Divergence Estimates Research Articles

Measures of divergence for binary data used in biodistance studies

Biodistance analysis can elucidate various aspects of past population structure. The most commonly adopted measure of divergence when estimating biodistances is the mean measure of divergence (MMD). The MMD is an unbiased estimator of population divergence but this property is lost when the dataset includes variables with very high or low frequency. In the present paper, we examine new measures of divergence based on untransformed binary data and the logit and probit transformations. It is shown that a measure of divergence based on untransformed data is a better unbiased estimator of population divergence. The conventional MMD is a satisfactory distance measure for binary data; however, it may produce biased estimations of population divergence when there are many traits with frequencies lower than 0.1 or/and greater than 0.9. Finally, the measures of divergence based on the probit and logit transformations are usually biased estimators.

Pixy: Unbiased estimation of nucleotide diversity and divergence in the presence of missing data.

Population genetic analyses often use summary statistics to describe patterns of genetic variation and provide insight into evolutionary processes. Among the most fundamental of these summary statistics are π and dXY , which are used to describe genetic diversity within and between populations, respectively. Here, we address a widespread issue in π and dXY calculation: systematic bias generated by missing data of various types. Many popular methods for calculating π and dXY operate on data encoded in the variant call format (VCF), which condenses genetic data by omitting invariant sites. When calculating π and dXY using a VCF, it is often implicitly assumed that missing genotypes (including those at sites not represented in the VCF) are homozygous for the reference allele. Here, we show how this assumption can result in substantial downward bias in estimates of π and dXY that is directly proportional to the amount of missing data. We discuss the pervasive nature and importance of this problem in population genetics, and introduce a user-friendly UNIX command line utility, pixy, that solves this problem via an algorithm that generates unbiased estimates of π and dXY in the face of missing data. We compare pixy to existing methods using both simulated and empirical data, and show that pixy alone produces unbiased estimates of π and dXY regardless of the form or amount of missing data. In summary, our software solves a long-standing problem in applied population genetics and highlights the importance of properly accounting for missing data in population genetic analyses.

Improving the Efficiency of Robust Estimators for the Generalized Linear Model

The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared; the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed.

Population differentiation in the Persian Gulf and Gulf of Oman: insights from the ghost shrimp's associated copepods, Clausidium iranensis and Clausidium persiaensis

AbstractEvolution and population genetic structure of marine species across the Persian Gulf and Gulf of Oman are shaped by two complex factors: the geological history and the present pattern of marine currents. Characterizing and comparing the genetic structures of co-existing species, such as host–parasite associations, allow the discrimination of the relative importance of environmental factors and life history traits that influenced gene flow and demographic events. In this study, we compare two associated Clausidium copepod species (C. persiaensis Sepahvand & Kihara 2017 and C. iranensis Sepahvand, Kihara & Boxshall 2019) along the south coast of Iran in two geological settings. We analysed partial nucleotide sequences of the mtCOI gene using divergence estimates (FST) and haplotype networks to infer intraspecific population connectivity in the two Gulfs. The results obtained demonstrate the existence of two genetically and geographically distinct clades, corresponding to the Persian Gulf and Gulf of Oman populations. Our results also indicate high diversity, population expansion and high connectivity among populations of C. persiaensis and C. iranensis in the Persian Gulf and Gulf of Oman.

Cumulative divergence revisited

We revisit cumulative divergence, a robust metric to measure the conditional mean independence between two random variables. First, we prove that if ${\\rm~E}(Y\\mid~~X)$ does not varies with $X$, then the corresponding sample estimator of cumulative divergence is $n$ consistent; otherwise, it is root-$n$ consistent. We propose a wild bootstrap procedure to approximate the asymptotic null distribution and prove that this bootstrap method is consistent. Second, we propose an independent screening procedure using cumulative divergence to filter out unimportant covariates in ultrahigh dimensional mean regressions. We establish the ranking consistency property and the sure screening property for our proposal and demonstrate its robust performance through comprehensive numerical studies.

