Maximum likelihood estimation for rician distributed data in analytical q-ball imaging

Analytical q-ball imaging is widely used for reconstruction of orientation distribution function (ODF) using diffusion weighted MRI data. Estimating the spherical harmonic coefficients is a critical step in this method. Least squares (LS) is widely used for this purpose assuming the noise to be additive Gaussian. However, Rician noise is considered as a more appropriate model to describe noise in MR signal. Therefore, the current estimation techniques are valid only for high SNRs with Gaussian distribution approximating the Rician distribution. The aim of this study is to present an estimation approach considering the actual distribution of the data to provide reliable results particularly for the case of low SNR values. Maximum likelihood (ML) is investigated as a more effective estimation method. However, no closed form estimator is presented as the estimator becomes nonlinear for the noise assumption of the Rician distribution. Consequently, the results of LS estimator is used as an initial guess and the more refined answer is achieved using iterative numerical methods. According to the results, the ODFs reconstructed from low SNR data are in close agreement with ODFs reconstructed from high SNRs when Rician distribution is considered. Also, the error between the estimated and actual fiber orientations was compared using ML and LS estimator. In low SNRs, ML estimator achieves less error compared to the LS estimator.

Maximum likelihood approach for tracking multiple mobile agents with a moving doppler radar system

Tracking mobile agents with a Doppler radar system mounted on a moving vehicle is considered in this paper. Dopplers modulated from mobile agents on the single frequency continuous wave signals are analyzed in order to estimate the positions and velocities of multiple mobile agents. The measurement noise is assumed to be Gaussian and the maximum likelihood estimation is utilized to enhance the localization accuracy.

Maximum-likelihood based estimation for Q-ball imaging using diffusion-weighted MRI data

Q-ball imaging has been presented to reconstruct diffusion orientation distribution function using diffusion weighted MRI. In this thesiis, we present a novel and robust approach to satisfy the smoothness constraint required in Q-ball imaging. Moreover, we developed an improved estimator based on the actual distribution of the MR data.

Generalized pseudo-likelihood estimates for markov random fields on lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Joint space-time trellis decoding and channel estimation in correlated fading channels

This letter addresses the issue of joint space-time trellis decoding and channel estimation in time-varying fading channels that are spatially and temporally correlated. A recursive space-time receiver which incorporates per-survivor processing (PSP) and Kalman filtering into the Viterbi algorithm is proposed. This approach generalizes existing work to the correlated fading channel case. The channel time-evolution is modeled by a multichannel autoregressive process, and a bank of Kalman filters is used to track the channel variations. Computer simulation results show that a performance close to the maximum likelihood receiver with perfect channel state information (CSI) can be obtained. The effects of the spatial correlation on the performance of a receiver that assumes independent fading channels are examined.

Estimating mean exposures from censored data: exposure to benzene in the Australian petroleum industry

A retrospective assessment of exposure to benzene was carried out for a nested case control study of lympho-haematopoietic cancers, including leukaemia, in the Australian petroleum industry. Each job or task in the industry was assigned a Base Estimate (BE) of exposure derived from task-based personal exposure assessments carried out by the company occupational hygienists. The BEs corresponded to the estimated arithmetic mean exposure to benzene for each job or task and were used in a deterministic algorithm to estimate the exposure of subjects in the study. Nearly all of the data sets underlying the BEs were found to contain some values below the limit of detection (LOD) of the sampling and analytical methods and some were very heavily censored; up to 95% of the data were below the LOD in some data sets. It was necessary, therefore, to use a method of calculating the arithmetic mean exposures that took into account the censored data. Three different methods were employed in an attempt to select the most appropriate method for the particular data in the study. A common method is to replace the missing (censored) values with half the detection limit. This method has been recommended for data sets where much of the data are below the limit of detection or where the data are highly skewed; with a geometric standard deviation of 3 or more. Another method, involving replacing the censored data with the limit of detection divided by the square root of 2, has been recommended when relatively few data are below the detection limit or where data are not highly skewed. A third method that was examined is Cohen's method. This involves mathematical extrapolation of the left-hand tail of the distribution, based on the distribution of the uncensored data, and calculation of the maximum likelihood estimate of the arithmetic mean. When these three methods were applied to the data in this study it was found that the first two simple methods give similar results in most cases. Cohen's method on the other hand, gave results that were generally, but not always, higher than simpler methods and in some cases gave extremely high and even implausible estimates of the mean. It appears that if the data deviate substantially from a simple log-normal distribution, particularly if high outliers are present, then Cohen's method produces erratic and unreliable estimates. After examining these results, and both the distributions and proportions of censored data, it was decided that the half limit of detection method was most suitable in this particular study.

The effects of clustered data on standard error estimates in covariance structure analysis : a field data application

Purpose – The purpose of this article is to present an empirical analysis of complex sample data with regard to the biasing effect of non-independence of observations on standard error parameter estimates. Using field data structured in the form of repeated measurements it is to be shown, in a two-factor confirmatory factor analysis model, how the bias in SE can be derived when the non-independence is ignored.

