Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustme...Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustment Kalman filter（EAKF） and sequential importance resampling particle filter（SIR-PF）, using a well-known nonlinear and non-Gaussian model（Lorenz ＇63 model）. The EAKF, which is a deterministic scheme of the ensemble Kalman filter（En KF）, performs better than the classical（stochastic） En KF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter（EAKPF）, is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic En KF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz ＇63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.展开更多
Estimation of large covariance matrices is of great importance in multivariate analysis.The modified Cholesky decomposition is a commonly used technique in covariance matrix estimation given a specific order of variab...Estimation of large covariance matrices is of great importance in multivariate analysis.The modified Cholesky decomposition is a commonly used technique in covariance matrix estimation given a specific order of variables.However,information on the order of variables is often unknown,or cannot be reasonably assumed in practice.In this work,we propose a Choleskybased model averaging approach of covariance matrix estimation for high dimensional datawith proper regularisation imposed on the Cholesky factor matrix.The proposed method not only guarantees the positive definiteness of the covariance matrix estimate,but also is applicable in general situations without the order of variables being pre-specified.Numerical simulations are conducted to evaluate the performance of the proposed method in comparison with several other covariance matrix estimates.The advantage of our proposed method is further illustrated by a real case study of equity portfolio allocation.展开更多
基金The National Natural Science Foundation of China under contract Nos 41276029 and 41321004the Project of State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography under contract No.SOEDZZ1404the National Basic Research Program(973 Program)of China under contract No.2013CB430302
文摘Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustment Kalman filter（EAKF） and sequential importance resampling particle filter（SIR-PF）, using a well-known nonlinear and non-Gaussian model（Lorenz ＇63 model）. The EAKF, which is a deterministic scheme of the ensemble Kalman filter（En KF）, performs better than the classical（stochastic） En KF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter（EAKPF）, is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic En KF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz ＇63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.
基金National Science of Foundation of China[grant number NSFC-71531004]NNSF.
文摘Estimation of large covariance matrices is of great importance in multivariate analysis.The modified Cholesky decomposition is a commonly used technique in covariance matrix estimation given a specific order of variables.However,information on the order of variables is often unknown,or cannot be reasonably assumed in practice.In this work,we propose a Choleskybased model averaging approach of covariance matrix estimation for high dimensional datawith proper regularisation imposed on the Cholesky factor matrix.The proposed method not only guarantees the positive definiteness of the covariance matrix estimate,but also is applicable in general situations without the order of variables being pre-specified.Numerical simulations are conducted to evaluate the performance of the proposed method in comparison with several other covariance matrix estimates.The advantage of our proposed method is further illustrated by a real case study of equity portfolio allocation.