On the choice of the aperture diameter of the probe laser in ground-based adaptive optoelectronic systems in the formation of a sodium reference star

Subject of study. The authors propose an integrated approach to the problem of determining the aperture diameter of a probe laser that forms a laser reference star used in ground-based adaptive optoelectronic systems. The relevance of this study is due to the fact that modern large-aperture optical systems for tracking natural stars and artificial objects (spacecraft or fragments of space debris) widely implement the technology of forming laser stars and use them as reference sources for correcting phase distortions of a turbulent atmosphere. The choice of the energy and spatiotemporal characteristics of laser guide stars is related both to the parameters of the probe laser (radiation power and aperture diameter), which forms the guide star, and to the spatiotemporal characteristics of the atmosphere. Method. The diameter of the probe laser aperture (for the near and far radiation zones) is estimated taking into account the spatial coherence radius of the atmosphere r0, the radiation intensity and angular divergence of the laser beam, its random root-mean-square angular deviation (jitter) with respect to the calculated direction to the space objects. Main results. The estimation of the angular divergence of a laser beam is based on a comparative analysis and generalization of theoretical results obtained by calculating the optical resolution in systems for acquiring images of natural space objects. It is shown, in particular, that when determining the size of the aperture along with the value of the angular divergence of the probe beam, it is necessary to take into consideration the decrease in its radiation intensity with an increase in the diameter with respect to the radius of atmosphere coherence. The practical significance. The results are essential, firstly, for the development of ground-based adaptive optoelectronic systems for tracking artificial space objects, and secondly, for determining the geographic locations of the optoelectronic systems taking into account the astronomical climate.

Minimum Divergence Estimators, Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.

Patterns of variation of mutation rates of mitochondrial and nuclear genes of gastropods

BackgroundAlthough mitochondrial DNA (mtDNA) of many animals tends to mutate at higher rates than nuclear DNA (nuDNA), a recent survey of mutation rates of various animal groups found that the gastropod family Bradybaenidae (suborder Helicina) shows a nearly 40-fold difference in mutation rates of mtDNA (mum) and nuDNA (mun), while other gastropod taxa exhibit only two to five-fold differences. To determine if Bradybaenidae represents an outlier within Gastropoda, I compared estimated values of mum/mun of additional gastropod groups. In particular, I reconstructed mtDNA and nuDNA gene trees of 121 datasets that include members of various clades contained within the gastropod subclasses Caenogastropoda, Heterobranchia, Patellogastropoda, and Vetigastropoda and then used total branch length estimates of these gene trees to infer mum/mun.ResultsEstimated values of mum/mun range from 1.4 to 91.9. Datasets that exhibit relatively large values of mum/mun (i.e., > 20), however, show relatively lower estimates of mun (and not elevated mum) in comparison to groups with lower values. These datasets also tend to contain sequences of recently diverged species. In addition, datasets with low levels of phylogenetic breadth (i.e., contain members of single genera or families) exhibit higher values of mum/mun than those with high levels (i.e., those that contain representatives of single superfamilies or higher taxonomic ranks).ConclusionsGastropods exhibit considerable variation in estimates of mum/mun. Large values of mum/mun that have been calculated for Bradybaenidae and other gastropod taxa may be overestimated due to possible sampling artifacts or processes that depress estimates of total molecular divergence of nuDNA in groups that recently diversified.

Elasticity index evaluation based on Le Cam divergence and kernel density estimator in PM space

This work focuses on the application of Preisach-Mayergoyz (PM) model applied to the evaluation of elastic properties of hysteretic material. In the first part, essential concepts are explained such as material hysteresis, probability density functions of PM space, optimization algorithm used, and phi-divergence measures applied in the PM identification process. Next, two different characterizations of PM space of hysterons based on kernel density estimators are proposed, either for one-dimensional PM space projection or for fully two-dimensional pyramid kernel. Finally, new index of elasticity is built up by means of the squared Le Cam divergence between probability density corresponding to the super-elastic distribution and the probability density found by our optimized PM identification process, respectively. This elasticity index describes ability of the material to absorb mechanical deformation, or alternatively, it gives an evidence about the certain degree of damage of the material. This proposed index of elasticity (IE) is evaluated for the case of experimental data measured on the steel dampers used for the protection against earthquakes.

