The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.

A laboratory study of directional spectra with maximum likelihood method─I Developing wind wave

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.

Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models

Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.

Maximum Entropy Empirical Likelihood Methods Based on Laplace Transforms for Nonnegative Continuous Distribution with Actuarial Applications

Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.

CONVERGENCE OF ITERATION METHODS OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS APPLICATIONS

Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.

Maximum likelihood spectrum estimation method and its application in seismo－magnet－icrelation

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A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Quasi Maximum Likelihood for MESS Varying Coefficient Panel Data Models with Fixed Effects

The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields,such as demog­raphy,epidemiology,regional economics,and psychology.With the deepening of research,some scholars find that there are some model specifications in spatial econometrics,such as spatial autoregressive(SAR)model and matrix exponential spatial specification(MESS),which cannot be nested within each other.Compared with the common SAR models,the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maxi­mum likelihood estimation and Bayesian estimation.Meanwhile,MESS models have theoretical advantages.However,the theoretical research and application of MESS models have not been promoted vigorously.Therefore,the study of MESS model theory has practical significance.This paper studies the quasi maximum likelihood estimation for ma­trix exponential spatial specification(MESS)varying coefficient panel data models with fixed effects.It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymp­totic normality to make a further supplement for the theoretical study of MESS model.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

Maximum Likelihood Estimation of the Identification Parameters and Its Correction

By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.

Unified Asymptotic Results for Maximum Spacing and Generalized Spacing Methods for Continuous Models

Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.

A laboratory study of directional spectrawith maximum likelihood mehod─ⅡDecaying swell

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the directional spreading of swell, qualitatively similar to that of developing wind wave which is narrowest in the region of Peak frequency and bxoadens with increasing or decreasing frequency, can be effectively described by cos2s(θ/2) introduced by Longuet-Higgins et al. (1963,Ocean Wave Spectra, 111~136). It is intriguing that bimodal distribution found in our experiments appers at the forward face instead of the rear face of a frequency spectrum in the cases of nonlinearity being very weak. Parameterized by nonlinearity, formulations which can be applied to swell as well as wind wave are proposed. It is concluded that nonlinear interaction plays a central role in controlling the development of directional angular spreading even for the swell.

On the Maximum Likelihood and Least Squares Estimation for the Inverse Weibull Parameters with Progressively First-Failure Censoring

In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.

A Fast Bayesian Evaluation Algorithm Based on the Second Category of Maximum Likelihood

Directing at evaluation for qualifying rate in weaponry test,this article discusses firstly how field test information is flooded with lots of prior information.Then a fast Bayesian evaluation algorithm is presented based on the elaborate analysis of prior information reliability and the second category of maximum likelihood.The example demonstrates that the algorithm presented in this article is better and more robust compared with classical evaluation algorithm for safe-or-failure test and normal Bayesian method,which can make the best of prior information.

部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法

主要研究了部分线性变系数空间自回归模型的变量选择问题。结合拟最大似然方法、局部线性光滑方法以及一类非凸罚函数,提出了一个变量选择方法用于同时选择该模型的参数部分中重要解释变量和估计相应的非零参数。大量模拟研究表明,所提出的变量选择方法具有满意的有限样本性质,并且关于空间权矩阵的稀疏度、空间相关强度、系数函数的复杂度以及误差分布的非正态性非常稳健。特别地,当样本容量较大且罚函数选择合适时,即使解释变量的相关性较强或者模型中含有较多不重要解释变量,所提出的变量选择方法仍然具有比较满意的有限样本性质。通过分析波士顿房屋价格数据考察了所提出的变量选择方法的实际应用效果。

2022年9月5日四川泸定6.8级地震及其余震前后b值变化

收集2012年1月1日—2023年2月8日四川泸定地区(29.28°~30.04°N,101.82°~102.28°E)记录的地震资料,利用最大似然法进行b值的空间扫描,揭示泸定主震区及周边区域b值的时空变化特征。计算结果显示,2022年泸定6.8级地震前5个月,主震区及其东南区b值出现加速下降变化,可能预示着局部岩石受力变形接近临界状态;5.6级强余震前,震中区b值仍然维持低值异常,显示出区域内的应力水平仍然偏高,预示着可能会发生强余震;5.6级余震发生后,异常区域明显缩小但未消失,预示着余震可能还将持续,但再次发生强余震的可能性较小。

