PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Likelihood Functions”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17Linked to original sources
PubMed2002

Statistical image reconstruction for polyenergetic X-ray computed tomography.

This paper describes a statistical image reconstruction method for X-ray computed tomography (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. We assume that the object consists of a given number of nonoverlapping materials, such as soft tissue and bone. The attenuation coefficient of each voxel is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this polyenergetic model and develop an ordered-subsets iterative algorithm for estimating the unknown densities in each voxel. The algorithm monotonically decreases the cost function at each iteration when one subset is used. Applying this method to simulated X-ray CT measurements of objects containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.

Algorithms↗
PubMedDate not supplied

A generalized framework for network component analysis.

The authors recently introduced a framework, named Network Component Analysis (NCA), for the reconstruction of the dynamics of transcriptional regulators' activities from gene expression assays. The original formulation had certain shortcomings that limited NCA's application to a wide class of network dynamics reconstruction problems, either because of limitations in the sample size or because of the stringent requirements imposed by the set of identifiability conditions. In addition, the performance characteristics of the method for various levels of data noise or in the presence of model inaccuracies were never investigated. In this article, the following aspects of NCA have been addressed, resulting in a set of extensions to the original framework: 1) The sufficient conditions on the a priori connectivity information (required for successful reconstructions via NCA) are made less stringent, allowing easier verification of whether a network topology is identifiable, as well as extending the class of identifiable systems. Such a result is accomplished by introducing a set of identifiability requirements that can be directly tested on the regulatory architecture, rather than on specific instances of the system matrix. 2) The two-stage least square iterative procedure used in NCA is proven to identify stationary points of the likelihood function, under Gaussian noise assumption, thus reinforcing the statistical foundations of the method. 3) A framework for the simultaneous reconstruction of multiple regulatory subnetworks is introduced, thus overcoming one of the critical limitations of the original formulation of the decomposition, for example, occurring for poorly sampled data (typical of microarray experiments). A set of monte carlo simulations we conducted with synthetic data suggests that the approach is indeed capable of accurately reconstructing regulatory signals when these are the input of large-scale networks that satisfy the suggested identifiability criteria, even under fairly noisy conditions. The sensitivity of the reconstructed signals to inaccuracies in the hypothesized network topology is also investigated. We demonstrate the feasibility of our approach for the simultaneous reconstruction of multiple regulatory subnetworks from the same data set with a successful application of the technique to gene expression measurements of the bacterium Escherichia coli.

Algorithms↗
PubMed2026

Sparse Logistic Regression on Genomic Data for Prediction of Tumour Pathological Subtype.

The correct prediction of tumour subtype is critical for the treatment of cancer patients to maximise the chance of survival. The patients' genomic information, such as copy number alterations (CNA) profile, has increasingly become an important factor in the prediction to supplement the traditional pathological subtyping. The incorporation of the CNA information in a prediction model, such as logistic regression, faces two major statistical challenges: first, how to estimate the model parameters in the thousands and, second, how to deal with the correlation of CNA between genomic regions. To address them, we propose a sparse logistic regression model with random effects where some of its parameters are estimated to zero while the other parameters are non-zero. In effect, a variable selection is embedded in the modelling. To deal with the correlation of CNA across genomic regions, we extend further the model to incorporate an additional penalty in the corresponding likelihood function in the logistic regression. The results show that we can identify selected genomic regions that are informative to distinguish different tumour subtypes, while giving a good prediction ability. We illustrate the methodology using CNA dataset from a lung cancer cohort.

Journal Article↗
PubMed2005

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing.

We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. In this paper, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive--it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.

Algorithms↗
PubMed2006

Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification.

We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and two-dimensional Gabor wavelet transform responses taken at multiple scales. The Gabor wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The method's performance is evaluated on publicly available DRIVE (Staal et al., 2004) and STARE (Hoover et al., 2000) databases of manually labeled images. On the DRIVE database, it achieves an area under the receiver operating characteristic curve of 0.9614, being slightly superior than that presented by state-of-the-art approaches. We are making our implementation available as open source MATLAB scripts for researchers interested in implementation details, evaluation, or development of methods.

Algorithms↗
PubMed2005

Statistical analysis of network traffic for adaptive faults detection.

