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1.
文中证明了泊松分布中未知参数的矩估计和最大似然估计,一定存在一个先验分布,使其贝叶斯估计就是该经典估计的结论.  相似文献   

2.
贝叶斯统计的发展及其争鸣   总被引:2,自引:0,他引:2  
概述了贝叶斯统计的基本思想,通过实例分析了确定先验信息方法的思维合理性。探讨了贝叶斯统计未来理论发展及其应用空间。  相似文献   

3.
贝叶斯方法是对多项分布参数进行点估计的重要方法.在统计学家对无信息先验作了大量的研究工作的基础上,通过推导得到一组关于该无信息先验分布的结论并利用这组结论研究其后验均值.结果表明:后验均值可使后验均方差达到最小.  相似文献   

4.
借助矩阵范数和向量范数的概念,结合矩阵幂级数的有关结论 ,给出了矩阵逆的误差估计。  相似文献   

5.
    
Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the t distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. The analysis of mathematical development data shows that the robust latent basis growth curve model better describes the mathematical growth trajectory than the corresponding normal growth curve model and can reveal the individual differences in mathematical development. Simulation studies further confirm that the robust growth curve models significantly outperform the normal growth curve models for both heavy-tailed t data and normal data with outliers but lose only slight efficiency for normal data. It appears convincing to replace the normal distribution with the t distribution for growth curve analysis. Three information criteria are evaluated for model selection. Online software is also provided for conducting robust analysis discussed in this study.  相似文献   

6.
当期望信号导向矢量失配以及采样协方差矩阵中包含期望信号时,传统自适应波束形成器性能会下降。对此问题,提出了一种基于协方差矩阵重构的稳健波束形成算法。该算法首先通过对期望信号和干扰的大致来波方向范围进行积分以估计出导向矢量,然后利用主模式抑制去除信号间多余的相干性,并重构出最终的协方差矩阵。仿真实验表明,该算法提高了期望信号导向矢量失配时的稳健性,降低了对快拍数的敏感性。  相似文献   

7.
采用Bayes方法从无先验信息出发,得到了非线性模型中方差和协方差分量的估计(包含相关系数),最后通过实例解算,结果表明:非线性模型中方差和协方差分量的估计,与ρ的理论值-0.5偏差不大,当没有先验信息时,该方法是可行的.  相似文献   

8.
    
Latent growth curve models are widely used in the social and behavioral sciences to study complex developmental patterns of change over time. The trajectories of these developmental patterns frequently exhibit distinct segments in the studied variables. Latent growth models with piecewise functions for repeated measurements of variables have become increasingly popular for modeling such developmental trajectories. A major problem with using piecewise models is determining the precise location of the point where the change in the process has occurred and uncovering the related number of segments. The purpose of this paper is to introduce an optimization procedure that can be used to determine both the segments and location of the knots in piecewise linear latent growth models. The procedure is illustrated using empirical data in order to detect the number of segments and change points. The results demonstrate the capabilities of the procedure for fitting latent growth curve models.  相似文献   

9.
讨论了某些4×4阶分块矩阵的可逆性条件并给出了可逆时的求逆公式.  相似文献   

10.
The authors examined the robustness of multilevel linear growth curve modeling to misspecification of an autoregressive moving average process. As previous research has shown (J. Ferron, R. Dailey, &; Q. Yi, 2002; O. Kwok, S. G. West, &; S. B. Green, 2007; S. Sivo, X. Fan, &; L. Witta, 2005), estimates of the fixed effects were unbiased, and Type I error rates for the tests of the fixed effects were generally accurate when the present authors correctly specified or underspecified the model. However, random effects were poorly estimated under many conditions, even under correct model specification. Further, fit criteria performed inconsistently and were especially inaccurate when small sample sizes and short series lengths were combined. With the exception of elevated Type I error rates that occurred under some conditions, the best performance was obtained by use of an unstructured covariance matrix at the first level of the growth curve model.  相似文献   

11.
首先给出同时用初等行变换与初等列变换求可逆矩阵的逆矩阵的方法,然后将此方法推广,得到求一般矩阵广义逆矩阵的具有实用性的方法。  相似文献   

12.
    
