A linear programming method for generating the most favorable weights from a pairwise comparison matrix

This paper proposes a linear programming method for generating the most favorable weights (LP-GFW) from pairwise comparison matrices, which incorporates the variable weight concept of data envelopment analysis (DEA) into the priority scheme of the analytic hierarchy process (AHP) to generate the most favorable weights for the underlying criteria and alternatives on the basis of a crisp pairwise comparison matrix. The proposed LP-GFW method can generate precise weights for perfectly consistent pairwise comparison matrices and approximate weights for inconsistent pairwise comparison matrices, which are not too far from Saaty's principal right eigenvector weights. The issue of aggregation of local most favorable weights and rank preservation methods is also discussed. Four numerical examples are examined using the LP-GFW method to illustrate its potential applications and significant advantages over some existing priority methods.     

Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification

For identifying errors-in-variables models, the time domain maximum likelihood (TML) method and the sample maximum likelihood (SML) method are two approaches. Both methods give optimal estimation accuracy but under different assumptions. In the TML method, an important assumption is that the noise-free input signal is modelled as a stationary process with rational spectrum. For SML, the noise-free input needs to be periodic. It is interesting to know which of these assumptions contain more information to boost the estimation performance. In this paper, the estimation accuracy of the two methods is analyzed statistically for both errors-in-variables (EIV) and output error models (OEM). Numerical comparisons between these two estimates are also done under different signal-to-noise ratios (SNRs). The results suggest that TML and SML have similar estimation accuracy at moderate or high SNR for EIV. For OEM identification, these two methods have the same accuracy at any SNR.     

Deriving weights from a pairwise comparison matrix over an alo-group

In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of odotodot-normal vectors, the relation of odotodot-proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighting ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.     

Threshold behaviour of the maximum likelihood method in population decoding

We study the performance of the maximum likelihood (ML) method in population decoding as a function of the population size. Assuming uncorrelated noise in neural responses, the ML performance, quantified by the expected square difference between the estimated and the actual quantity, follows closely the optimal Cramer-Rao bound, provided that the population size is sufficiently large. However, when the population size decreases below a certain threshold, the performance of the ML method undergoes a rapid deterioration, experiencing a large deviation from the optimal bound. We explain the cause of such threshold behaviour, and present a phenomenological approach for estimating the threshold population size, which is found to be linearly proportional to the inverse of the square of the system's signal-to-noise ratio. If the ML method is used by neural systems, we expect the number of neurons involved in population coding to be above this threshold.     

Using the maximum likelihood method to estimate test complexity levels

Consideration was given to the problem of estimating the levels of complexity of the test tasks for the remote education system. It was assumed that the random responses of the subjects obey the logistic distribution and the levels of student readiness are not known in advance. An algorithm based on the methods of maximum likelihood and Broyden-Fletcher-Goldfarb-Shanno was proposed to calculate the task complexity. Strict concavity of the logarithmic likelihood function was established, and an example was considered.     

A recursive (on-line) maximum likelihood identification method

A recursive (on-line) identification algorithm is developed based upon the off-line maximum likelihood method by Åström and Bohlin. The basic idea of the algorithm consists in two modifications to the classical method. First an approximate noisemodel is applied to eliminate auto-regressive filtering in the computation of the noise-derivatives. Second, some approximations are introduced to make the direct recursive version of the iteration equations really on-line. The combination of the two modifications yields a compact on-line algorithm.     

Analysis of empirical estimates obtained for gibbs distribution parameters by the maximum likelihood method

The paper examines the properties of consistency and asymptotic normality of the maximum likelihood estimate for Markov sequences with Gibbs distribution. Theorems are formulated and proved that allow approximating the criterion function of a Markov process with a unique minimum point by its empirical estimate. The results can be used to analyze the convergence of unknown parameters to their true values.     

