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PubMed2005

Stepwise mutation likelihood computation by sequential importance sampling in subdivided population models.

An importance sampling algorithm for computing the likelihood of a sample of genes at loci under a stepwise mutation model in a subdivided population is developed. This allows maximum likelihood estimation of migration rates between subpopulations. The time to the most recent common ancestor of the sample can also be computed. The technique is illustrated by an analysis of a data set of Australian red fox populations.

Algorithms↗

PubMed2004

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used.

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.

Algorithms↗

PubMed1999

A heuristic approach of maximum likelihood method for inferring phylogenetic tree and an application to the mammalian SOX-3 origin of the testis-determining gene SRY.

Applying the tree bisection and reconnection (TBR) algorithm, we have developed a heuristic method (maximum likelihood (ML)-TBR) for inferring the ML tree based on tree topology search. For initial trees from which iterative processes start in ML-TBR, two cases were considered: one is 100 neighbor-joining (NJ) trees based on the bootstrap resampling and the other is 100 randomly generated trees. The same ML tree was obtained in both cases. All different iterative processes started from 100 independent initial trees ultimately converged on one optimum tree with the largest log-likelihood value, suggesting that a limited number of initial trees will be quite enough in ML-TBR. This also suggests that the optimum tree corresponds to the global optimum in tree topology space and thus probably coincides with the ML tree inferred by intact ML analysis. This method has been applied to the inference of phylogenetic tree of the SOX family members. The mammalian testis-determining gene SRY is believed to have evolved from SOX-3, a member of the SOX family, based on several lines of evidence, including their sequence similarity, the location of SOX-3 on the X chromosome and some aspects of their expression. This model should be supported directly from the phylogenetic tree of the SOX family, but no evidence has been provided to date. A recently published NJ tree shows implausibly remote origin of SRY, suggesting that a more sophisticated method is required for understanding this problem. The ML tree inferred by the present method showed that the SRYs of marsupial and placental mammals form a monophyletic cluster which had diverged from the mammalian SOX-3 in the early evolution of mammals.

Algorithms↗

PubMedDate not supplied

The effect of relatives on the likelihood ratio associated with DNA profile evidence in criminal cases.

In DNA profiling sometimes a match is declared between the DNA profile from a suspect and that from a scene-of-crime DNA sample. DNA evidence has frequently been presented in the form of a likelihood ratio, the ratio of the probabilities of the data set under the two hypotheses of a single and two sources for the matching DNA profiles. The calculation of the probability of a match is usually performed using a product rule with information from an appropriate database. This approach has been criticized for failing to allow for genetic relatedness, such that the suspect could be a close relative of the source of the scene-of-crime DNA profile. This paper suggests ways of incorporating the possibility of relatives into the likelihood ratio, and shows that unless there is strong evidence implicating a full sibling of the accused, allowing for possible relatedness has very little impact.

Criminology↗

PubMed1998

Trauma admissions in the elderly: how does a patient's age affect the likelihood of their being admitted to hospital after a fracture?

In two projects we have studied patients presenting to Accident and Emergency (A&E) departments with a fracture, to examine how their age influences their likelihood of admission. Over 1 year from April 1994 we collected data on all 6467 Cardiff residents who presented to the city's A&E department with a fracture. In total 1226 (19%) were admitted. Overall, only 12% of those under 65, but 47% of older patients required admission. This was largely a reflection of the age-distribution of hip fracture, an injury for which admission is inevitable. In a subsequent study of eight A&E departments in South Wales we therefore considered the proportion of patients admitted following fractures at specific anatomical sites. In people over the age of 55 we identified 6889 fractures, 2115 (31%) of which led to admission. After standardisation to control for the age-distribution of incidence for different fracture sites, we found that the likelihood of admission was 22% greater for people aged over 65 years. Elderly people very often require hospital admission after a fracture, primarily as a consequence of the types of fractures that they tend to sustain. Admissions directly attributable to the effects of age and age-related medical, psychiatric and social comorbidity appear of more limited significance.

Adolescent↗

PubMed1992

Relative likelihood of bronchopulmonary dysplasia based on pulmonary mechanics measured in preterm neonates during the first week of life.