Individual growth trajectories of psychological phenomena are often theorized to be nonlinear. Additionally, individuals’ measurement schedules might be unique. In a structural equation framework, latent growth curve model (LGM) applications typically have either (a) modeled nonlinearity assuming some degree of balance in measurement schedules, or (b) accommodated truly individually varying time points, assuming linear growth. This article describes how to fit 4 popular nonlinear LGMs (polynomial, shape-factor, piecewise, and structured latent curve) with truly individually varying time points, via a definition variable approach. The extension is straightforward for certain nonlinear LGMs (e.g., polynomial and structured latent curve) but in the case of shape-factor LGMs requires a reexpression of the model, and in the case of piecewise LGMs requires introduction of a general framework for imparting piecewise structure, along with tools for its automation. All 4 nonlinear LGMs with individually varying time scores are demonstrated using an empirical example on infant weight, and software syntax is provided. The discussion highlights some advantages of modeling nonlinear growth within structural equation versus multilevel frameworks, when time scores individually vary.  相似文献   

13.
We compared six common methods in estimating the 2-1-1 (level-2 independent, level-1 mediator, level-1 dependent) multilevel mediation model with a random slope. They were the Bayesian with informative priors, the Bayesian with non-informative priors, the Monte-Carlo, the distribution of the product, the bias-corrected, and the bias-uncorrected parametric percentile residual bootstrap. The Bayesian method with informative priors was superior in relative mean square error (RMSE), power, interval width, and interval imbalance. The prior variance and prior mean were also varied and examined. Decreasing the prior variance increased the power, reduced RMSE and interval width when the prior mean was the true value, but decreasing the prior variance reduced the power when the prior mean was set incorrectly. The influence of misspecification of prior information of the b coefficient on multilevel mediation analysis was greater than that on coefficient a. An illustrate example with the Bayesian multilevel mediation was provided.  相似文献   

14.
一种求摄动矩阵的逆矩阵的方法   总被引:2,自引:0,他引:2  
应用矩阵的运算法则和逆矩阵的定义,对摄动矩阵(A+δuv^T)和它的更一般形式(A+UBV)给出了具体的求逆矩阵公式。  相似文献   

15.
针对 MIMO-OFDM 系统,提出了一种最大后验概率的信道矩阵和干扰协方差矩阵估计方法,并设计了迭代求解算法。利用所估计的信道矩阵和干扰协方差矩阵,采用 IRC 接收机完成同信道干扰的抑制。利用干扰协方差阵的共轭对称与半正定等特性,提出2种干扰协方差矩阵的处理方案以提高其估计精度。第1种方案将每个子载波上干扰协方差矩阵表征为一系列时域矩阵之和,第2种方案将每个子载波上的干扰协方差矩阵用低阶模型来建模,其中模型阶数通过最小描述长度算法估计。仿真结果表明了所提方案的有效性。  相似文献   

16.
Within Bayesian estimation, prior distributions are placed on model parameters and these distributions can take on many different levels of informativeness. Although much of the research conducted within this estimation framework uses what are called diffuse (or noninformative) priors, there are certain models and modeling circumstances where it is more optimal to use what are referred to as informative priors. This study focuses on the latter situation and examines the effects of inaccurate informative priors on the growth parameters within the context of growth mixture modeling. Overall, results indicated that growth mixture modeling is relatively robust to the use of inaccurate mean hyperparameters for the growth parameters, as long as the variance hyperparameters are somewhat large.  相似文献   

17.
    
This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting models on the search of the true mean growth model was investigated in terms of the mean and within-subject variance-covariance (V-C) structure model. The results showed that specifying the most complex (i.e., unstructured) within-subject V-C structure with the use of LRT, ΔAIC, and ΔBIC achieved the highest recovery rate (>85%) of the true mean trajectory. Implications of the findings and limitations are discussed.  相似文献   

18.
本文给出了用特殊分块法求逆矩阵的充要条件及一些推导结果和应用.  相似文献   

19.
对几类特殊矩阵的逆矩阵问题进行了研究,讨论了它们可逆的条件,分析了这些矩阵与其逆矩阵之间的关系,并给出了其逆矩阵的特征或求逆矩阵的公式.  相似文献   

20.
循环矩阵的逆问题   总被引:3,自引:0,他引:3  
本文对循环矩阵的逆问题进行了探讨,提出了求解循环矩阵的逆的两个方法,文中所提方法比现有的方法简单实用。  相似文献   

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