Design/methodology/approach – Three estimation procedures are compared: normal asymptotic theory (maximum likelihood); non-parametric standard error estimation (naïve bootstrap); and sandwich (robust covariance matrix) estimation (pseudo-maximum likelihood).

Findings – The study reveals that, when using either normal asymptotic theory or non-parametric standard error estimation, the SE bias produced by the non-independence of observations can be noteworthy.

Research limitations/implications – Considering the methodological constraints in employing field data, the three analyses examined must be interpreted independently and as a result taxonomic generalisations are limited. However, the study still provides “case study” evidence suggesting the existence of the relationship between non-independence of observations and standard error bias estimates.

Originality/value – Given the increasing popularity of structural equation models in the social sciences and in particular in the marketing discipline, the paper provides a theoretical and practical insight into how to treat repeated measures and clustered data in general, adding to previous methodological research. Some conclusions and suggestions for researchers who make use of partial least squares modelling are also drawn.

Exploiting geometry for improved hybrid AOA/TDOA-based localization

In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of  arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

Optimal range-difference-based localization considering geometrical constraints

This paper proposes a new type of algorithm aimed at finding the traditional maximum-likelihood (TML) estimate of the position of a target given time-difference-of-arrival (TDOA) information, contaminated by noise. The novelty lies in the fact that a performance index, akin to but not identical with that in maximum likelihood (ML), is a minimized subject to a number of constraints, which flow from geometric constraints inherent in the underlying problem. The minimization is in a higher dimensional space than for TML, and has the advantage that the algorithm can be very straightforwardly and systematically initialized. Simulation evidence shows that failure to converge to a solution of the localization problem near the true value is less likely to occur with this new algorithm than with TML. This makes it attractive to use in adverse geometric situations.

Position estimation and tracking of an autonomous mobile sensor using received signal strength

In this paper, an algorithm for approximating the path of a moving autonomous mobile sensor with an unknown position location using Received Signal Strength (RSS) measurements is proposed. Using a Least Squares (LS) estimation method as an input, a Maximum-Likelihood (ML) approach is used to determine the location of the unknown mobile sensor. For the mobile sensor case, as the sensor changes position the characteristics of the RSS measurements also change; therefore the proposed method adapts the RSS measurement model by dynamically changing the pass loss value alpha to aid in position estimation. Secondly, a Recursive Least-Squares (RLS) algorithm is used to estimate the path of a moving mobile sensor using the Maximum-Likelihood position estimation as an input. The performance of the proposed algorithm is evaluated via simulation and it is shown that this method can accurately determine the position of the mobile sensor, and can efficiently track the position of the mobile sensor during motion.

Phylogenetic relationships among nine scallop species (Bivalvia : Pectinidae) inferred from nucleotide sequences of one mitochondrial and three nuclear gene regions

Current knowledge of the evolutionary relationships among scallop species (Mollusca: Bivalvia: Pectinidae) in the Indo-Pacific region is rather scanty. To enhance the understanding of the relationships within this group, phylogenies of nine species of scallops with the majority from coastal regions of Thailand, were reconstructed by maximum parsimony, maximum likelihood, and Bayesian methods using sequences of the 16S rRNA of the mitochondrial genome, and a fragment containing the ITS1, 5.8S and ITS2 genes of the nuclear DNA. The trees that resulted from the three methods of analysis were topologically identical, however, gained different levels of support at some nodes. Nine species were clustered into two major clades, corresponding to two subfamilies (Pectininae and Chlamydinae) of the three currently recognized subfamilies within Pectinidae. Overall, the relationships reported herein are mostly in accordance with the previous molecular studies that used sequences of the mtDNA cytochrome oxidase subunit I, and the classification system based on microsculpture of shell features and morphological characteristics of juveniles. Levels of divergences were different among genes (i.e., the 5.8S gene showed the lowest levels of nucleotide divergence at all levels, whereas the 16S rRNA showed the highest level of variation within species, and ITS2 gene revealed the highest level of divergence at higher levels).

Selection of working correlation structure and best model in GEE analyses of longitudinal data

The Generalized Estimating Equations (GEE) method is one of the most commonly used statistical methods for the analysis of longitudinal data in epidemiological studies. A working correlation structure for the repeated measures of the outcome variable of a subject needs to be specified by this method. However, statistical criteria for selecting the best correlation structure and the best subset of explanatory variables in GEE are only available recently because the GEE method is developed on the basis of quasi-likelihood theory. Maximum likelihood based model selection methods, such as the widely used Akaike Information Criterion (AIC), are not applicable to GEE directly. Pan (2001) proposed a selection method called QIC which can be used to select the best correlation structure and the best subset of explanatory variables. Based on the QIC method, we developed a computing program to calculate the QIC value for a range of different distributions, link functions and correlation structures. This program was written in Stata software. In this article, we introduce this program and demonstrate how to use it to select the most parsimonious model in GEE analyses of longitudinal data through several representative examples.