考虑历史洪水资料的三峡水库运行期非一致性设计洪水估算

水利水电工程规划设计采用单站的天然年最大洪水系列资料和P-Ⅲ型适线法推求设计洪水,确定水库特征水位。然而上游水库的建成运行,破坏了下游洪水资料系列的一致性假定。本文通过构建非一致性洪水频率分析时变矩模型,计算了长江上游重点水库群的水库系数;并根据连续型随机变量分布函数单调递增的特性,提出了基于Q-Q图的时变P-Ⅲ型适线法;推求出考虑历史洪水资料的三峡水库运行期非一致性设计洪水,并与极大似然法的估算成果进行比较。结果表明:①水库系数作为时变P-Ⅲ型分布的协变量,可以反映洪水系列的非一致性变化规律;②时变P-Ⅲ型适线法侧重考虑历史洪水点据的拟合,拟合效果优于极大似然法;③相较原设计成果,三峡水库运行期1000年一遇设计洪峰Q m、洪量W 3d和W 7d削减18%左右,洪量W 15d和W 30d削减14%左右,长江上游水库群的调蓄作用直接影响三峡水库运行期的防洪库容和特征水位。

利用微卫星标记鉴定核桃杂交子代的亲本

杂交育种是目前核桃育种的主要方法,为了快速有效地鉴别杂交子代的真实性,加速杂交育种进程,利用微卫星标记方法辅助进行核桃亲子鉴定。研究从已发表的60对核桃属植物微卫星标记中筛选出12个多态性相对较高且稳定扩增的微卫星位点,对5个杂交组合子代159个个体通过基因型排除法和最大似然法进行亲子关系鉴定。基因型排除法鉴定出121个子代的正确亲本,鉴定率较高,总鉴定率76.10%;最大似然法亲权分析显示,双亲未知情形达到置信区间预测出正确亲本的子代有12个,总鉴定率7.55%。父本未知情形达到置信区间推算出正确亲本的子代有19个,总体鉴定率11.95%。整体鉴定率较低。

综合后向散射特征与极化特征的L波段SAR数据岩石分类

以菲律宾民都洛岛为研究区域,选取ALOS PALSAR双极化数据(极化方式为HH和HV极化)作为数据源,通过提取后向散射系数(Sigma0 HH和Sigma0 HV)和极化分解参数(熵、角和反熵),使用最大似然分类方法实现研究区的岩石单元分类和填图。在加入了极化分解参数之后,总体精度由仅使用后向散射系数的36.706%提高到65.000%。海岸带沼泽和珊瑚礁的F1分数超过了0.80,辉长岩和Mansalay组的F1分数超过了0.75。引入极化特征后,岩石单元的边界被更好地提取,Mansalay组和Mindoro变质岩与其他岩石的可分性增强。3个极化分解参数弥补了多种岩石单元的后向散射系数难以区分的不足,显著提高了岩石单元的可分性。研究表明,L波段SAR数据的极化分解参数和后向散射系数相结合能提高植被覆盖区岩石单元的分类精度。

基于多应用场景的改进DV-Hop定位模型

针对距离矢量跳(DV-Hop)定位模型定位精度低、优化策略场景依赖性强的问题,提出一种基于函数分析和模拟定参的改进DV-Hop模型——函数修正距离矢量跳(FuncDV-Hop)定位模型。首先,分析DV-Hop模型的平均跳距、距离估计和最小二乘法中的误差原因,引入待定系数优化、阶跃函数分段实验、带等效点的权重函数策略和极大似然估计修正;其次,考虑多应用场景,用控制变量法,分别将总节点数、信标节点比例、通信半径、信标节点数和待测节点数作为变量,设计对照实验;最后,进行仿真定参和整合优化测试两阶段实验,最终的改进策略较原DV-Hop模型的定位精度提高了23.70%~75.76%,平均优化率57.23%。实验结果表明,FuncDV-Hop模型的优化率最高达到了50.73%,与基于遗传算法和神经动力学改进的DV-Hop模型相比,FuncDV-Hop模型的优化率提升了0.55%~18.77%。所提模型不引入其他参量,不增加无线传感器网络(WSN)的协议开销,且有效提高定位精度。