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Results for “Likelihood Functions”

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PubMed1995

Complex segregation analysis of Gerbera flower colour.

The distribution of hue (CIELAB colour notation) classes among flowers of the Davis population of gerbera (Gerbera jamesonii H. Bolus ex Hooker) appears bimodal. This suggests that the genetic control of hue is determined by the segregation of a gene with large effect modified by additional genes with smaller effects. Complex segregation analysis (CSA), routinely employed in human genetic epidemiology, was used to study both qualitative and quantitative variation. CSA applies pedigree analysis through the consideration of transmission probabilities to optimize likelihood functions of various genetic models. Applying this technique to study flower hue of a sample representing generations 14, 15 and 16 of the Davis population, allowed identification of a putative dominant major gene with genotypic values for the dominant homozygote, heterozygote and recessive homozygote of 32, 32 and 71 degrees, respectively. This corresponds to the modes of the hue frequency distribution for the population. The putative major gene represents 0.66 of the total variation. The residual parent-offspring correlation (rho po = 0.2) measures the genetic contribution to the remainder of the variance.

Heterozygote↗

PubMed1996

Number of lethal equivalents in human populations: how good are the previous estimates?

Lee et al. (1996) recently developed a method for interval estimation of the number of lethal equivalents by using a hierarchical structure of likelihood functions. This hierarchical model consists of two multinomial trials: one of the sampling process of the parents from the population of interest, and the other for the survival of the offspring of the families obtained by mating the parents. The method, initially developed for selfing and full-sib mating, is extended here to include more general mating systems as well as mixtures of mating systems. We applied it to human data sets for which confidence intervals were previously not available. Our point estimates were close to previous ones, and the standard deviations were generally quite small. Thus, even if debate over the meaning of the concept of lethal equivalents has not been entirely resolved, our results showed that the previous estimates are at least statistically meaningful.

Alleles↗

PubMed2002

Morphological and mechanical information of coronary arteries obtained with intravascular elastography; feasibility study in vivo.

AIMS: Plaque composition is a major determinant of coronary related clinical syndromes. In vitro experiments on human coronary and femoral arteries have demonstrated that different plaque types were detectable with intravascular ultrasound elastography. The aim of this study was to investigate the feasibility of applying intravascular elastography during interventional catheterization procedures. METHODS AND RESULTS: Data were acquired in patients (n=12) during PTCA procedures with an EndoSonics InVision echoapparatus equipped with radiofrequency output. The systemic pressure was used to strain the tissue, and the strain was determined using cross-correlation analysis of sequential frames. A likelihood function was determined to obtain the frames with minimal motion of the catheter in the lumen, since motion of the catheter prevents reliable strain estimation. Minimal motion was observed near end-diastole. Reproducible strain estimates were obtained within one pressure cycle and over several pressure cycles. Validation of the results was limited to the information provided by the echogram. Strain in calcified material (0.20%+/-0.07) was lower (P<0.001) than in non-calcified tissue (0.51%+/-0.20). CONCLUSION: In vivo intravascular elastography is feasible. Significantly higher strain values were found in non-calcified plaques than in calcified plaques.

Adult↗

PubMed2005

Molecular phylogeny of the carnivora (mammalia): assessing the impact of increased sampling on resolving enigmatic relationships.

