise variances,and applying the unbiased linear minimum variance(ULMV)optimal estimation rule,we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources,and guarantee that the actual filtering error variances have a less-conservative upper-bound.A Lyapunov equation method for robustness analysis is proposed,by which the robustness of the local and fused Kalman filters is proved.The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved.It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter.A simulation example for a tracking system verifies the robustness and robust accuracy relations.
基金supported by the National 973 Foundation of China(61322201)the National Natural Science Foundation of China(41304022,41174026,41104047)Key Laboratory Foundation of Geo-space Environment and Geodesy,Ministry of Education(11-01-03)
文摘When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.
文摘Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.
文摘The current standard for measuring tumor response using X-ray, CT and MRI is based on the response evaluation criterion in solid tumors (RECIST) which, while providing simplifications over previous (WHO) 2-D methods, stipulate four response categories: CR (complete response), PR (partial response), PD (progressive disease), SD (stable disease) based purely on percentage changes without consideration of any measurement uncertainty. In this paper, we propose a statistical procedure for tumor response assessment based on uncertainty measures of radiologist’s measurement data. We present several variance estimation methods using time series methods and empirical Bayes methods when a small number of serial observations are available on each member of a group of subjects. We use a publically available database which contains a set of over 100 CT scan images on 23 patients with annotated RECIST measurements by two radiologist readers. We show that despite of bias in each individual reader’s measurements, statistical decisions on tumor change can be made on each individual subject. The consistency of the two readers can be established based on the intra-reader change assessments. Our proposal compares favorably with the RECIST standard protocol, raising the hope that, statistically sound decision on change analysis can be made in future based on careful variability and measurement uncertainty analysis.
文摘This paper studies the estimation of variance and covariance compo-nents for GPS baseline network by MINQUE method.The fundamental rule forselecting variance-covariance model has been presented,and the alternative algo-rithm which simultaneouly estimates fixed variance components and scalled vari-ance components of the distance,azimuth and geodetic height difference for a GPSbaseline vector has been developed.
文摘In order to improve the robustness and noise resistance of generalized minimum valance cothrol systems, several generalizedminimum variance control schemes are synthetically analyzed. The output variance caused by stochastic noise is decomposed to two parts. One part accords with the output variance of minboum vedance control and the other is the additional term of output variance causedby the control weighting factors. At the same time, the sensitivity function of modeling error is also deduced. A new robast design method that can minimize the sensitivity and the additional part of output variance is Presented by regulating variable parameters of contollers. The simulation results of self-tuning control show the effect of this method.
基金Support was provided by Research Joint Venture Agreement 17-JV-11242306045,“Old Growth Forest Dynamics and Structure,”between the USDA Forest Service and the University of New HampshireAdditional support to MJD was provided by the USDA National Institute of Food and Agriculture McIntire-Stennis Project Accession Number 1020142,“Forest Structure,Volume,and Biomass in the Northeastern United States.”+1 种基金supported by the USDA National Institute of Food and Agriculture,McIntire-Stennis project OKL02834the Division of Agricultural Sciences and Natural Resources at Oklahoma State University.
文摘Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.
文摘This paper presents a new method for detection of edges in digital angiographic images. It is found that variances of local regions across edges of images are statistically different from that of those where no edge is crossed. This difference can be utilized for the detection of edges of angiographic images. An algorithm based on local variance is proposed. As a result, the edge-detection algorithm is not sensitive to noise and low-level textures of images. A computer program based on the new algorithm has been developed and used by several hospitals.
