Maximum likelihood – Expectation maximization (ML-EM)

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Expectation-Maximization Algorithms for Obtaining Estimations of Generalized Failure Intensity Parameters

Expectation-Maximization Algorithms for Obtaining Estimations of Generalized Failure Intensity Parameters

methods are implemented to exploit the failures and maintenances data raised by experts to evaluate the performance of these systems. In this context, different methods as MLE, moment estimation, and EM algorithm are presented in Doyen (2012). Sethuraman and Hollander (2009) developed a non-parametric Bayes estimator for a general imperfect repair model including Brown-Proschan model. Doyen (2011) generalized this approach and considered the maximum likelihood estimation. The performance of the Brown-Proschan model when repair effects are unknown as resulting in the work of Krit and Rebai (2012) and Krit (2014). Babykina and Couallier (2012) used EM algorithm to estimate the parameters of a generalization of this model wich allows first-order dependency between two consecutive repair effects, they assumed that only some repair effects were unknown. Lim and Lie (2000) proposed another method based on Bayesian analysis: they assumed a prior beta distribution for parameter p. Langseth and Lindqvist (2003) generalized the Brown-Proschan model for imperfect preventive maintenance, and they proposed to estimate the parameters of the model with the likelihood function. Franco and al. (2011) study the classification of the aging properties of generalized mixtures of two or three weibull distributions in terms of the mixing weights, scale parameters and a common shape parameter, which extends the cases of exponential distributions.
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DNA Motif Discovery Based on Ant Colony Optimization and Expectation Maximization

DNA Motif Discovery Based on Ant Colony Optimization and Expectation Maximization

In this study, we propose a motif discovery method based on Ant Colony Optimization (ACO) [18] and the Expectation Maximization (EM) algorithm. ACO is a global optimization metaheuristic originating from research on the foraging behavior of some ant species. Since its introduction, applications to several different NP-hard problems [19] have empirically shown its effectiveness. EM is a standard algorithm widely used for maximum likelihood and maximum a posterior parameter estimation in statistical models. The EM algorithm is used in Consensus, one of the earliest motif discovery methods, and a generalized mixture model was later implemented in MEME. We have modified the ACO algorithm such that each individual ant builds a potential motif using the consensus representation. At each iteration, ACO considers the total contribution from each of the potential motifs built by the ants and increases or decreases the pheromones accordingly. By sensing pheromone levels, the ants have higher probability of constructing a better motif at the next iteration. Given the stochastic nature of metaheuristic algorithms, the results provided by ACO could be further refined. The underlying principle of the EM algorithm guarantees that, starting from an initial setting, the likelihood of missing variables given the observed data only increases or remains even, thus we apply it to maximize the likelihood of ACO’s motif predictions. We have conducted experiments on real biological datasets to evaluate the search capabilities of our method, and the results indicate this combined approach has promise in motif discovery.
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Comparison of Mixture and Classification Maximum Likelihood Approaches in Poisson Regression Models

Comparison of Mixture and Classification Maximum Likelihood Approaches in Poisson Regression Models

In this work, we study the procedure for fitting Poisson mixture regres- sion models, which are commonly used to analyze heterogeneous count data (see Wedel et al. (1993)), by means of maximum likelihood. We apply two maximization algorithms to obtain the maximum likelihood estimates: the Expectation Maximization (EM) algorithm (see Dempster et al.(1977)) and the Classification Expectation Maximization (CEM) algorithm (see Celeux et al. (1992)).

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Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden’s method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden’s method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
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A New Method for Segmentation of Multiple Sclerosis (MS) Lesions on Brain MR Images

A New Method for Segmentation of Multiple Sclerosis (MS) Lesions on Brain MR Images

A utomatic segmentation of multiple sclerosis (MS) lesions in brain MRI has been widely investigated in recent years with the goal of helping MS diagnosis and patient follow-up. In this study we applied gaussian mixture model (GMM) to segment MS lesions in MR images. Usually, GMM is optimized using expectation-maximization (EM) algorithm. One of the drawbacks of this optimization method is that, it does not convergence to optimal maximum or minimum. Starting from different initial points and saving best result, is a strategy which is used to reach the near optimal. This approach is time consuming and we used another way to initiate the EM algorithm. Also, FAST- Trimmed Likelihood Estimator (FAST-TLE) algorithm was applied to determine which voxels should be rejected. The automatically segmentation outputs were scored by two specialists and the results show that our method has capability to segment the MS lesions with Dice similarity coefficient (DSC) score of 0.82.
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UNIVERSIDADE FEDERAL DE UBERLÂNDIA

