Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.

Adaptive evolution of color vision as seen through the eyes of butterflies

Butterflies and primates are interesting for comparative color vision studies, because both have evolved middle- (M) and long-wavelength- (L) sensitive photopigments with overlapping absorbance spectrum maxima (lambda(max) values). Although positive selection is important for the maintenance of spectral variation within the primate pigments, it remains an open question whether it contributes similarly to the diversification of butterfly pigments. To examine this issue, we performed epimicrospectrophotometry on the eyes of five Limenitis butterfly species and found a 31-nm range of variation in the lambda(max) values of the L-sensitive photopigments (514-545 nm). We cloned partial Limenitis L opsin gene sequences and found a significant excess of replacement substitutions relative to polymorphisms among species. Mapping of these L photopigment lambda(max) values onto a phylogeny revealed two instances within Lepidoptera of convergently evolved L photopigment lineages whose lambda(max) values were blue-shifted. A codon-based maximum-likelihood analysis indicated that, associated with the two blue spectral shifts, four amino acid sites (Ile17Met, Ala64Ser, Asn70Ser, and Ser137Ala) have evolved substitutions in parallel and exhibit significant d(N)/d(S) >1. Homology modeling of the full-length Limenitis arthemis astyanax L opsin placed all four substitutions within the chromophore-binding pocket. Strikingly, the Ser137Ala substitution is in the same position as a site that in primates is responsible for a 5- to 7-nm blue spectral shift. Our data show that some of the same amino acid sites are under positive selection in the photopigments of both butterflies and primates, spanning an evolutionary distance >500 million years.

A unique isolate of beak and feather disease virus isolated from budgerigars (Melopsittacus undulatus) in South Africa

Beak and feather disease virus (BFDV), the causative agent of psittacine beak and feather disease (PBFD) infects psittaciformes worldwide. We provide an annotated sequence record of three full-length unique genomes of BFDV isolates from budgerigars (Melopsittacus undulatus) from a breeding farm in South Africa. The isolates share >99% nucleotide sequence identity with each other and ~96% nucleotide sequence identity to two recent isolates (Melopsittacus undulatus) from Thailand but only between 91. 6 and 86. 6% identity with all other full-length BFDV sequences. Maximum-likelihood analysis and recombination analysis suggest that the South African budgerigar BFDV isolates are unique to budgerigars, are non-recombinant in origin, and represent a new genotype of BFDV. © 2010 Springer-Verlag.

Growth and species interactions of Eucalyptus pellita in a mixed and monoculture plantation in the humid tropics of north Queensland

This study investigated whether mixed-species designs can increase the growth of a tropical eucalypt when compared to monocultures. Monocultures of Eucalyptus pellita (E) and Acacia peregrina (A) and mixtures in various proportions (75E:25A, 50E:50A, 25E:75A) were planted in a replacement series design on the Atherton Tablelands of north Queensland, Australia. High mortality in the establishment phase due to repeated damage by tropical cyclones altered the trial design. Effects of experimental designs on tree growth were estimated using a linear mixed-effects model with restricted maximum likelihood analysis (REML). Volume growth of individual eucalypt trees were positively affected by the presence of acacia trees at age 5 years and this effect generally increased with time up to age 10 years. However, the stand volume and basal area increased with increasing proportions of E. pellita, due to its larger individual tree size. Conventional analysis did not offer convincing support for mixed-species designs. Preliminary individual-based modelling using a modified Hegyi competition index offered a solution and an equation that indicates acacias have positive ecological interactions (facilitation or competitive reduction) and definitely do not cause competition like a eucalypt. These results suggest that significantly increased in growth rates could be achieved with mixed-species designs. This statistical methodology could enable a better understanding of species interactions in similarly altered experiments, or undesigned mixed-species plantations.

Responses in carcass lean pH at 24 hours post-mortem in lines of Large White pigs selected for growth rate on a fixed ration over a set time

A restricted maximum likelihood analysis applied to an animal model showed no significant differences (P > 0.05) in pH value of the longissimus dorsi measured at 24 h post-mortem (pH24) between high and low lines of Large White pigs selected over 4 years for post-weaning growth rate on restricted feeding. Genetic and phenotypic correlations between pH24 and production and carcass traits were estimated using all performance testing records combined with the pH24 measurements (5.05-7.02) on slaughtered animals. The estimate of heritability for pH24 was moderate (0.29 ± 0.18). Genetic correlations between pH24 and production or carcass composition traits, except for ultrasonic backfat (UBF), were not significantly different from zero. UBF had a moderate, positive genetic correlation with pH24 (0.24 ± 0.33). These estimates of genetic correlations affirmed that selection for increased growth rate on restricted feeding is likely to result in limited changes in pH24 and pork quality since the selection does not put a high emphasis on reduced fatness.