This paper addresses the problem of normal operation baselining for automatic detection of network anomalies. A model of network traffic is presented in which studied variables are viewed as sampled from a finite mixture model. Based on the stochastic approximation of the maximum likelihood function, we propose baselining network normal operation, using the asymptotic distribution of the difference between successive estimates of model parameters. The baseline random variable is shown to be stationary, with mean zero under normal operation. Anomalous events are shown to induce an abrupt jump in the mean. Detection is formulated as an online change point problem, where the task is to process the baseline random variable realizations, sequentially, and raise alarms as soon as anomalies occur. An analytical expression of false alarm rate allows us to choose the design threshold, automatically. Extensive experimental results on a real network showed that our monitoring agent is able to detect unusual changes in the characteristics of network traffic, adapt to diurnal traffic patterns, while maintaining a low alarm rate. Despite large fluctuations in network traffic, this work proves that tailoring traffic modeling to specific goals can be efficiently achieved.

Algorithms↗
PubMed2005

Approximate estimates of limiting errors of passive wireless SAW sensing with DPM.

This paper discusses approximate statistical estimates of limiting errors associated with single differential phase measurement of a time delay (phase difference) between two reflectors of the passive surface acoustic wave (SAW) sensor. The remote wireless measurement is provided at the ideal coherent receiver using the maximum likelihood function approach. Approximate estimates of the mean error, mean square error, estimate variance, and Cramér-Rao bound are derived along with the error probability to exceed a threshold in a wide range of signal-to-noise ratio (SNR) values. The von Mises/Tikhonov distribution is used as an approximation for the phase difference and differential phase diversity. Simulation of the random phase difference and limiting errors also is applied.

Journal Article↗
PubMed1978

Ancestral inference. I. The problem and the method.

A method for inferring the ancestral genotypes for the founders of a population is developed. This method uses the algorithms for the computation of probabilities on pedigrees of arbitrary complexity, developed by Cannings et al. (1978) and implemented by Thompson (1977b). When characteristics are simply determined by underlying genotypes the inference problem is simplified, and larger and more complex pedigrees may therefore be analysed. The problem of estimating the allele frequencies to be used in computing prior genotype probabilities for those founders on whom a likelihood function is not required is discussed. The same method allows us to compute extinction probabilities for any combination of original founder genes; these probabilities are interesting parameters of pedigree structure, which, since they relate to the actual genes present in a population, help to provide a clearer understanding of observed distributions of autosomal traits.

Gene Frequency↗
PubMedDate not supplied

Reliability of the compensation comparison stray-light measurement method.

The compensation comparison (CC) method is a psychophysical technique to measure retinal stray light. It uses a two alternative forced choice (2AFC) measurement paradigm. The 25 binary (0 and 1) responses resulting from the 2AFC test are analyzed using maximum likelihood estimates. The likelihood function is used to give two quantities: the most likely stray-light level of the eye under investigation, and the accuracy of this estimate [called expected standard deviation (ESD)]. The CC method is used in 2422 subjects of the GLARE study. Each eye is tested twice to allow analysis of measurement repeatability. Furthermore, the large amount of responses is used to evaluate the shape of the psychometric function, for which a mathematical model is used. The shape of the psychometric function found by averaging the 0 and 1 responses fit well to the model function. Data sorted according to ESD show differences in the shape of the psychometric function between good and bad observers. These different shapes for the psychometric function are used to reanalyze the data, but the stray-light results remain virtually identical. ESD proves to be an efficient tool to detect unreliable measurements. In clinical practice, ESD may be used to decide whether to repeat a measurement.

Europe↗
PubMed2005

Partial volume segmentation of brain magnetic resonance images based on maximum a posteriori probability.

Noise, partial volume (PV) effect, and image-intensity inhomogeneity render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the above-mentioned effects. The objective of this paper is to propose a unified framework, based on the maximum a posteriori probability principle, by taking all these effects into account simultaneously in order to improve image segmentation performance. Instead of labeling each image voxel with a unique tissue type, the percentage of each voxel belonging to different tissues, which we call a mixture, is considered to address the PV effect. A Markov random field model is used to describe the noise effect by considering the nearby spatial information of the tissue mixture. The inhomogeneity effect is modeled as a bias field characterized by a zero mean Gaussian prior probability. The well-known fuzzy C-mean model is extended to define the likelihood function of the observed image. This framework reduces theoretically, under some assumptions, to the adaptive fuzzy C-mean (AFCM) algorithm proposed by Pham and Prince. Digital phantom and real clinical MR images were used to test the proposed framework. Improved performance over the AFCM algorithm was observed in a clinical environment where the inhomogeneity, noise level, and PV effect are commonly encountered.