Machine Learning for Technical Debt Identification

Technical Debt (TD) is a successful metaphor in conveying the consequences of software inefficiencies and their elimination to both technical and non-technical stakeholders, primarily due to its monetary nature. The identification and quantification of TD rely heavily on the use of a small handful of sophisticated tools that check for violations of certain predefined rules, usually through static analysis. Different tools result in divergent TD estimates calling into question the reliability of findings derived by a single tool. To alleviate this issue we use 18 metrics pertaining to source code, repository activity, issue tracking, refactorings, duplication and commenting rates of each class as features for statistical and Machine Learning models, so as to classify them as High-TD or not. As a benchmark we exploit 18.857 classes obtained from 25 Java projects, whose high levels of TD has been confirmed by three leading tools. The findings indicate that it is feasible to identify TD issues with sufficient accuracy and reasonable effort: a subset of superior classifiers achieved an F2-measure score of approximately 0.79 with an associated Module Inspection ratio of approximately 0.10. Based on the results a tool prototype for automatically assessing the TD of Java projects has been implemented.

Limit Distribution of the φ-Divergence Based Change Point Estimator

The assumption of stationarity is too restrictive especially for long time series. This paper studies the change point problem through a change point estimator based on the φ-divergence which provides a rich set of distance like measures between pairs of distributions. The change point problem is considered in the following sub-fields: the problem of divergence estimation, testing for the homogeneity between two samples as well as estimating the time of change. The asymptotic distribution of the change point estimator is estimated by the limiting distribution of a stochastic process within given bounds through asymptotic theory surrounding the likelihood theory. The distribution is found to converge to that of a standardized Brownian bridge process.

The second known stygomorphic freshwater crab from China, Phasmon typhlops gen. nov. et sp. nov. (Crustacea, Decapoda, Potamidae), diverged at the beginning of the Late Miocene.

A new genus and new species of blind freshwater cave crab are described from Chongzuo City, Guangxi Zhuang Autonomous Region, China based on morphology and mitochondrial 16S rDNA sequences. The new genus, Phasmongen. nov., is established for P. typhlopssp. nov., which is only the second blind cave crab known from China and East Asia. The combination of a very wide carapace, overall depigmentation, reduced orbits and vestigial unpigmented eyes of Phasmon immediately separates it from all known potamid genera. Molecular divergence estimates based on 16S rDNA suggest that the lineage to which the new genus belongs diverged from other potamids at the beginning of the Late Miocene (10.8 million years ago), much earlier than other Chinese cave crabs.

Robust Wald-type tests under random censoring.

Randomly censored survival data are frequently encountered in biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood-based tests, under a fully parametric model, are extremely nonrobust against outliers in the data. Although there exists a few robust estimators given randomly censored data, there is hardly any robust testing procedure available in the literature in this context. One of the major difficulties here is the construction of a suitable consistent estimator of the asymptotic variance of robust estimators, since the latter is a function of the unknown censoring distribution. In this article, we take the first step in this direction by proposing a consistent estimator of asymptotic variance of the M-estimators based on randomly censored data without any assumption on the censoring scheme. We then describe and study a class of robust Wald-type tests for parametric statistical hypothesis, both simple as well as composite, under such a set-up. Robust tests for comparing two independent randomly censored samples and robust tests against one sided alternatives are also discussed. Their advantages and usefulness are demonstrated for the tests based on the minimum density power divergence estimators and illustrated with clinical trials and other medical data.

General inference in semiparametric models through divergences and the duality technique with applications

In this paper, we extend the dual divergence approach to general semiparametric models and study dual divergence estimators for semiparametric models. Asymptotic properties such as consistency, asymptotic normality of the proposed estimators are deeply investigated by mean the sophisticated modern empirical theory. We investigate the exchangeably weighted estimators in this setting and establish the consistency. We finally consider the functional M-estimator and obtain its weak convergence result.

Genetic diversity of pituitary transcription factor 1 (PIT 1) gene in Nigerian local and exotic chicken

This study was carried out to investigate the genetic diversity of PIT1 gene in Nigerian local and exotic chicken breeds. Genomic DNA was extracted from the blood of Isa brown, Shika brown and Naked neck chickens which was used to amplify the PIT1 gene and later sequenced. Sequences were aligned and analyzed using Mega 6.0 and DNASp. The results revealed that Naked neck had 181 monomorphic sites and the least was observed in Isa brown (34). However, Isa brown had the highest number of polymorphic site (181) and the least was observed in Shika brown. Singleton variable sites also varied across breeds. Number of segregating sites was highest in Isa brown (174). The highest number of haplotypes was observed in Isa brown (11). Highest number of indel sites were observed in Isa brown (46) chickens. The highest estimates of average evolutionary divergence over sequence pairs within chicken breeds was observed in Isa brown (0.766) and the least in Shika brown (0.15). The highest genetic distance is between Isa brown and Naked neck and the least between Naked neck and Shika brown. The result obtained from this study revealed a clearer understanding of the genetic diversity in PIT1 gene across the different breeds. This information can be harnessed for better policies for conservation and breeding programs.