UNIVERSIDADE FEDERAL DE UBERLÂNDIA

Analisar o desempenho de algumas técnicas de pré-processamento e agrupamento de dados, como k-means, canopy e expectation maximization (EM), os quais são algoritmos simples e eficientes,[r]

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Evolution of immune genes in Antarctic fish

Evolution of immune genes in Antarctic fish

While the number of TLR genes may vary between species, it is now established to a certain degree that teleost fish have 20 TLR members (Rauta et al., 2014). The difference between the total number of TLR found in D. rerio and other teleosts with O. niloticus and L. chalumnae both presenting the second highest count of TLR genes, is most probably due to D. rerio specific duplications (Palti, 2011; Rauta et al., 2014). In this study, a maximum of 19 TLR genes have been found in D. rerio which is in concordance with the literature (Jault et al., 2004). The TLR members could be classified into the six known TLR gene families (Fig3.2) (Roach et al., 2005). The TLR1 family was represented by TLR-1, 2 and 18 but did not form a monophyletic group. The TLR4 family regrouped into one well supported clade, presenting three paralogs (TLR4al, TLR4ba, TLR4bb) identified in D. rerio and with only ortholog TLR4ba present in L. oculatus. For TLR5, two paralogs (TLR5a, TLR5b) were found and their clade was supported. TLR19 was found only in D. rerio and L. chalumnae. TLR20 with its four duplications and TLR21-22 belong to the TLR11 family and formed a monophyletic clade. The TLR3 gene was the only one who had an orthologous gene in all the species studied, which formed a monophyletic group supported by a high bootstrap value. The function of the TLR3 gene is to recognize double-stranded RNA (Roach et al., 2005) and might explain why it was kept in all the species. It has been found that in several teleost infected by dsRNA viruses TLR3 expression increased (Su et al., 2008; Sahoo et al., 2015). Also, when exposed to Gram- negative bacteria up regulation of TLR3 expression was observed in zebrafish (Phelan et al., 2005), catfish (Bilodeau & Waldbieser, 2005) and catfish hybrids (Bilodeau et al., 2006).
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Long branch effects distort maximum likelihood phylogenies in simulations despite selection of the correct model.

Long branch effects distort maximum likelihood phylogenies in simulations despite selection of the correct model.

Our results show that the risk of obtaining a wrong topology using ML is dependent on the arrangement of the edges (corresponding to which LBA classes the tree is susceptible to). Although our results depend on simulated nucleotid data it can be expected that amino acid sequences are also prone to long branch effects if branch lengths combinations of BL1 and BL2 differ strongly from each other, even though the possibility of obtaining long branch effects increase with a decreasing alphabet of character states. It is also clear that good ‘‘support values’’ are no guarantee for the correctness of the tree topology. Also, we have to keep in mind that empirical data can evolve in a much more heterogeneous way than in our simulations. Although we show that ML is not immune to different long branch artefacts, we hope that our work will not be taken as evidence for the continued use of Maximum Parsimony for molecular data. Maximum Parsimony has been shown to be seriously affected by long branch attraction [2,6,8,15–17,19], therefore we consider Maximum Parsimony as entirely inappropriate for molecular data.
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Image Enhancement with Statistical Estimation

Image Enhancement with Statistical Estimation

Contrast enhancement is an important area of research for the image analysis. Over the decade, the researcher worked on this domain to develop an efficient and adequate algorithm. The proposed method will enhance the contrast of image using Binarization method with the help of Maximum Likelihood Estimation (MLE). The paper aims to enhance the image contrast of bimodal and multi-modal images. The proposed methodology use to collect mathematical information retrieves from the image. In this paper, we are using binarization method that generates the desired histogram by separating image nodes. It generates the enhanced image using histogram specification with binarization method. The proposed method has showed an improvement in the image contrast enhancement compare with the other image.
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Analyzing pathogen suppressiveness in bioassays with natural soils using integrative maximum likelihood methods in R

Analyzing pathogen suppressiveness in bioassays with natural soils using integrative maximum likelihood methods in R

are built out of a soil or substrate inoculated with a pathogen and a pathogen sensitive plant. Data is collected at just a single point in time (Maurhofer et al., 1994; Pierson & Weller, 1994; Postma et al., 2008) or at multiple points in time (e.g., Postma et al., 2008; Hanse et al., 2011; Latz et al., 2012; Latz et al., 2016). Remarkably, in the latter case often only one single point in time is chosen for evaluation (e.g., Postma et al., 2008; Hanse et al., 2011; Latz et al., 2012), or the increase from one to the next point in time is evaluated (Kushalappa & Ludwig, 1982). However, disease progression is more precisely described by classical growth curve models (Neher & Campbell, 1992). Out of the plethora of growth models (Paine et al., 2012), the mono-molecular model has often been used to describe bioassays with soil-borne pathogens (Stanghellini et al., 2004; Wilson et al., 2008). The mono-molecular infection model describes the disease progression (the change of infections over time) with an initial linear increase of infections (the infection rate), followed by a saturation (given by the maximum number of infectable plants, also known as carrying capacity or asymptotic growth).
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Land use in Permanent Preservation Areas of Grande River (MG)