改进的基于最大似然的快速拓扑估计方法

基于最大似然的网络拓扑估计方法能够获得全局最优的估计结果,优于一般局部最优化和节点对融合方法,但在网络规模较大时存在计算复杂度较高的缺点。首先证明了网络拓扑估计似然函数是单峰的（即只有一个极值）且峰值为最大值;然后利用单峰特征,改进了现有基于最大似然的拓扑估计方法,在最大似然树搜索过程中无需返回到似然值小的状态,降低了计算复杂度。最后,Matlab和ns-2仿真结果证明在不降低拓扑估计准确率的情况下,改进的算法将计算复杂度减少了30%~46%.     

A maximum likelihood method for an asymmetric MDS model

A maximum likelihood estimation method is proposed to fit an asymmetric multidimensional scaling model to a set of asymmetric data. This method is based on successive categories scaling, and enables us to analyze asymmetric proximity data measured, at least, at an ordinal scale level. It enables us to examine not only the appropriate scaling level of the data, but also the appropriate dimensionality of the model, using AIC. Prior to or in fitting the asymmetric MDS model, it is important to verify that the data are sufficiently asymmetric. Some variants of symmetry hypotheses are developed for this purpose. Since the emphasis in our paper is not on hypothesis testing, but on model diagnosis, we compare several candidate models including models with these hypotheses based on a similar model comparison idea using AIC. The method is applied to artificial data and a set of friendship data among nations in East Asia and the USA. Relations to other methods are also discussed.     

A maximum likelihood approximation method for Dirichlet's parameter estimation

Dirichlet distributions are natural choices to analyse data described by frequencies or proportions since they are the simplest known distributions for such data apart from the uniform distribution. They are often used whenever proportions are involved, for example, in text-mining, image analysis, biology or as a prior of a multinomial distribution in Bayesian statistics. As the Dirichlet distribution belongs to the exponential family, its parameters can be easily inferred by maximum likelihood. Parameter estimation is usually performed with the Newton-Raphson algorithm after an initialisation step using either the moments or Ronning's methods. However this initialisation can result in parameters that lie outside the admissible region. A simple and very efficient alternative based on a maximum likelihood approximation is presented. The advantages of the presented method compared to two other methods are demonstrated on synthetic data sets as well as for a practical biological problem: the clustering of protein sequences based on their amino acid compositions.     

A perceptual similarity method by pairwise comparison in a medical image case

The evolution of image techniques in medicine has improved decision making based on physicians’ experience by means of computer-aided diagnosis (CAD). This paper focuses on the development of content-based image retrieval (CBIR) and CAD techniques applied to bronchoscopies and according to different pathologies. A novel pairwise comparison method based on binary logistic regression is developed to determine those images must alike to a new image from incomplete property information, after accounting for the physicians’ appreciation of the image similarity. This method is particularly useful when problems with both a large number of features and few images are involved.     

MIMO雷达最大似然参数估计

多输入多输出(MIMO)雷达使用多个天线同时发射多个独立探测信号,并使用多个天线接收目标回波信号.本文考虑了发射空域分集、相干接收MIMO雷达模型及其最大似然(ML)参数估计方法.基于最大似然准则,本文推导了两种渐近最大似然算法.仿真实验的结果表明,在均匀噪声模型中,其中一种渐近算法与基于延迟求和波束形成的最大似然算法性能接近,而另一种渐近算法性能略差,但具有较低的计算复杂度.而在非均匀噪声模型中,本文所提出的两种渐近最大似然算法的性能均优于基于延迟求和波束形成的最大似然算法.     