Adaptive diversification of vomeronasal receptor 1 genes in rodents

The vomeronasal receptor 1 (V1R) are believed to be pheromone receptors in rodents. Here we used computational methods to identify 95 and 62 new putative V1R genes from the draft rat and mouse genome sequence, respectively. The rat V1R repertoire consists of 11 subfamilies, 10 of which are shared with the mouse, while rat appears to lack the H and I subfamilies found in mouse and possesses one unique subfamily (M). The estimations of the relative divergence times suggest that many subfamilies originated after the split of rodents and primates. The analysis also reveals that these clusters underwent an expansion very close to the split of mouse and rat. In addition, maximum likelihood analysis showed that the nonsynonymous and synonymous rate ratio for most of these clusters was much higher than one, suggesting the role of positive selection in the diversification of these duplicated V1R genes. Because V1R are thought to mediate the process of signal transduction in response to pheromone detection, we speculate that the V1R genes have evolved under positive Darwinian selection to maintain the ability to discriminate between large and complex pheromonal mixtures.

A Stochastic Model for Electron Multiplication Charge-Coupled Devices - From Theory to Practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images. © 2013 Hirsch et al.

Phylogenetic variation in the tolerance and uptake of organic contaminants

An investigation into the phylogenetic variation of plant tolerance and the root and shoot uptake of organic contaminants was undertaken. The aim was to determine if particular families or genera were tolerant of, or accumulated organic pollutants. Data were collected from sixty-nine studies. The variation between experiments was accounted for using a residual maximum likelihood analysis to approximate means for individual taxa. A nested ANOVA was subsequently used to determine differences at a number of differing phylogenetic levels. Significant differences were observed at a number of phylogenetic levels for the tolerance to TPH, the root concentration factor and the shoot concentration factor. There was no correlation between the uptake of organic pollutants and that of heavy metals. The data indicate that plant phylogeny is an important influence on both the plant tolerance and uptake of organic pollutants. If this study can be expanded, such information can be used when designing plantings for phytoremediation or risk reduction during the restoration of contaminated sites.

Avaliação do uso da terra em micro̧bacia utilizando uma matriz de partição fuzzy

Informatics evolution presently offers the possibility of new technique and methodology development for studies in all human knowledge areas. In addition, the present personal computer capacity of handling a large volume of data makes the creation and application of new analysis tools easy. This paper aimed the application of a fuzzy partition matrix to analyze data obtained from the Landsat 5 TMN sensor, in order to elaborate the supervised classification of land use in Arroio das Pombas microbasin in Botucatu, SP, Brazil. It was possible that one single training area present input in more than one covering class due to weight attribution at the signature creation moment. A change in the classification result was also observed when compared to maximum likelihood classification, mainly when related to bigger uniformity and better class edges classification.

Reinforcing and expanding the predictions of the disturbance vicariance hypothesis in Amazonian harlequin frogs: A molecular phylogenetic and climate envelope modelling approach

The disturbance vicariance hypothesis (DV) has been proposed to explain speciation in Amazonia, especially its edge regions, e. g. in eastern Guiana Shield harlequin frogs (Atelopus) which are suggested to have derived from a cool-adapted Andean ancestor. In concordance with DV predictions we studied that (i) these amphibians display a natural distribution gap in central Amazonia; (ii) east of this gap they constitute a monophyletic lineage which is nested within a pre-Andean/western clade; (iii) climate envelopes of Atelopus west and east of the distribution gap show some macroclimatic divergence due to a regional climate envelope shift; (iv) geographic distributions of climate envelopes of western and eastern Atelopus range into central Amazonia but with limited spatial overlap. We tested if presence and apparent absence data points of Atelopus were homogenously distributed with Ripley's K function. A molecular phylogeny (mitochondrial 16S rRNA gene) was reconstructed using Maximum Likelihood and Bayesian Inference to study if Guianan Atelopus constitute a clade nested within a larger genus phylogeny. We focused on climate envelope divergence and geographic distribution by computing climatic envelope models with MaxEnt based on macroscale bioclimatic parameters and testing them by using Schoener's index and modified Hellinger distance. We corroborated existing DV predictions and, for the first time, formulated new DV predictions aiming on species' climate envelope change. Our results suggest that cool-adapted Andean Atelopus ancestors had dispersed into the Amazon basin and further onto the eastern Guiana Shield where, under warm conditions, they were forced to change climate envelopes. © 2010 The Author(s).

