This paper presents a time-domain stochastic system identification method based on MaximumLikelihood Estimation (MLE) with the Expectation Maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring . Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure (see Figure 2) have been estimated using both Stochastic Subspace Identification (SSI) method and the proposed MLE+EM method. SSI identification method is a well known method and computes accurate estimates of the modal parameters (, ), and for this reason it has been used for compar- ison. The principles of the SSI method have been introduced in the paper and next the proposed MaximumLikelihood Estimation with Expectation Maximization algo- rithm has been explained in detail. Finally, the results obtained with both methods are compared.
The Direction of Arrival (DoA) is applied to detection of multiple sources, and is one of the most studied problem in smart antennas technology. For this purpose, there had been studied many methods, based on optimal and sub-optimal techniques. Sub-space based methods had been most popular given their advantages such as speed and easy implementation. Thinking in improve performance algorithms which had better resolution on localization of near field sources, less estimation error, and a good efficiency under high noise scenarios is necessary the use of methods that solves the source localization problem in a more efficient way. Due to many attractive characteristics of the statistical inference methods such as consistence, minimum variance and asymptotic unbiasedness, is interesting to considerate the MaximumLikelihood Estimation methods for the application on the source localization problem on mobile communications systems. Also, they could be applied to wideband signals systems, for multiple sources and for aggressive scenarios with a low Signal to Noise Ratio (SNR).
fact that, when evaluating the distribution of galaxies in photo- metric space, in principle, any galaxy population at any redshift can contribute to the galaxy counts at a given point in photometric space. It is not possible to clearly separate samples by the SED type and redshift. This implies that the likelihood found by the PML algorithm is calculated as a likelihood for all LFs of all galaxy pop- ulations throughout cosmic history. This appears at first as a draw- back, greatly enlarging the number of free parameters involved in the problem. However, as has been pointed out above, in the con- ventional approach, it is not strictly possible to clearly separate a sample by redshift and SED type either. Any association of an indi- vidual galaxy with a given redshift and SED type is only a statistical one, and under proper Bayesian consideration, the probability for any such association is dependent on the prior assumptions about the LFs of all galaxy populations that a galaxy could in principle have been drawn from. Whereas this dependence usually goes un- acknowledged, it is made explicit in the PML, and the problem of introducing external priors is (in an ideal case) eliminated by solving for all contributing LFs simultaneously.
The example shows that in order to have a good posterior, given a good likeli- hood but an extremely unlikely prior, the evidence must be nearly as rare as the prior. Please check again Eq. 72 to make sure you follow the train of thought. If the evidence is not as unlikely, it means that the alternatives to our hypothesis, that make up the set of complementary hypotheses, also have a high likelihood of explaining the evidence. The larger the difference in probability in favor of the evidence, or in other words the more likely the evidence in comparison to the prior, the more likely it is that the evidence is due to the complementary hypotheses. This of course translates into a lower posterior probability. This means that the posterior is actually quantifying how much of the probability of the evidence is explained by the probability that our hypothesis occurs along with the observed data. This can be clearly seen in Eq. 87, where the posterior is the proportion of obtaining a positive result along with having the disease, to this very same probability plus the probability of not having the disease and still obtaining a positive result. If our hypothesis accounts for much of the observed data, then it will revamp our prior belief in the hypothesis. If not, it will downplay our belief.
rearrangements); this should be considered in the design of studies. The lizard genus Liolaemus is widely distributed in southern South America and includes more than 250 described species. The number of taxa and the distribution of Liolaemus species/populations makes them a good model for testing different hypotheses in systematics. Methods: We studied two Liolaemus species, Liolaemus nigroviridis and L. monticola as focal species to evaluate their monophyly and the influence of adding new samples from related taxa in the resulting phylogenies. We performed phylogenetic analyses (maximumlikelihood and Bayesian inference) using 141 sequences of the mitochondrial DNA Cytochrome b (cyt-b) of 11 Liolaemus species.
5. econometric estimates of learning and error parameters As noted above, it is straightforward to obtain numerical solutions for the equilibrium densities for specific values of the error parameter l, given the buyer responsiveness parameter a. This solution then can be used to calculate the densities associated with the particular prices selected by all subjects under each treatment. These densities, in turn, are used to calculate the value of the likelihood function, that is, the likelihood of drawing the prices actually selected, given the assumed value of l. 17 Then a grid search yields a maximumlikelihood estimate of l=6:7 with a standard error of 0.3 (see Table 3). This is of the same magnitude as the value of the error parameter (8.3) used from Capra et al. (1999) to calculate the logit equilibrium predictions in Section 2 above, which explains the accuracy of those predictions. It should be noted that the equilibrium model was estimated using only the data for the final five periods, since it is apparent from Figure 5 that the data do not stabilize until after period 5.
outlying observations. A fuzzy Classification MaximumLikelihood approach is applied in the three considered approaches. The maximization of fuzzified likelihoods is not a new idea in fuzzy clustering [15, 28, 23, 27]. It is impor- tant to fix some type of constraint on the scatters parameters because that maximization is a mathematically ill-defined problem otherwise. Therefore, appropriate constraints on the scatter parameters must be added. These con- straints are also useful to avoid the detection of non-interesting (“spurious”) local maxima.