Land use in Permanent Preservation Areas of Grande River (MG)

The Brazilian Forestry Code established the Permanent Preservation Areas (PPAs) to preserve environmentally significant areas, such as the banks of waterways. Grande River is an important Brazilian river whose watercourse contains several hydroelectric plants, with few PPAs containing original features. Thus, this study analyzed land use in PPAs of a non-dammed stretch of the upper Rio Grande, in southern Minas Gerais. For this analysis, we used an image of the Rapideye sensor and the Maximum Likelihood classification method. The results showed the occurrence of pastures (49.63%), exposed soil (9.13%), others (0.77%), water (0.15%) and ornamental vegetation (0.13%) while the remaining native vegetation represented only 40.19% of PPAs. These numbers show that environmental laws have not been fulfilled in this area and there is strong human intervention in the PPAs studied.
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Estimation of P{X < Y} for gamma exponential model

Estimation of P{X < Y} for gamma exponential model

In this paper, we have considered the estimation of the probability P{X < Y} when X and Y are two independent random variables from gamma and exponential distributions, respectively. We found maximum likelihood estimator and used its asymptotic distribution to construct confidence intervals. We performed a simulation study to show the consistency property of the MLE estimators of R.

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A topological restricted maximum likelihood (TopREML) approach to regionalize trended runoff signatures in stream networks

A topological restricted maximum likelihood (TopREML) approach to regionalize trended runoff signatures in stream networks

to account for the stronger spatial correlation between flow-connected basins. The re- stricted maximum likelihood (REML) framework generates the best linear unbiased predictor (BLUP) of both the predicted variable and the associated prediction uncer- tainty, even when incorporating observable covariates into the model. The method was successfully tested in cross validation analyses on mean streamflow and runoff fre-

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Efficiency of QTL mapping based on least squares, maximum likelihood, and Bayesian approaches under high marker density

Efficiency of QTL mapping based on least squares, maximum likelihood, and Bayesian approaches under high marker density

Based on relevant papers on QTL mapping efficiency (Zheng, 1994; Haley and Knott, 1992; Lander and Botstein, 1989), our prior expectation was that QTL mapping would prove to be highly efficient, i.e., it would provide a high power of QTL detection, no false-positives but eventually some ghost QTLs (Martinez and Curnow, 1992), a precise mapping of the QTLs underlying the trait, and slightly biased estimates of QTL effects and variances. This was partially confirmed by our study. Our study shares some similarities, such as the magnitude of the QTL effects and variances, and some differences, such as greater number of minor genes and markers, with the above- mentioned important papers. In the cited papers, the power of QTL detection ranged from 40 (Zeng, 1994) to 80% (Lander and Botstein, 1989), from analyses based on interval mapping, regression analysis, and composite interval. Lander and Botstein (1989) did not declare QTLs in chromosomes with no genes.
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Target Localization and Tracking in Wireless Sensor Networks

Target Localization and Tracking in Wireless Sensor Networks

Keywords: Target localization, target tracking, wireless sensor network, received signal strength (RSS), angle of arrival (AoA), convex optimization, maximum likelihood (ML) estimation, [r]

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REPOSITORIO INSTITUCIONAL DA UFOP: The role of fusion in ant chromosome evolution : insights from cytogenetic analysis using a molecular phylogenetic approach in the Genus Mycetophylax.

REPOSITORIO INSTITUCIONAL DA UFOP: The role of fusion in ant chromosome evolution : insights from cytogenetic analysis using a molecular phylogenetic approach in the Genus Mycetophylax.