This study analyzed 76 species of Carnivora using a concatenated sequence of 6243 bp from six genes (nuclear TR-i-I, TBG, and IRBP; mitochondrial ND2, CYTB, and 12S rRNA), representing the most comprehensive sampling yet undertaken for reconstructing the phylogeny of this clade. Maximum parsimony and Bayesian methods were remarkably congruent in topologies observed and in nodal support measures. We recovered all of the higher level carnivoran clades that had been robustly supported in previous analyses (by analyses of morphological and molecular data), including the monophyly of Caniformia, Feliformia, Arctoidea, Pinnipedia, Musteloidea, Procyonidae + Mustelidae sensu stricto, and a clade of (Hyaenidae + (Herpestidae + Malagasy carnivorans)). All of the traditional "families," with the exception of Viverridae and Mustelidae, were robustly supported as monophyletic groups. We further have determined the relative positions of the major lineages within the Caniformia, which previous studies could not resolve, including the first robust support for the phylogenetic position of marine carnivorans (Pinnipedia) within the Arctoidea (as the sister-group to musteloids [sensu lato], with ursids as their sister group). Within the pinnipeds, Odobenidae (walrus) was more closely allied with otariids (sea lions/fur seals) than with phocids ("true" seals). In addition, we recovered a monophyletic clade of skunks and stink badgers (Mephitidae) and resolved the topology of musteloid interrelationships as: Ailurus (Mephitidae (Procyonidae, Mustelidae [sensu stricto])). This pattern of interrelationships of living caniforms suggests a novel inference that large body size may have been the primitive condition for Arctoidea, with secondary size reduction evolving later in some musteloids. Within Mustelidae, Bayesian analyses are unambiguous in supporting otter monophyly (Lutrinae), and in both MP and Bayesian analyses Martes is paraphyletic with respect to Gulo and Eira, as has been observed in some previous molecular studies. Within Feliformia, we have confirmed that Nandinia is the outgroup to all other extant feliforms, and that the Malagasy Carnivora are a monophyletic clade closely allied with the mongooses (Herpestidae [sensu stricto]). Although the monophyly of each of the three major feliform clades (Viverridae sensu stricto, Felidae, and the clade of Hyaenidae + (Herpestidae + Malagasy carnivorans)) is robust in all of our analyses, the relative phylogenetic positions of these three lineages is not resolvable at present. Our analyses document the monophyly of the "social mongooses," strengthening evidence for a single origin of eusociality within the Herpestidae. For a single caniform node, the position of pinnipeds relative to Ursidae and Musteloidea, parsimony analyses of data for the entire Carnivora did not replicate the robust support observed for both parsimony and Bayesian analyses of the caniform ingroup alone. More detailed analyses and these results demonstrate that outgroup choice can have a considerable effect on the strength of support for a particular topology. Therefore, the use of exemplar taxa as proxies for entire clades with diverse evolutionary histories should be approached with caution. The Bayesian analysis likelihood functions generally were better able to reconstruct phylogenetic relationships (increased resolution and more robust support for various nodes) than parsimony analyses when incompletely sampled taxa were included. Bayesian analyses were not immune, however, to the effects of missing data; lower resolution and support in those analyses likely arise from non-overlap of gene sequence data among less well-sampled taxa. These issues are a concern for similar studies, in which different gene sequences are concatenated in an effort to increase resolving power.

Animals↗

PubMed2003

Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation.

This paper describes a statistical image reconstruction method for x-ray CT that is based on a physical model that accounts for the polyenergetic x-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. Unlike our earlier work, the proposed algorithm does not require pre-segmentation of the object into the various tissue classes (e.g., bone and soft tissue) and allows mixed pixels. The attenuation coefficient of each voxel is modelled as the product of its unknown density and a weighted sum of energy-dependent mass attenuation coefficients. We formulate a penalized-likelihood function for this polyenergetic model and develop an iterative algorithm for estimating the unknown density of each voxel. Applying this method to simulated x-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artefacts relative to conventional beam hardening correction methods. We also apply the method to real data acquired from a phantom containing various concentrations of potassium phosphate solution. The algorithm reconstructs an image with accurate density values for the different concentrations, demonstrating its potential for quantitative CT applications.

Absorptiometry, Photon↗

PubMed1992

AIDS in Ireland: the reporting delay distribution and the implementation of integral equation models.

This paper deals with two basic aspects concerning the modelling of AIDS incidence in the context of Irish data. We describe initially the adjustment of the number of AIDS cases (Xij) to allow for reporting delays, where a simple form of the likelihood function for the Xij is supported by GLIM. Subsequently, we consider the accessibility of numerical solution (through a NAG routine) of the integral equation models generated by the back-projection method for the adjusted AIDS cases. Results for the Irish data are summarized for various choices of the incidence distribution.

Acquired Immunodeficiency Syndrome↗

PubMed2004

Bayesian hierarchical error model for analysis of gene expression data.

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.

Algorithms↗

PubMed2006

Identifiability assumptions for missing covariate data in failure time regression models.

Methods in the literature for missing covariate data in survival models have relied on the missing at random (MAR) assumption to render regression parameters identifiable. MAR means that missingness can depend on the observed exit time, and whether or not that exit is a failure or a censoring event. By considering ways in which missingness of covariate X could depend on the true but possibly censored failure time T and the true censoring time C, we attempt to identify missingness mechanisms which would yield MAR data. We find that, under various reasonable assumptions about how missingness might depend on T and/or C, additional strong assumptions are needed to obtain MAR. We conclude that MAR is difficult to justify in practical applications. One exception arises when missingness is independent of T, and C is independent of the value of the missing X. As alternatives to MAR, we propose two new missingness assumptions. In one, the missingness depends on T but not on C; in the other, the situation is reversed. For each, we show that the failure time model is identifiable. When missingness is independent of T, we show that the naive complete record analysis will yield a consistent estimator of the failure time distribution. When missingness is independent of C, we develop a complete record likelihood function and a corresponding estimator for parametric failure time models. We propose analyses to evaluate the plausibility of either assumption in a particular data set, and illustrate the ideas using data from the literature on this problem.