4.013906212. Estimated log likelihood and maximum log likelihood are found to be - 61.37416426 and -59.12778444 respectively. So, the difference is only 2.246379822. In other words we can say if we replace our estimated shape and rate by maximumlikelihood shape and rate, then the joint probability density function value will increase only by an amount 1.873153e-26 which is very small. To see how accurately we approximate a given curve of Erlang distribution, simulation is done taking k=5 and µ =5 for a random sample of data with 100 samples until we get different values of estimated log likelihood and maximum log likelihood. A screen shot of such case is given below.
Maximumlikelihood phylogenetic analysis (Fig. 2) recovered the 3 newly generated cox1 sequences from the Xochimilco specimens in a single group and nested within species of the genus Prostoma with 100% BS. Prostoma graecense from Sweden and Macedonia exhibit marginal genetic distances (> 0.2%) when compared to the Mexican samples. This group is sister to a moderately supported group (BS = 64%) formed by Prostoma cf. eilhardi from USA and a sample labeled as Nemertea sp. from Italy. The genetic distances between the members of these 2 latter groups are lower than 0.8%. Sister to this group are 2 identical sequences of unidentified Prostoma specimens from Los Angeles, California, USA with an average cox1 divergence of 3.2% with respect to the P. graecense group + the sample from Xochimilco.
This work is concerned with basic aspects of the theory of point es- timation in the context of parametric statistical models. The main objective of the exposition is to illustrate fundamental notions, like unbiasedness, consistency and asymptotic normality, presenting a series of fully analyzed examples. To achieve this goal, two meth- ods of constructing estimators, namely, the maximumlikelihood technique and the method of moments, are carefully presented and, combining the central limit theorem with the invariance property of the asymptotic normality under the application of smooth func- tions, a detailed derivation of the limit distribution of moments estimators is given.
This paper presents a review about the usage of eigenvalues restrictions for constrained estimation, that serves a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) maximizers, related to complex likelihood surfaces. From the seminal paper of Hathaway (1985), we will see how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned review of the constraints and their applications, along the contributions of many authors, spanning the literature of the last thirty years. Applications of the constraints in robustness, jointly with trimming techniques, requires an extensive discussion per se, hence it will be the argument of a further paper, see Garc´ıa-Escudero et al. (2017). The plan of the paper is the following. Max- imum likelihood estimation for mixture models is brieﬂy recalled in Section 2, along with conditions assuring the existence and consistency of the esti- mator, in Section 3 diﬀerent constrained formulations of maximum-likelihood estimation are presented, in Section 4 degeneracy of the maximumlikelihood estimation is investigated. The last part of the paper is devoted to the role of eigenvalues in parsimonious models: Gaussian parsimonious clustering models are summarized in Section 5 while in Section 6 mixture of factor analyzers are presented. Finally, conclusions are given in Section 7.
In order to compare our sample with other Raja species from the Mediterranean and North-eastern Atlantic, we downloaded from the GenBank the COI sequences of the phylogenetically and morphologically closest species present in the area (Ball et al. 2016). The maximumlikelihood (ML) method was used to infer phylogenetic relation between taxa, using the Hasegawa-Kishino-Yano (1985) methodology with invariant sites (HKY+I) as substitution model, selected by AIC test implemented in jModelTest v.2.1.7 (Darriba et al. 2012). The phylogenetic tree was assessed by bootstrap procedure (1000 replicates) using Mega v.6 (Tamura et al. 2013). This software was also used to estimate the genetic distance (p-distance) and identity percentage between DNA sequences.
In this context, the objective of this study was to analyze the dynamics on urban LUCC at local scale. The methodology was developed through the analysis and processing of four Landsat satellite images corresponding to the years 1973, 1985, 2000 and 2015. To find the best fit and obtain the different land use classes, three supervised classification methods were applied: MaximumLikelihood Classification (MLC), Support Vector Machines (SVMs) and Artificial Neural Networks (ANNs). The results were validated with control points (ground truth). Then, to identify the significant transitions between different land uses—especially in the urban land use changes—losses, gains, changes and interchanges were obtained through the cross-tabulation matrix and according to the methodology of Pontius .