We studied 143 low birth weight infants (less than or equal to 1500 gm) with respiratory distress syndrome who required mechanical ventilation, and determined the efficacy of using the alterations in pulmonary mechanics (measured at 1 to 3 days, 4 to 7 days, 2 weeks, and 4 weeks) as possible predictors for the subsequent diagnosis of bronchopulmonary dysplasia (BPD). The sensitivity and specificity of pulmonary compliance and resistance as predictors of BPD were ascertained by logistic regression correlation (p less than 0.01) and receiver operating characteristic curves. With these pulmonary mechanics data and logistic discriminant analysis techniques, we developed BPD prediction models based on pulmonary mechanics, measured between 4 and 7 days of age, to define the likelihood ratio for the subsequent diagnosis of BPD. Eight different BPD prediction models were developed by using combinations of four vectors (pulmonary compliance, total pulmonary resistance, birth weight, gestational age), and each model was validated in a subsequent low birth weight study population (n = 53). All models were deemed accurate for negative prediction of BPD. The models dependent on gestational age and dynamic pulmonary compliance had the highest positive predictive accuracy. The predictive impact of total pulmonary resistance appeared to be minimal. These prediction models may be used to calculate the likelihood ratio for a subsequent BPD diagnosis and thereby objectively categorize both the risk and the magnitude of acute lung injury by the first week of life.

Airway Resistance↗

PubMed2001

Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood.

The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.

Animals↗

PubMed2003

A simulated annealing algorithm for maximum likelihood pedigree reconstruction.

The calculation of maximum likelihood pedigrees for related organisms using genotypic data is considered. The problem is formulated so that the domain of optimization is a permutation space. This is a feature shared by the travelling salesman problem, for which simulated annealing is known to be effective. Using this technique it is found that pedigrees can be reconstructed with minimal error using genotypic data of a quality currently realizable. In complex pedigrees accurate reconstruction can be done with no a priori age or sex information. For smaller numbers of individuals a method of efficiently enumerating all admissible pedigrees of nonzero likelihood is given.

Algorithms↗

PubMed2003

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data.

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).

Bayes Theorem↗

PubMed2003

Likelihood-based inference for genetic correlation coefficients.

We review Wright's original definitions of the genetic correlation coefficients F(ST), F(IT), and F(IS), pointing out ambiguities and the difficulties that these have generated. We also briefly survey some subsequent approaches to defining and estimating the coefficients. We then propose a general framework in which the coefficients are defined, their properties established, and likelihood-based inference implemented. Likelihood methods of inference are proposed both for bi-allelic and multi-allelic loci, within a hierarchical model which allows sharing of information both across subpopulations and across loci, but without assuming constancy in either case. This framework can be used, for example, to detect environment-related diversifying selection.

Alleles↗

PubMed2005

Maximum-likelihood methods for phylogeny estimation.

Maximum-likelihood (ML) estimation of phylogenies has reached a rather high level of sophistication because of algorithmic advances, improvements in models of sequence evolution, and improvements in statistical approaches and application of cluster computing. Here, I provide a brief basic background in application of the general principle of ML estimation to phylogenetics and provide an example of selecting among a nested set of ML models using a dynamic approach to hierarchical likelihood-ratio tests. I focus attention on PAUP* because it provides unique ease of switching among alternative optimality criteria (e.g., minimum evolution, parsimony, and ML). Further, examples of parametric bootstrap tests are provided that demonstrate statistical tests of phylogenetic hypotheses and model adequacy, in an absolute rather than relative sense. The increasing availability of clustered, parallelized computation makes use of such parametric approaches feasible.

Algorithms↗

PubMed1998

Clinical utility of likelihood ratios.

Test-performance characteristics can be derived from a simple 2x2 table displaying the dichotomous relationship between a positive or negative test result and the presence or absence of a target disorder. Sensitivity and specificity, including a summary display of their reciprocal relationship as a receiver operating characteristics curve, are relatively stable test characteristics. Unfortunately, they represent an inversion of customary clinical logic and fail to tell us precisely what we wish to know. Predictive values, on the other hand, provide us with the requisite information but-because they are vulnerable to variation in disease prevalence-are numerically unstable. Likelihood ratios (LRs), in contrast, combine the stability of sensitivity and specificity to provide an omnibus index of test performance far more useful than its constituent parts. Application of Bayes' theorem to LRs produces the following summary equation: Clinically estimated pretest odds of disease x LR=Posttest odds of disease. This simple equation illustrates a concordance between the mathematical properties of likelihood ratios and the central strategy underlying diagnostic testing: the revision of disease probability.

Likelihood Functions↗

PubMed2002

New applications of maximum likelihood and Bayesian statistics in macromolecular crystallography.

Maximum likelihood methods are well known to macromolecular crystallographers as the methods of choice for isomorphous phasing and structure refinement. Recently, the use of maximum likelihood and Bayesian statistics has extended to the areas of molecular replacement and density modification, placing these methods on a stronger statistical foundation and making them more accurate and effective.