Humans↗

PubMed1996

Estimating the age of the common ancestor of a DNA sample using the number of segregating sites.

The number of segregating sites in a sample of DNA sequences and the age of the most recent common ancestor (MRCA) of the sequences in the sample are positively correlated. The value of the former can be used to estimate the value of the latter. Using the coalescent approach, we derive in this paper the joint probability distribution of the number of segregating sites and the age of the MRCA of a sample under the neutral Wright-Fisher model. From this distribution, we are able to compute the likelihood function of the number of segregating sites and the posterior probability of the age of the MRCA of a sample. Three point estimators and one interval estimator of the age of the MRCA are developed; their relationships and properties are investigated. The estimation of the age of the MRCA of human Y chromosomes from a sample of no variation is discussed.

DNA↗

PubMed1997

The sampling distribution of disease-associated alleles.

A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.

Alleles↗

PubMed2003

The application of Bayesian techniques in the interpretation of bioassay data.

The inverse problem of internal dosimetry is naturally posed as a problem of Bayesian inference. The Bayesian approach is of practical importance in three areas: (1) avoiding false positives in the detection of rare events, (2) the calculation of uncertainties, and (3) the calculation of multiple intakes, all of which are important for internal dosimetry. In this paper, the Bayesian approach to the interpretation of measurements is first reviewed using a simple conceptual example. Then, a simple 239Pu case using IMBA expert is discussed, and finally a current cutting-edge example is discussed involving real 238Pu data calculated with a Markov Chain Monte Carlo algorithm and with exact calculation of poisson likelihood functions.

Algorithms↗

PubMed1999

Quantitative evaluation of alternative mechanisms of blood and testes disposition of di(2-ethylhexyl) phthalate and mono(2-ethylhexyl) phthalate in rats.

Di(2-ethylhexyl) phthalate (DEHP), a commercially important plasticizer, induces testicular toxicity in laboratory animals at high doses. After oral exposure, most of the DEHP is rapidly metabolized in the gut to mono(2-ethylhexyl) phthalate (MEHP), which is the active metabolite for induction of testicular toxicity. To quantify the testes dose of MEHP with various routes of exposure and dose levels, we developed a physiologically based pharmacokinetic (PBPK) model for DEHP and MEHP in rats. Tissue:blood partition coefficients for DEHP were estimated from the n-octanol: water partition coefficient, while partition coefficients for MEHP were determined experimentally using a vial equilibration technique. All other parameters were either found in the literature or estimated from blood or tissue levels following oral or intravenous exposure to DEHP or MEHP. A flow-limited model failed to adequately simulate the available data. Alternative plausible mechanisms were explored, including diffusion-limited membrane transport, enterohepatic circulation, and MEHP ionization (pH-trapping model). In the pH-trapping model, only nonionized MEHP is free to become partitioned into the tissues, where it is equilibrated and trapped as ionized MEHP until it is deionized and released. All three alternative models significantly improved predictions of DEHP and MEHP blood concentrations over the flow-limited model predictions. The pH-trapping model gave the best predictions with the largest value of the log likelihood function. Predicted MEHP blood and testes concentrations were compared to measured concentrations in juvenile rats to validate the pH-trapping model. Thus, MEHP ionization may be an important mechanism of MEHP blood and testes disposition in rats.

Animals↗

PubMed2000

Quantitative evaluation of alternative mechanisms of blood disposition of di(n-butyl) phthalate and mono(n-butyl) phthalate in rats.

Phthalate esters are ubiquitous, low-level environmental contaminants that induce testicular toxicity in laboratory animals. The diester is rapidly metabolized in the gut to the monoester, which causes the testicular toxicity. Several physiologically based pharmacokinetic (PBPK) model structures have been evaluated for di(2-ethylhexyl) phthalate (DEHP) and mono(2-ethylhexyl) phthalate (MEHP). The objective of this study was to test these PBPK models for a less lipophilic phthalate diester, di(n-butyl) phthalate (DBP), and monoester, mono(n-butyl) phthalate (MBP). Alternate models describing enterohepatic circulation, diffusion-limitation, tissue pH gradients (pH trapping), and a simpler, flow-limited model were evaluated. A combined diffusion-limited and pH trapping model was also tested. MBP tissue:blood partition coefficients were similar when determined either experimentally by a nonvolatile, vial equilibration technique or algorithmically. All other parameters were obtained from the literature or estimated from MBP blood concentrations following intravenous or oral exposure to DBP or MBP. A flow-limited model was unable to predict MBP blood levels, whereas each alternative model had statistically better predictions. The combined diffusion-limited and pH trapping model was the best overall, having the highest log-likelihood function value. This result is consistent with a previous finding that the pH trapping model was the best model for describing DEHP and MEHP blood dosimetry, though it was necessary to extend the model to include diffusion-limitation. The application of the pH trapping model is a step toward developing a generic model structure for all phthalate esters, though more work is required before a generic structure can be identified with confidence. Development of a PBPK model structure applicable to all phthalate esters would support more realistic assessments of risk to human health from exposure to one or more members of this class of compounds.