Algorithms↗
PubMed1995

A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm.

We have derived a maximum a posteriori (MAP) approach for iterative reconstruction based on a weighted least-squares conjugate gradient (WLS-CG) algorithm. The WLS-CG algorithm has been shown to have initial convergence rates up to 10x faster than the maximum-likelihood expectation maximization (ML-EM) algorithm, but WLS-CG suffers from rapidly increasing image noise at higher iteration numbers. In our MAP-CG algorithm, the increasing noise is controlled by a Gibbs smoothing prior, resulting in stable, convergent solutions. Our formulation assumes a Gaussian noise model for the likelihood function. When a linear transformation of the pixel space is performed (the "relaxation" acceleration method), the MAP-CG algorithm obtains a low-noise, stable solution (one that does not change with further iterations) in 10-30 iterations, compared to 100-200 iterations for MAP-EM. Each iteration of MAP-CG requires approximately the same amount of processing time as one iteration of ML-EM or MAP-EM. We show that the use of an initial image estimate obtained from a single iteration of the Chang method helps the algorithm to converge faster when acceleration is not used, but does not help when acceleration is applied. While both the WLS-CG and MAP-CG methods suffer from the potential for obtaining negative pixel values in the iterated image estimates, the use of the Gibbs prior substantially reduces the number of pixels with negative values and restricts them to regions of little or no activity. We use SPECT data from simulated hot-sphere phantoms and from patient studies to demonstrate the advantages of the MAP-CG algorithm. We conclude that the MAP-CG algorithm requires 10%-25% of the processing time of EM techniques, and provides images of comparable or superior quality.

Algorithms↗
PubMed2002

Effects of incoherent and coherent source spectral information in geoacoustic inversion.

This paper examines the effect on matched-field geoacoustic inversion of including source spectral information, as can be available in controlled-source acoustic surveys. Source information can consist of relative or absolute knowledge of the source amplitude and/or phase spectra, and can allow frequency-coherent processing of spatial acoustic-field data. A number of multi-frequency acoustic processors, appropriate for specific types of source information, are defined based on the likelihood function for complex acoustic-field data with Gaussian noise. The information content of the various processors is quantified in terms of marginal probability distributions and highest-probability density intervals for the unknown geoacoustic and geometric parameters, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. The analysis is illustrated for incoherent and coherent processors corresponding to several types of source knowledge ranging from complete information to no information, and the results are considered as a function of the spatial and frequency sampling of the acoustic fields.

Acoustics↗
PubMed1989

Likelihood estimation of quantitative genetic parameters when selection occurs: models and problems.

Conceptual aspects of estimation of genetic components of variance and covariance under selection are discussed, with special attention to likelihood methods. Certain selection processes are described and alternative likelihoods that can be used for analysis are specified. There is a mathematical relationship between the likelihoods that permits comparing the relative amount of information contained in them. Theoretical arguments and evidence indicate that point inferences made from likelihood functions are not affected by some forms of selection.

Animals↗
PubMed1990

Classification of human muscle stretch receptor afferents: a Bayesian approach.

1. A sample of 124 human muscle afferents originating from the finger extensor muscles were recorded from the radial nerve in the upper arm. A method is described to formalize the classification of units in muscle spindle primary and secondary afferents and Golgi tendon organ afferents on the basis of a few, nonrigorous assumptions. The classification was based on experimental data that largely have been described in a series of previous papers, although some additional data were collected in the present study. 2. The units were subjected to five tests providing identification data: twitch contraction test, ramp-and-hold stretch, small-amplitude sinusoidal stretches superimposed on ramp stretch, stretch sensitization, and isometric contraction/relaxation. From these five tests the following eight response features were extracted: response to maximal isometric twitch contractions, type of stretch sensitization, correlation between discharge rate and contractile force, response to sudden isometric relaxation, presence or absence of an initial burst, deceleration response, prompt silencing at slow muscle shortening, and driving by small-amplitude sinusoidal stretches. 3. A Bayesian decision procedure was adopted to classify the units on the basis of the eight discriminators. As a first step, units were provisionally classified into muscle spindle primary and secondary afferents, and Golgi tendon organ afferents, by intuitively weighting their responses to the identification tests. Prior probabilities were estimated on the basis of the provisional classification. The eight response features were analyzed and tabulated for all afferents, and the likelihood functions of the tests were directly calculated on the basis of these data.(ABSTRACT TRUNCATED AT 250 WORDS)

Electrophysiology↗
PubMedDate not supplied

Estimation of transmission probabilities in families ascertained through a proband with variable age-at-onset disease: application to the HLA A, B and DR loci in Finnish families with type 1 diabetes. The DiMe Study Group.