Bayes Theorem↗

PubMed2003

Xantusiid "night" lizards: a puzzling phylogenetic problem revisited using likelihood-based Bayesian methods on mtDNA sequences.

Contentious issues in Night Lizard (Xantusiidae) evolution are revisited using Maximum Likelihood-based Bayesian methods and compared with results from Neighbor-Joining and Maximum Parsimony analyses. Fragments of three mitochondrial genes, the 12S and 16S ribosomal genes, and the cytochrome b gene, are sampled across an ingroup composed of seven xantusiid species and a 12-species outgroup chosen to bracket ancestral states for six additional clades of scleroglossan lizards. Our phylogenetic analyses afford robust support for the following conclusions: Xantusiidae is part of Scincomorpha, rather than being allied with Gekkota; Lepidophyma is sister to Xantusia, rather than to Cricosaura; Xantusia riversiana is imbedded within, rather than being sister to, other Xantusia species; and rock-morph Xantusia are not closely related to one another. Convergence related to retarded rates of growth and development, or to physical constraints imposed by living in rock crevices, may be responsible for much of the character discordance underlying conflicts in xantusiid phylogeny. Fossil-calibrated Maximum Likelihood-based divergence time estimates suggest that although the xantusiid stem may have originated in the Mesozoic, the crown clade is exclusively Tertiary in age. Thus, the clade including extant Cricosaura does not appear to have been extant during the K-T boundary bolide impact, as has been suggested. Moreover, our divergence-time estimates indicate that the xantusiid island endemics, Cricosaura typica on Cuba and Xantusia riversiana on the California Channel Islands, arrived via dispersal rather than vicariance, as previously proposed.

Animals↗

PubMed2003

Molecular phylogenetics of myliobatiform fishes (Chondrichthyes: Myliobatiformes), with comments on the effects of missing data on parsimony and likelihood.

Mitochondrial DNA sequences from the 12S rRNA gene, four tRNA genes, and a portion of two protein coding genes were used to investigate the relationship of myliobatoid genera. In addition, we conducted an investigation of the sister group to the freshwater stingrays by sampling additional DNA sequences from GenBank. Consequently, two datasets were used to examine myliobatoid relationships. The first consisted of the genes sequenced in this study. The second dataset was compiled by combining the first dataset with cytochrome b sequences from GenBank. The second dataset, however, included a number of missing characters due to differences in sampling. The effect of the missing characters on both maximum parsimony and maximum likelihood analysis was investigated by conducting a simulation study. Results of the simulation study indicated that maximum likelihood was not sensitive to the missing data, whereas the accuracy of maximum parsimony analysis was expected to decrease. Phylogenetic analysis of this group had several areas concordant with morphological studies, however, the analysis also revealed two novel relationships. In addition, placement of two taxa (Gymnura and Himantura) were dependent both on the dataset and analytical method used.

Animals↗

PubMedDate not supplied

An extended likelihood ratio framework for interpreting evidence.

This paper reviews some current methods, the likelihood ratio-based approach and the full Bayesian approach for the interpretation of evidence and discusses previously identified shortcomings in them. It suggests an approach based on a compromise--based on an extended likelihood ratio--that may combine the merits of logic without overstepping acceptable bounds for the forensic scientist in the presentation of evidence. The approach is exposed formally and takes advantage of inferential networks called Bayesian networks.

Criminology↗

PubMed2005

Bayesian and maximum likelihood estimation of genetic maps.

There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances.

Algorithms↗

PubMedDate not supplied

Comparison of probability and likelihood models for peptide identification from tandem mass spectrometry data.

We evaluate statistical models used in two-hypothesis tests for identifying peptides from tandem mass spectrometry data. The null hypothesis H(0), that a peptide matches a spectrum by chance, requires information on the probability of by-chance matches between peptide fragments and peaks in the spectrum. Likewise, the alternate hypothesis H(A), that the spectrum is due to a particular peptide, requires probabilities that the peptide fragments would indeed be observed if it was the causative agent. We compare models for these probabilities by determining the identification rates produced by the models using an independent data set. The initial models use different probabilities depending on fragment ion type, but uniform probabilities for each ion type across all of the labile bonds along the backbone. More sophisticated models for probabilities under both H(A) and H(0) are introduced that do not assume uniform probabilities for each ion type. In addition, the performance of these models using a standard likelihood model is compared to an information theory approach derived from the likelihood model. Also, a simple but effective model for incorporating peak intensities is described. Finally, a support-vector machine is used to discriminate between correct and incorrect identifications based on multiple characteristics of the scoring functions. The results are shown to reduce the misidentification rate significantly when compared to a benchmark cross-correlation based approach.

Databases, Protein↗