Bayesian using Importance Sampling Technique of Weibull Regression with Type II Censored Data

Keeping in view the Bayesian approach, the study aims to develop methods through the utilization of Jeffreys prior and modified Jeffreys prior to the covariate obtained by using the Importance sampling technique. For maximum likelihood estimator, covariate parameters, and the shape parameter of Weibull regression distribution with the censored data of Type II will be estimated by the study. It is shown that the obtained estimators in closed forms are not available, but through the usage of appropriate numerical methods, they can be solved. The mean square error is the criterion of comparison. With the use of simulation, performances of these three estimates are assessed, bearing in mind different censored percentages, and various sizes of the sample.

Quantifying Precipitation Uncertainty for Land Data Assimilation Applications

Ensemble-based data assimilation techniques are often applied to land surface models in order to estimate components of terrestrial water and energy balance. Precipitation forcing uncertainty is the principal source of spread among the ensembles that is required for utilizing information in observations to correct model priors. Precipitation fields may have both position and magnitude errors. However, current uncertainty characterizations of precipitation forcing in land data assimilation systems often do no more than applying multiplicative errors to precipitation fields. In this paper, an ensemble-based Bayesian method for characterization of uncertainties associated with precipitation retrievals from spaceborne instruments is introduced. This method is used to produce stochastic replicates of precipitation fields that are conditioned on precipitation observations. Unlike previous studies, the error likelihood is derived using an archive of historical measurements. The ensemble replicates are generated using a stochastic method, and they are intermittent in space and time. The replicates are first projected in a low-dimension subspace using a problem-specific set of attributes. The attributes are derived using a dimensionality reduction scheme that takes advantage of singular value decomposition. A nonparametric importance sampling technique is formulated in terms of the attribute vectors to solve the Bayesian sampling problem. Examples are presented using retrievals from operational passive microwave instruments, and performance of the method is assessed using ground validation measurements from a surface weather radar network. Results indicate that this ensemble characterization approach provides a useful description of precipitation uncertainties with a posterior ensemble that is narrower in distribution than its prior while containing both precipitation position and magnitude errors.

Research on Foronline Short-Term Risk Assessment of Power System with Fast and Accurate Analysis Method Based on State Space Division

This paper proposed a state space division method to assess the online short-term risk of power system fast and accurately. This method divided all the possible operation system states into two mutually complementary subspaces according to the occurrence probability. In order to shorten the time-consuming, different method was used to calculate the risk of each subspace. Analytical method (AM) was used to calculate the risk of the first subspace comprised with the large occurrence probability states, which was identified using the Fast Sorting Technique (FST). System states that have a small occurrence probability comprised the second subspace, whose risk was calculated using Monte Carlo Simulation (MCS) combined with the adaptive importance sampling technique (AIST) and scattered sampling technique (SST). Through the case studies conducted on the MRTS, it is validated that the proposed method can assess the online short-term risk fast and accurately.