Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the divergence time between two populations, specifically designed for the analysis of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were derived, assuming that the population dynamics of rare alleles can be described by using a birth–death process approximation and that each mutation arose before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes and few alleles, whose age can be approximated, whereas the RDc estimator appears preferable when this is not the case. When applied to three cystic fibrosis mutations, the estimator RD could not exclude a very recent time of divergence among three Mediterranean populations. On the other hand, the divergence time between these populations and the Danish population was estimated to be, on the average, 4,500 or 15,000 years, assuming or not a selective advantage for cystic fibrosis carriers, respectively. Confidence intervals are large, however, and can probably be reduced only by analyzing more alleles or loci.

Didanosine-loaded Chitosan Microspheres Optimized By Surface-response Methodology: A Modified Maximum Likelihood Classification" Approach Formulation For Reverse Transcriptase Inhibitors."

Didanosine-loaded chitosan microspheres were developed applying a surface-response methodology and using a modified Maximum Likelihood Classification. The operational conditions were optimized with the aim of maintaining the active form of didanosine (ddI), which is sensitive to acid pH, and to develop a modified and mucoadhesive formulation. The loading of the drug within the chitosan microspheres was carried out by ionotropic gelation technique with sodium tripolyphosphate (TPP) as cross-linking agent and magnesium hydroxide (Mg(OH)2) to assure the stability of ddI. The optimization conditions were set using a surface-response methodology and applying the Maximum Likelihood Classification, where the initial chitosan concentration, TPP and ddI concentration were set as the independent variables. The maximum ddI-loaded in microspheres (i.e. 1433mg of ddI/g chitosan), was obtained with 2% (w/v) chitosan and 10% TPP. The microspheres depicted an average diameter of 11.42μm and ddI was gradually released during 2h in simulated enteric fluid.

An integrated molecular map of yellow passion fruit based on simultaneous maximum-likelihood estimation of linkage and linkage phases

The development of genetic maps for auto-incompatible species, such as the yellow passion fruit (Passiflora edulis Sims f.flavicarpa Deg.) is restricted due to the unfeasibility of obtaining traditional mapping populations based on inbred lines. For this reason, yellow passion fruit linkage maps were generally constructed using a strategy known as two-way pseudo-testeross, based on monoparental dominant markers segregating in a 1:1 fashion. Due to the lack of information from these markers in one of the parents, two individual (parental) maps were obtained. However, integration of these maps is essential, and biparental markers can be used for such an operation. The objective of our study was to construct an integrated molecular map for a full-sib population of yellow passion fruit combining different loci configuration generated from amplified fragment length polymorphisms (AFLPs) and microsatellite markers and using a novel approach based on simultaneous maximum-likelihood estimation of linkage and linkage phases, specially designed for outcrossing species. Of the total number of loci, approximate to 76%, 21%, 0.7%, and 2.3% did segregate in 1:1, 3:1, 1:2:1, and 1:1:1:1 ratios, respectively. Ten linkage groups (LGs) were established with a logarithm of the odds (LOD) score >= 5.0 assuming a recombination fraction : <= 0.35. On average, 24 markers were assigned per LG, representing a total map length of 1687 cM, with a marker density of 6.9 cM. No markers were placed as accessories on the map as was done with previously constructed individual maps.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Maximum likelihood detection for OFDM signals with strong nonlinear distortion effects

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

Fourth order pseudo maximum likelihood methods

We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

A new maximum likelihood method for luminosity calibrations

A new statistical parallax method using the Maximum Likelihood principle is presented, allowing the simultaneous determination of a luminosity calibration, kinematic characteristics and spatial distribution of a given sample. This method has been developed for the exploitation of the Hipparcos data and presents several improvements with respect to the previous ones: the effects of the selection of the sample, the observational errors, the galactic rotation and the interstellar absorption are taken into account as an intrinsic part of the formulation (as opposed to external corrections). Furthermore, the method is able to identify and characterize physically distinct groups in inhomogeneous samples, thus avoiding biases due to unidentified components. Moreover, the implementation used by the authors is based on the extensive use of numerical methods, so avoiding the need for simplification of the equations and thus the bias they could introduce. Several examples of application using simulated samples are presented, to be followed by applications to real samples in forthcoming articles.

Comparison between artificial neural networks and maximum likelihood classification in digital soil mapping

Soil surveys are the main source of spatial information on soils and have a range of different applications, mainly in agriculture. The continuity of this activity has however been severely compromised, mainly due to a lack of governmental funding. The purpose of this study was to evaluate the feasibility of two different classifiers (artificial neural networks and a maximum likelihood algorithm) in the prediction of soil classes in the northwest of the state of Rio de Janeiro. Terrain attributes such as elevation, slope, aspect, plan curvature and compound topographic index (CTI) and indices of clay minerals, iron oxide and Normalized Difference Vegetation Index (NDVI), derived from Landsat 7 ETM+ sensor imagery, were used as discriminating variables. The two classifiers were trained and validated for each soil class using 300 and 150 samples respectively, representing the characteristics of these classes in terms of the discriminating variables. According to the statistical tests, the accuracy of the classifier based on artificial neural networks (ANNs) was greater than of the classic Maximum Likelihood Classifier (MLC). Comparing the results with 126 points of reference showed that the resulting ANN map (73.81 %) was superior to the MLC map (57.94 %). The main errors when using the two classifiers were caused by: a) the geological heterogeneity of the area coupled with problems related to the geological map; b) the depth of lithic contact and/or rock exposure, and c) problems with the environmental correlation model used due to the polygenetic nature of the soils. This study confirms that the use of terrain attributes together with remote sensing data by an ANN approach can be a tool to facilitate soil mapping in Brazil, primarily due to the availability of low-cost remote sensing data and the ease by which terrain attributes can be obtained.

Maximum likelihood Linear Programming Data Fusion for Speaker Recognition

Biometric system performance can be improved by means of data fusion. Several kinds of information can be fused in order to obtain a more accurate classification (identification or verification) of an input sample. In this paper we present a method for computing the weights in a weighted sum fusion for score combinations, by means of a likelihood model. The maximum likelihood estimation is set as a linear programming problem. The scores are derived from a GMM classifier working on a different feature extractor. Our experimental results assesed the robustness of the system in front a changes on time (different sessions) and robustness in front a change of microphone. The improvements obtained were significantly better (error bars of two standard deviations) than a uniform weighted sum or a uniform weighted product or the best single classifier. The proposed method scales computationaly with the number of scores to be fussioned as the simplex method for linear programming.

Conditional maximum likelihood timing recovery: estimators and bounds

This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical low-SNR unconditional ML (UML) formulationthat is systematically applied in the literature for the derivationof non-data-aided (NDA) timing-error-detectors (TEDs). A new CML TED is derived and proved to be self-noise free, in contrast to the conventional low-SNR-UML TED. In addition, the paper provides a derivation of the conditional Cramér–Rao Bound (CRB ), which is higher (less optimistic) than the modified CRB (MCRB)[which is only reached by decision-directed (DD) methods]. It is shown that the CRB is a lower bound on the asymptotic statisticalaccuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained boundis not general, it applies to most NDA synchronizers proposed in the literature. A closed-form expression of the conditional CRBis obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high Eg/No.