Among insect taxa, ants exhibit one of the most variable chromosome numbers ranging from n = 1 to n = 60. This high karyotype diversity is suggested to be correlated to ants diversification. The karyotype evolution of ants is usually understood in terms of Robertsonian rearrangements towards an increase in chromosome numbers. The ant genus Mycetophylax is a small monogynous basal Attini ant (Formicidae: Myrmicinae), endemic to sand dunes along the Brazilian coastlines. A recent taxonomic revision validates three species, Mycetophylax morschi, M. conformis and M. simplex. In this paper, we cytogenetically characterized all species that belongs to the genus and analyzed the karyotypic evolution of Mycetophylax in the context of a molecular phylogeny and ancestral character state reconstruction. M. morschi showed a polymorphic number of chromosomes, with colonies showing 2n = 26 and 2n = 30 chromosomes. M. conformis presented a diploid chromosome number of 30 chromosomes, while M. simplex showed 36 chromosomes. The probabilistic models suggest that the ancestral haploid chromosome number of Mycetophylax was 17 (Likelihood framework) or 18 (Bayesian framework). The analysis also suggested that fusions were responsible for the evolutionary reduction in chromosome numbers of M. conformis and M. morschi karyotypes whereas fission may determines the M. simplex karyotype. These results obtained show the importance of fusions in chromosome changes towards a chromosome number reduction in Formicidae and how a phylogenetic background can be used to reconstruct hypotheses about chromosomes evolution.
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Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach.

Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach.

ever, the assumed underlying logistic function may also not be entirely correct, and such viola- tions of assumptions may bias estimates of λ/(1-λ). For example, it seems unlikely that the probability of esophageal cancer can really approximate 1, as all cases must have been non- cases prior to developing their disease, with the same covariable pattern (except perhaps for a slightly lower age). The P-value of likelihood ratio test comparing LR and DLR is 0.021, thus suggesting likely superiority of the DLR over the LR. Of course, as the hypothesis λ = 0 is on the boundary of the parameter space this P-value has to be taken with a grain of salt. Using the
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Circulation of Different Lineages of Dengue Virus 2, Genotype American/Asian in Brazil: Dynamics and Molecular and Phylogenetic Characterization

Circulation of Different Lineages of Dengue Virus 2, Genotype American/Asian in Brazil: Dynamics and Molecular and Phylogenetic Characterization

Phylogenetic analyses, based on the genome sequence, demon- strate that all Brazilian and other isolates from Central and South America and from the Caribbean grouped within American/Asian genotypes apart from strains from Southeast Asia (Figure 1). Brazilian strains are subdivided into three well-supported lineages (bootstrap values of 100%), which are placed in two different clades (Figure 1). Lineage BR1 groups two Brazilian strains isolated in 1998 and 2000 that also clusters strains from Venezuela, Colombia and Puerto Rico, isolated from 1990 to 1998. Lineage BR2 contains strains isolated from 2000 to 2006, in the Northern region of the country and these sequences are closely related to strains isolated in 1998 in Puerto Rico. Finally, the 12 DENV-2 strains sequenced here cluster together with two Brazilian strains from the North region, in a lineage, called BR3. These strains also cluster with a strain isolated in Jamaica in 2007. When a greater number of E sequences were included (total of 144 E sequences including 77 E sequences from Brazilian isolates), similar clustering patterns are observed in the Maximum likelihood tree (data not shown).
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Modelling carbon overconsumption and the formation of extracellular particulate organic carbon

Modelling carbon overconsumption and the formation of extracellular particulate organic carbon

Fig. 2. A priori and a posteriori probability distribution of the data-model misfits (initial values and minima of cost function J). Repeating the optimisation with any other resampled data will probably yield a minimum of J in the range shown in the zoomed subplot. Most likely the minimum will be distributed close around J=280. The value of expectation is J=122, which can only be achieved if the exact moment of sampling was known and if the assumed model equations were free of error.

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Distributed Algorithms for Target Localization in Wireless Sensor Networks Using Hybrid Measurements

Distributed Algorithms for Target Localization in Wireless Sensor Networks Using Hybrid Measurements

other hand, it can be seen that the objective functions in (c) and (d) are much smoother. The estimated target’s coordinates were obtained by solving the “SOCP” and “SR-WLS” algorithms, in (c) and (d) respectively, and their respective minimums are located in [2.17; 3.77] and [2.24; 3.93]. This algorithms allow to obtain their respective objective functions’ global minimums effortlessly far all targets via interior-point algorithms [11] and bisection procedure [7]. While the estimation accuracy depends on the tightness of the performed relaxation, we can conclude that the objective functions in (3.11) and (3.15) are excellent approximations of the original problem in (3.7) as it is shown in Chapter 4. The authors in [68] proposed Algorithm 1, which summarizes the distributed SOCP and SR-WLS algorithms, where T max is the maximum number of iterations and C the set of used colors in the coloring scheme. Algorithm 1 is distributed in the sense that there is no central processor in the network, its coordination is carried out according to the applied coloring scheme, information exchange occurs between two incident sensors exclusively, and data processing is performed locally by each target. Lines 5 − 7 are executed simultaneously by all targets i ∈ C c , which may decrease the execution time of
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