New Insights on the Evolution of the Sweet Taste Receptor of Primates Adapted to Harsh Environments.

Simple SummaryA sense of taste is vital to an animal’s fitness. It enables animals to select and ingest beneficial foods and avoid harmful substances in their daily lives. There have been relatively few studies regarding the evolution of the taste receptor gene for sweetness, particularly in regard to endemic Bornean primates. We constructed TAS1R2 gene phylogenies for 20 anthropoid primate species using four different methods as well as established the phylogenic time divergence. The phylogenetic analysis successfully separated the primates into their taxonomic groups and as per their dietary preferences. Of note, the estimated time of divergence for the primate speciation pattern in this study was more recent than the previously published estimates. This difference may have been due to environmental changes, such as food scarcity and climate change, during the late Miocene epoch, which likely forced primates to adapt their dietary preferences. These findings establish a foundation for further investigations.Taste perception is an essential function that provides valuable dietary and sensory information, which is crucial for the survival of animals. Studies into the evolution of the sweet taste receptor gene (TAS1R2) are scarce, especially for Bornean endemic primates such as Nasalis larvatus (proboscis monkey), Pongo pygmaeus (Bornean orangutan), and Hylobates muelleri (Muller’s Bornean gibbon). Primates are the perfect taxa to study as they are diverse dietary feeders, comprising specialist folivores, frugivores, gummivores, herbivores, and omnivores. We constructed phylogenetic trees of the TAS1R2 gene for 20 species of anthropoid primates using four different methods (neighbor-joining, maximum parsimony, maximum-likelihood, and Bayesian) and also established the time divergence of the phylogeny. The phylogeny successfully separated the primates into their taxonomic groups as well as by their dietary preferences. Of note, the reviewed time of divergence estimation for the primate speciation pattern in this study was more recent than the previously published estimates. It is believed that this difference may be due to environmental changes, such as food scarcity and climate change, during the late Miocene epoch, which forced primates to change their dietary preferences. These findings provide a starting point for further investigation.

An estimation of Phi divergence and its application in testing normality

In this article, a new goodness of fit test for normality is introduced based on Phi divergence. The test statistic is estimated using spacing and the consistency of the test is proved. Then with replacing some special cases of Phi divergence, the efficiency of each test statistic is analyzed by Monte Carlo simulation against some competitors (based on Phi divergence using kernel density function and also some classical competitors). It is shown that each special case of Phi divergence based test is the most powerful in each group of alternatives (depending on symmetry or support).

First partial mitogenome of a new Seira Lubbock species (Collembola,br /Entomobryidae, Seirinae) from Cambodia reveals a possible separate br /lineage from the Neotropical Seirinae.

A new species of Seira from Koh Rong Sanloem Island, Cambodia, as well as its mitochondrial genome information, are herein described. Seira sanloemensis sp. nov. has a similar colour pattern compared to nine other species of Seira worldwide distributed, but the dorsal chaetotaxy is more similar to S. arunachala Mitra from India, S. camgiangensis Nguyễn from Vietnam, and S. gobalezai Christiansen Bellinger from Hawaii. However, the new species differs from these species by dorsal chaetotaxy of head, Th II-III and Abd II, collophore chaetotaxy, and morphology of the empodial complex. This is the third Collembola species described for Cambodia. Its assembled incomplete mitogenome from MGI reads, has a length of 13,953 bp, and contains all protein-coding genes except for tree tRNAs missing; the gene order is the same of the Pancrustacean ancestral gene order. Based on the alignment of the 13 coding genes, a maximum likelihood phylogenetic tree of medium bootstrap values suggested that the Asian Seira species can represent a different lineage from the Neotropical Seirinae, but further biogeographic and divergence estimation analyses plus the inclusion of more Asian taxa are necessary to test such hypothesis.

Robust semiparametric inference for polytomous logistic regression with complex survey design

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Using the new estimators, robust testing of general linear hypotheses on the regression coefficients are proposed. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study.

Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator.

In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.