Improving methods in gap ecology: Revisiting size and shape distributions using a model selection approach

Questions: We assess gap size and shape distributions, two important descriptors of the forest disturbance regime, by asking: which statistical model best describes gap size distribution; can simple geometric forms adequately describe gap shape; does gap size or shape vary with forest type, gap age or the method used for gap delimitation; and how similar are the studied forests and other tropical and temperate forests? Location: Southeastern Atlantic Forest, Brazil. Methods: Analysing over 150 gaps in two distinct forest types (seasonal and rain forests), a model selection framework was used to select appropriate probability distributions and functions to describe gap size and gap shape. The first was described using univariate probability distributions, whereas the latter was assessed based on the gap area-perimeter relationship. Comparisons of gap size and shape between sites, as well as size and age classes were then made based on the likelihood of models having different assumptions for the values of their parameters. Results: The log-normal distribution was the best descriptor of gap size distribution, independently of the forest type or gap delimitation method. Because gaps became more irregular as they increased in size, all geometric forms (triangle, rectangle and ellipse) were poor descriptors of gap shape. Only when small and large gaps (> 100 or 400m2 depending on the delimitation method) were treated separately did the rectangle and isosceles triangle become accurate predictors of gap shape. Ellipsoidal shapes were poor descriptors. At both sites, gaps were at least 50% longer than they were wide, a finding with important implications for gap microclimate (e.g. light entrance regime) and, consequently, for gap regeneration. Conclusions: In addition to more appropriate descriptions of gap size and shape, the model selection framework used here efficiently provided a means by which to compare the patterns of two different types of forest. With this framework we were able to recommend the log-normal parameters μ and σ for future comparisons of gap size distribution, and to propose possible mechanisms related to random rates of gap expansion and closure. We also showed that gap shape varied highly and that no single geometric form was able to predict the shape of all gaps, the ellipse in particular should no longer be used as a standard gap shape. © 2012 International Association for Vegetation Science.

A new method for calculating the convergent point of a moving group

Context. Convergent point (CP) search methods are important tools for studying the kinematic properties of open clusters and young associations whose members share the same spatial motion. Aims. We present a new CP search strategy based on proper motion data. We test the new algorithm on synthetic data and compare it with previous versions of the CP search method. As an illustration and validation of the new method we also present an application to the Hyades open cluster and a comparison with independent results. Methods. The new algorithm rests on the idea of representing the stellar proper motions by great circles over the celestial sphere and visualizing their intersections as the CP of the moving group. The new strategy combines a maximum-likelihood analysis for simultaneously determining the CP and selecting the most likely group members and a minimization procedure that returns a refined CP position and its uncertainties. The method allows one to correct for internal motions within the group and takes into account that the stars in the group lie at different distances. Results. Based on Monte Carlo simulations, we find that the new CP search method in many cases returns a more precise solution than its previous versions. The new method is able to find and eliminate more field stars in the sample and is not biased towards distant stars. The CP solution for the Hyades open cluster is in excellent agreement with previous determinations.

Responses in carcass lean pH at 24 hours post-mortem in lines of Large White pigs selected for growth rate on a fixed ration over a set time

A restricted maximum likelihood analysis applied to an animal model showed no significant differences (P > 0.05) in pH value of the longissimus dorsi measured at 24 h post-mortem (pH24) between high and low lines of Large White pigs selected over 4 years for post-weaning growth rate on restricted feeding. Genetic and phenotypic correlations between pH24 and production and carcass traits were estimated using all performance testing records combined with the pH24 measurements (5.05–7.02) on slaughtered animals. The estimate of heritability for pH24 was moderate (0.29 ± 0.18). Genetic correlations between pH24 and production or carcass composition traits, except for ultrasonic backfat (UBF), were not significantly different from zero. UBF had a moderate, positive genetic correlation with pH24 (0.24 ± 0.33). These estimates of genetic correlations affirmed that selection for increased growth rate on restricted feeding is likely to result in limited changes in pH24 and pork quality since the selection does not put a high emphasis on reduced fatness.