An open problem of some interest in the study of HLA has been the possible existence of transmission distortion in the human HLA complex. In this paper, transmission probabilities are estimated and tested using data on HLA A, B and DR loci genotypes of parents and offspring ascertained from the entire population of Finland (Childhood Diabetes in Finland Study) through one or more offspring diagnosed with insulin-dependent diabetes mellitus (IDDM) during the recruitment period from September 1986 to July 1989. First, we show how to get unbiased estimates of transmission probabilities from the family data collected in the disease registry of incident cases. This is accomplished by assuming that transmission of HLA genes to children in the general population is conditionally independent given the parents' genotypes, and the birth dates of all offspring. Based on the sampling (ascertainment) process in the study on Childhood Diabetes in Finland, younger siblings of the index child (the oldest proband) are independent of the ascertainment and therefore give rise to unbiased inference regarding allele transmission. The hypothesis of Mendelian transmission of alleles at each locus was tested using the standard chi(2) test. Goodness-of-fit of the Mendelian inheritance model to the individual locus data is calculated by maximizing the likelihood function over allele transmission intensities at each locus. The existence of a strong transmission distortion is not supported by this study at the loci considered.

Adolescent↗
PubMed1991

Familial aggregation of lipids and lipoproteins in families ascertained through random and nonrandom probands in the Iowa Lipid Research Clinics family study.

The aggregation of lipids [total cholesterol (CH) and triglyceride (TG)] and lipoproteins [high-density lipoprotein cholesterol (HDL) and low-density lipoprotein cholesterol (LDL)] in families ascertained through random and nonrandom probands in the Iowa Lipid Research Clinics family study was examined. Nonrandom probands were selected because their lipid levels (at a prior screening visit) exceeded a certain pre-specified threshold. The statistical method conditions the likelihood function on the actual event that the proband's value is beyond the threshold. This method allows for estimation of the path model parameters in randomly and nonrandomly ascertained families jointly and separately, thus enabling tests of heterogeneity between the two types of samples. Marked heterogeneity between the random and the hyperlipidemic samples is detected in the multifactorial transmission for TG and HDL, and moderate heterogeneity is detected for CH and LDL, with a pattern of higher genetic heritability estimates in the random than nonrandom samples. The observed pattern of heterogeneity is compatible with a higher prevalence in the random sample of certain dyslipoproteinemias that are associated with nonelevated lipids. For the random samples, genetic heritabilities are higher for CH and HDL (about 60%) than for TG and LDL (about 50%). For the nonrandom samples those estimates are about 45, 40, 35 and 30% for HDL, CH, LDL and TG, respectively. Little to no cultural (familial environmental) heritability is evident for CH and LDL, although 10-20% of the phenotypic variance is due to cultural factors for TG and HDL. These results suggest that the etiologies for lipids and lipoproteins may be quite different in random versus hyperlipidemic samples.

Adult↗
PubMed2002

Natural discriminant analysis using interactive Potts models.

Natural discriminant analysis based on interactive Potts models is developed in this work. A generative model composed of piece-wise multivariate gaussian distributions is used to characterize the input space, exploring the embedded clustering and mixing structures and developing proper internal representations of input parameters. The maximization of a log-likelihood function measuring the fitness of all input parameters to the generative model, and the minimization of a design cost summing up square errors between posterior outputs and desired outputs constitutes a mathematical framework for discriminant analysis. We apply a hybrid of the mean-field annealing and the gradient-descent methods to the optimization of this framework and obtain multiple sets of interactive dynamics, which realize coupled Potts models for discriminant analysis. The new learning process is a whole process of component analysis, clustering analysis, and labeling analysis. Its major improvement compared to the radial basis function and the support vector machine is described by using some artificial examples and a real-world application to breast cancer diagnosis.

Journal Article↗