taking repeated random draws of coefficient vectors from this distribution and using them to generate an empirical distribution for the welfare measure, from which a confidence interval is computed. This approach was proposed by Krinsky and Robb (1986) and first applied to CV by Park, Loomis and Creel (1991). Bootstrapping and jackknife procedures (Efron & Tibshirani, 1993) simulate the distribution of the explanatory variables in the data set (i.e., the CV bid and any other covariates), using the actual data sample of N observations to simulate this distribution. Bootstrapping creates multiple simulated data sets, each formed by sampling N times with replacement from the actual data. The jackknife creates N simulated data sets, each formed by dropping one observation from the actual data. Given N simulated data sets for the explanatory variables, both approaches use the actual estimated maximumlikelihood coefficients to generate a set of N quantal responses, and then apply maximumlikelihood to these simulated data to obtain a new set of coefficient estimates, from which the welfare measure is computed. This is repeated over many simulated data sets to generate an empirical distribution for the welfare measure from which a confidence interval is computed. This was first applied to CV by Duffield and Patterson (1991). Cooper (1994) compares these methods for constructing confidence intervals for the welfare measure µ, along with the delta method (54), and finds they all perform fairly well, with the ranking of methods varying according to the size of the sample, the specification of the response probability distribution (e.g., logistic versus Weibull), and whether or not one allows for dispreference or indifference in the formula for the welfare measure. Poe et al. (1994) use bootstrapping to test for differences in WTP distributions (obtained, for example, through different elicitation procedures); they bootstrap the convolution distribution of the difference ∆ ≡ (WTP 1 - WTP 2 ) and use the resulting
The Andes Mountains particularly the forests along the mid-elevations of their eastern and western slopes, are a hotspot of biodiversity (high numbers of species and endemics). Among mammals, rodents are a priority group for study in the Tropical Andes given their high diversity and often relatively small geographic ranges. Here, we use DNA barcoding as a tool to help in the identification, and preliminary analysis of the phy- logenetic relationships, of rodents from two natural reserves: Otonga, a private forest reserve, located on the western slopes, and Sangay National Park, located on the eastern slopes of the Ecuadorian Andes. We sequenced 657 bp of the mitochondrial Cytochrome Oxidase I (COI) gene for 201 tissue samples of sigmodontine and echimyid rodents collected primarily in Otonga and Sangay. We conducted phylogenetic analyses using maximum-likelihood and Poisson tree processes (PTP) species delimitation analyses. Three sets of data were analyzed: 1) our newly generated sequences, 2) our Mesomys sequence plus DNA sequences of Echimyidae available in GenBank, and 3) all of our sequences (all Sigmodontinae and one Echimyidae) together with relevant DNA sequences of Sigmodontinae available in GenBank. Our samples consisted of 24 species; the molecular data indicated that only one species—Microryzomys minutus—was shared between both eastern and western localities. Contrary to the currently recognized distributions of Akodon mollis and Chilomys instans, our species delimitation analysis suggests that these species are not shared between Otonga and Sangay, and may actually represent two species each. The sample of Mesomys from the eastern slopes of the Andes differs minimally from that from the lowlands of the Ecuadorian Amazon, suggesting that both populations would correspond to the same spe- cies, Mesomys hispidus. Both Mindomys hammondi and an undescribed Mindomys from Otonga do not form a reciprocally monophyletic group with relation to Nephelomys. The Nephelomys of Sangay might correspond to two different species. The eastern and western slopes of the Tropical Andes harbor different species of rodents, with only one of our study species shared between both localities, implying that other cases of shared species between the eastern and the western slopes of the Andes need further assessment. Several lineages represented in our sample may require formal taxonomic description, highlighting the need for further systematic research. The new genetic data generated in our study could speed taxonomic discovery in the Andes and help to illuminate interesting evolutionary patterns, such as the radiation of Thomasomys.
Our view is that one must understand simple methods before trying to grasp more complex ones. Hence, after giving an overview of the supervis- ing learning problem in Chapter 2, we discuss linear methods for regression and classification in Chapters 3 and 4. In Chapter 5 we describe splines, wavelets and regularization/penalization methods for a single predictor, while Chapter 6 covers kernel methods and local regression. Both of these sets of methods are important building blocks for high-dimensional learn- ing techniques. Model assessment and selection is the topic of Chapter 7, covering the concepts of bias and variance, overfitting and methods such as cross-validation for choosing models. Chapter 8 discusses model inference and averaging, including an overview of maximumlikelihood, Bayesian in- ference and the bootstrap, the EM algorithm, Gibbs sampling and bagging, A related procedure called boosting is the focus of Chapter 10.
This work has presented a multihop node localization scheme based on a dead reckoning approach. Assuming exponentially distributed multipath interarrival times in the channel, it was shown that resultant vector magnitudes measured in a DRP can be closely approx- imated as M-Erlang distributed with parameter (λ) as long as the standard deviations of the angular delay spread of network nodes and AOA error measurements do not exceed 20 degrees. Based on the M-Erlang distributed range observations model, an exact iterative maximumlikelihood multilateration scheme (NR-ML) was applied to ﬁnd estimates of po- sition of a node in the network. Performance of the proposed estimator was analyzed with respect to the number of available APs, TOA estimation accuracy at each node, and node density in the network. The algorithm was compared to approximate linearized multilater- ation solutions such as the classical LWLS algorithm. Numerical calculations showed that the proposed localization scheme is asymptotically eﬃcient and fairly insensitive to knowl- edge of nuissance parameters. The relative performance of LWLS versus NR-ML was found to be between 50 and 33 % for several values of range estimation variances and diﬀerent number of APs.