Administration, Oral↗

PubMed1997

Level detection in ion channel records via idealization by statistical filtering and likelihood optimization.

A parameter-free method is presented for the level detection in ion channel records via recovery of step wise current changes. No assumptions about ion channel mechanism are made. The primary detection of the transitions is made by statistical filtering the data using the Student's t-test. The event currents are calculated as the average value of the current between two adjacent transitions. An optimal ideal trace is found by maximization of a likelihood function. The distribution of event currents recovered from the raw data is then analysed, again by using the Student's t-test, for their grouping into separate statistical ensembles, defining current levels. The method is subjected to rigorous test using simulated data, and is compared with several other methods. It produces the levels of channel current, their noise amplitudes and distributions of dwell times, the desired information for constructing the channel mechanism.

Ion Channels↗

PubMed2001

Fast Bayesian reconstruction of chaotic dynamical systems via extended Kalman filtering.

We present an improved Markov chain Monte Carlo (MCMC) algorithm for posterior computation in chaotic dynamical systems. Recent Bayesian approaches to estimate the parameters of chaotic maps have used the Gibbs sampler which exhibits slow convergence due to high posterior correlations. Using the extended Kalman filter to compute the likelihood function by integrating out all unknown system states, we obtain a very efficient MCMC technique. We compare the new algorithm to the Gibbs sampler using the logistic, the tent, and the Moran-Ricker maps as applications, measuring the performance in terms of CPU and integrated autocorrelation time.

Journal Article↗

PubMed1999

A feasible set approach to the crystallographic phase problem.

The connection between the crystallographic phase problem and the feasible set approach is explored. It is argued that solving the crystallographic phase problem is formally equivalent to a feasible set problem using a statistical operator interpretable via a log-likelihood functional, projection onto the non-convex set of experimental structure factors coupled with a phase-extension constraint and mapping onto atomic positions. In no way does this disagree with or dispute any of the existing statistical relationships available in the literature; instead it expands understanding of how the algorithms work. Making this connection opens the door to the application of a number of well developed mathematical tools in functional analysis. Furthermore, a number of known results in image recovery can be exploited both to optimize existing algorithms and to develop new and improved algorithms.

Journal Article↗

PubMed1997

Learning-based ventricle detection from cardiac MR and CT images.

The objective of this work is to investigate the issue of automatically detecting regions of interest (ROI's) in medical images. It is assumed that the regions to be detected can be roughly segmented by a threshold based on a likelihood measure of the ROI. First, an analysis of the global histogram is used to compute a preliminary threshold that is likely near the optimal one. The histogram analysis is motivated by the analytical result of a bell image intensity model proposed in this work. Then, the preliminary threshold is used to segment the input image, resulting in an attention map, which contains an attention region that approximates the ROI as well as many spurious ones. Due to the nonoptimality of the preliminary threshold, it can happen that the attention region contains a part of, or more regions than, the ROI. Learning takes place in two stages: 1) learning for automatic selection of the preliminary threshold value and 2) learning for automatically selecting the ROI from the attention map while dynamically tuning the threshold according to the learned-likelihood function. Experiments have been conducted to approximately locate the endocardium boundaries of the left and right ventricles from gradient-echo magnetic resonance (MR) images. Cardiac computed tomography (CT) images have also been used for testing. The boundary of the segmented region provided by this algorithm is not very accurate and is meant to be used for further fine tuning based on other application-specific measures.

Algorithms↗

PubMed1999

Segmentation, registration, and measurement of shape variation via image object shape.

A model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives. Metrics are described that compute an object representation's prior probability of local geometry by reflecting variabilities in the net's node and link parameter values, and that compute a likelihood function measuring the degree of match of an image to that object representation. A paradigm for image analysis of deforming such a model to optimize a posteriori probability is described, and this paradigm is shown to be usable as a uniform approach for object definition, object-based registration between images of the same or different imaging modalities, and measurement of shape variation of an abnormal anatomical object, compared with a normal anatomical object. Examples of applications of these methods in radiotherapy, surgery, and psychiatry are given.

Bayes Theorem↗