Maximum likelihood estimation of subsequence conservation

A statistical method is presented for comparing protein sequences by partitioning the polymers and estimating each subsegment's degree of conservation. Conservation is measured as a function of the number of transitions occurring in the underlying time homogeneous Markov process assumed to govern amino acid mutations. The Markovian assumption also permits estimation of the ancestral sequence. Partitioning and estimation are carried out via maximum likelihood. The method is contrasted with the commonly utilized percent homology measure. A moving likelihood ratio plot to aid in identifying regions of high conservation is suggested as an analogue to moving hydrophobicity plots. An application is presented which identifies highly conserved regions in thymidylate synthase from L. casei and E. coli.     

Maximum likelihood estimation of population growth rates based on the coalescent.

We describe a method for co-estimating 4Nemu (four times the product of effective population size and neutral mutation rate) and population growth rate from sequence samples using Metropolis-Hastings sampling. Population growth (or decline) is assumed to be exponential. The estimates of growth rate are biased upwards, especially when 4Nemu is low; there is also a slight upwards bias in the estimate of 4Nemu itself due to correlation between the parameters. This bias cannot be attributed solely to Metropolis-Hastings sampling but appears to be an inherent property of the estimator and is expected to appear in any approach which estimates growth rate from genealogy structure. Sampling additional unlinked loci is much more effective in reducing the bias than increasing the number or length of sequences from the same locus.     

Maximum likelihood estimation of primary productivity coefficients

Summary Computing parameters of primary productivity models from empirical data encounters the difficulty that Liebig's law of minimum is involved. For many of the data points used to fit the model it may not be evident which factor is the respective limiting one; it may even be different from the independent variables used. The introduction of a suitable statistical data model, however, allows a Maximum Likelihood procedure to be applied which simultaneously optimizes the parameters and classifies the data. Moreover, the proposed procedure is quite insensitive to data points whose limiting factor is not contained in the actual set of independent variables.Applicability of the method is demonstrated using a set of productivity measurements compiled by H. Lieth in 1975; numerical results, of course, may be subject to change as more data become available.     

Maximum likelihood estimation of ordered multinomial parameters

The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 相似文献   

Maximum likelihood estimation of human craniometric heritabilities

This study presents univariate narrow-sense heritability estimates for 33 common craniometric dimensions, calculated using the maximum likelihood variance components method on a skeletal sample of 298 pedigreed individuals from Hallstatt, Austria. Quantitative genetic studies that use skeletal cranial measurements as a basis for inferring microevolutionary processes in human populations usually employ heritability estimates to represent the genetic variance of the population. The heritabilities used are often problematic: most come from studies of living humans, and/or they were calculated using statistical techniques or assumptions violated by human groups. Most bilateral breadth measures in the current study show low heritability estimates, while cranial length and height measures have heritability values ranging between 0.102-0.729. There appear to be differences between the heritabilities calculated from crania and those from anthropometric studies of living humans, suggesting that the use of the latter in quantitative genetic models of skeletal data may be inappropriate. The univariate skeletal heritability estimates seem to group into distinct regions of the cranium, based on their relative values. The most salient group of measurements is for the midfacial/orbital region, with a number of measures showing heritabilities less than 0.30. Several possible reasons behind this pattern are examined. Given the fact that heritabilities calculated on one population should not be applied to others, suggestions are made for the use of the data presented.     

Maximum likelihood estimation of oncogenetic tree models

We present a new approach for modelling the dependences between genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependences between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.     

Maximum likelihood estimation for cytogenetic dose-response curves

In vitro dose-response curves are used to describe the relation between chromosome aberrations and radiation dose for human lymphocytes. The lymphocytes are exposed to low-LET radiation, and the resulting dicentric chromosome aberrations follow the Poisson distribution. The expected yield depends on both the magnitude and the temporal distribution of the dose. A general dose-response model that describes this relation has been presented by Kellerer and Rossi (1972, Current Topics on Radiation Research Quarterly 8, 85-158; 1978, Radiation Research 75, 471-488) using the theory of dual radiation action. Two special cases of practical interest are split-dose and continuous exposure experiments, and the resulting dose-time-response models are intrinsically nonlinear in the parameters. A general-purpose maximum likelihood estimation procedure is described, and estimation for the nonlinear models is illustrated with numerical examples from both experimental designs. Poisson regression analysis is used for estimation, hypothesis testing, and regression diagnostics. Results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure.     

Maximum likelihood estimation in dynamical models of HIV

The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these models leads to great difficulties for inference and only the Bayesian approach has been attempted by now. We propose a full likelihood inference, adapting a Newton-like algorithm for these particular models. We consider a relatively complex ODE model for HIV infection and a model for the observations including the issue of detection limits. We apply this approach to the analysis of a clinical trial of antiretroviral therapy (ALBI ANRS 070) and we show that the whole algorithm works well in a simulation study.     

Maximum likelihood estimation for stochastic first order reactions

Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ>0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.     

Maximum likelihood estimation in the additive hazards model

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non-parametric model, additive hazards offer a very flexible way of modeling time-varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non-negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log-likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non-negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least-squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least-squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided.     

Maximum likelihood estimation of the kinetics of receptor-mediated adhesion

Adhesion flow assays are commonly employed to characterize the kinetics and force-dependence of receptor-ligand interactions. As transient cellular adhesion events are often mediated by a small number of receptor-ligand complexes (tether bonds) their durations are highly variable, which in turn presents obstacles to standard methods of analysis. In this paper, we employ the stochastic approach to chemical kinetics to construct the pause time distribution. Using this distribution, we develop a robust maximum likelihood (ML) approach to the robust estimation of rate constants associated with receptor-mediated transient adhesion and their confidence intervals. We then formulate robust estimators of the parameters of models for the force-dependence of the off-rate. Lastly, we develop a robust method of elucidation of the force-dependence of the off-rate using Akaike's information criterion (AIC). Our findings conclusively demonstrate that ML estimators of adhesion kinetics are substantial improvements over more conventional approaches, and when combined with Fisher information, they may be used to objectively and reproducibly distinguish the kinetics of different receptor-ligand complexes. Software for the implementation of these methods with experimental data is publicly available as for download at http://www.laurenzi.net.     

Maximum likelihood estimation of recombination rates from population data

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.     

Maximum likelihood estimation of linkage disequilibrium in half-sib families

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.