A method for calibrated maximum likelihood classification of forest types

A modification to the maximum likelihood algorithm was developed for classification of forest types in Sweden's part of the CORINE land cover mapping project. The new method, called the “calibrated maximum likelihood classification” involves an automated and iterative adjustment of prior weights until class frequency in the output corresponds to class frequency as calculated from objective (field-inventoried) estimates. This modification compensates for the maximum likelihood algorithm's tendency to over-represent dominant classes and under-represent less frequent ones. National forest inventory plot data measured from a five-year period are used to estimate relative frequency of class occurrence and to derive spectral signatures for each forest class. The classification method was implemented operationally within an automated production system which allowed rapid production of a country-wide forest type map from Landsat TM/ETM+ satellite data. The production system automated the retrieval and updating of forest inventory plots, a plot-to-image matching routine, illumination and haze correction of satellite imagery, and classification into forest classes using the calibrated maximum likelihood classification. This paper describes the details of the method and demonstrates the result of using an iterative adjustment of prior weights versus unadjusted prior weights. It shows that the calibrated maximum likelihood algorithm adjusts for the overclassification of classes that are well represented in the training data as well as for other classes, resulting in an output where class proportions are close to those as expected based on forest inventory data.     

基于最大似然估计的小基高比立体匹配方法*

针对小高比立体匹配当中的亚像素精度和粘合现象问题,提出了一种基于最大似然估计的小基高比立体匹配方法。该方法首先根据混合式窗口选择策略为参考图像中的每一点确定匹配窗口;然后在视差范围内根据规范化互相关函数计算匹配代价,再利用胜者全取策略计算每一点视差;最后采用基于最大似然估计的亚像素匹配方法获得亚像素级视差。实验结果表明,该方法有效地减少了立体匹配中的粘合现象,同时获得了较高精度的亚像素视差,其平均亚像素精度可达1/20个像元。     

On the priority vector associated with a reciprocal relation and a pairwise comparison matrix

We propose two straightforward methods for deriving the priority vector associated with a reciprocal relation, by some authors called fuzzy preference relation. Then, using transformations between pairwise comparison matrices and reciprocal relations, we study the relationships between the priority vectors associated with these two types of preference relations. Eventually, we show a brief example involving the newly introduced characterizations.     

Faster ARMA maximum likelihood estimation

A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require O(n) flops per function evaluation. Using our new approximation, an algorithm is developed which requires only O(1) flops in repeated likelihood evaluations. In most cases, the new algorithm gives results identical to or very close to the exact maximum likelihood estimate (MLE). This algorithm is easily implemented in high level quantitative programming environments (QPEs) such as Mathematica, MatLab and R. In order to obtain reasonable speed, previous ARMA maximum likelihood algorithms are usually implemented in C or some other machine efficient language. With our algorithm it is easy to do maximum likelihood estimation for long time series directly in the QPE of your choice. The new algorithm is extended to obtain the MLE for the mean parameter. Simulation experiments which illustrate the effectiveness of the new algorithm are discussed. Mathematica and R packages which implement the algorithm discussed in this paper are available [McLeod, A.I., Zhang, Y., 2007. Online supplements to “Faster ARMA Maximum Likelihood Estimation”, 〈http://www.stats.uwo.ca/faculty/aim/2007/faster/〉]. Based on these package implementations, it is expected that the interested researcher would be able to implement this algorithm in other QPEs.     

Experimental comparison of algorithms for the problem of the maximum set of pairwise incomparable vertices in a digraph

Two branch-and-bound algorithms are analyzed for the problem of the maximum set of pairwise incomparable vertices in a digraph with additional constraints.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 161–165, September–October, 1992.     

Event-triggered maximum likelihood state estimation

The event-triggered state estimation problem for linear time-invariant systems is considered in the framework of Maximum Likelihood (ML) estimation in this paper. We show that the optimal estimate is parameterized by a special time-varying Riccati equation, and the computational complexity increases exponentially with respect to the time horizon. For ease in implementation, a one-step event-based ML estimation problem is further formulated and solved, and the solution behaves like a Kalman filter with intermittent observations. For the one-step problem, the calculation of upper and lower bounds of the communication rates from the process side is also briefly analyzed. An application example to sensorless event-based estimation of a DC motor system is presented and the benefits of the obtained one-step event-based estimator are demonstrated by comparative simulations.