Regressive logistic and proportional hazards disease models for within-family analyses of measured genotypes, with application to a CYP17 polymorphism and breast cancer

Various statistical methods have been proposed to evaluate associations between measured genetic variants and disease, including some using family designs. For breast cancer and rare variants, we applied a modified segregation analysis method that uses the population cancer incidence and population-based case families in which a mutation is known to be segregating. Here we extend the method to a common polymorphism, and use a regressive logistic approach to model familial aggregation by conditioning each individual on their mother's breast cancer history. We considered three models: 1) class A regressive logistic model; 2) age-of-onset regressive logistic model; and 3) proportional hazards familial model. Maximum likelihood estimates were calculated using the software MENDEL. We applied these methods to data from the Australian Breast Cancer Family Study on the CYP17 5UTR TC MspA1 polymorphism measured for 1,447 case probands, 787 controls, and 213 relatives of case probands found to have the CC genotype. Breast cancer data for first- and second-degree relatives of case probands were used. The three methods gave consistent estimates. The best-fitting model involved a recessive inheritance, with homozygotes being at an increased risk of 47% (95% CI, 28-68%). The cumulative risk of the disease up to age 70 years was estimated to be 10% or 22% for a CYP17 homozygote whose mother was unaffected or affected, respectively. This analytical approach is well-suited to the data that arise from population-based case-control-family studies, in which cases, controls and relatives are studied, and genotype is measured for some but not all subjects.

Variation of fibre diameter coefficient of variation and fibre curvature across mohair fleeces: Implications for animal selection, genetic selection and fleece evaluation

The presentwork aimed to determine howthe average fibre diameter coefficient of variation (CVD) and fibre curvature (FC) differences between nine sampling sites vary between sex and flock, to identify differences in variability between sampling sites as a result of between animal and between sire variability and to determine correlations between sampling sites in between animal and between sire variability. Australian Angoras (n = 313) from two farms in southern Australia were sampled at 12 and 18 months of age at nine sites (mid side, belly, brisket, hind flank, hip, hock, mid back, neck, shoulder). Staples were taken prior to shearing at skin level and CVD and FC determined. For each shearing, differences in CVD and FC between sampling sites, how these differences were affected by farm, sex, and sire, and the covariance between sites for sire and individual animal effects were investigated by restricted maximum likelihood (REML) analyses. The median mid side CVD at 12 and 18 months of age ranged from 23.6 to 25.1% but the actual range was 16.8–34.2%. The median mid side FC at 12 and 18 months of age ranged from 14.4 to 18.6◦/mm but the actual range was 10.5–26.3◦/mm. The general pattern for CVDwas for the mid back, hip and neck sites to have similar CVD, the brisket, hind flank and hock sites to have larger CVD and the belly to have smaller CVD than the mid side site. The between animal variation for CVD was lowest at the mid back site. This implies that the mid back would be the most effective site for between animal selection for CVD. Heritabilities for CVD (range at 18 months 0.18–0.30) were only about half the heritabilities for mean fibre diameter in the same study. There was a marked anterior–posterior increase in FC at both farms and with both ages. The results give no clear indication of the best site for between animal selection for FC, other than that the hock should be avoided. Heritabilities for FC are moderate to high (range at 18 months 0.44–0.77) and the genetic correlations are high except for the hock. Thus genetic selection for FC at any site, other than the hock, should be effective for changing FC over the entire fleece. There was more variability between animals than between sites and sires. These results are put into context with associated research on variation in mean fibre diameter and staple length.

Variation of mohair staple length across Angora goat fleeces : implications for animal selection and fleece evaluation

The present study aimed to determine how the average mohair staple length (SL) differences between nine sampling sites vary between sex and flock, to identify differences in SL variability between sampling sites as a result of between-animal and between-sire variability and to determine SL correlations between sampling sites in between-animal and between-sire variability. Australian Angora goats (n=301) from two farms in southern Australia were sampled at 12 and 18 months of age at nine sites (mid side, belly, brisket, hind flank, hip, hock, mid back, neck and shoulder). Staples were taken prior to shearing at skin level and stretched SL determined. For each shearing, differences in SL between sampling sites, how these differences were affected by farm, sex and sire, and the covariance between sites for sire and individual animal effects were investigated by restricted maximum likelihood (REML) analyses. The median mid-side SL at 12 and 18 months of age was 110 and 130 mm, respectively, but the actual range in mid-side SL was 65–165 mm. There was an anterior–posterior decline in SL with the hock being particularly short. There was no evidence that the between-site correlation of the sire effects differed from 1, indicating that genetic selection for SL at one site will be reflected in SL over the whole fleece. However, low heritabilities of SL at the hock, belly and brisket or at any site at 12 months of age were obtained. There was more variability between sites than between sires, but the between-animal variation was greater. The hip and mid-back sites can be recommended for within-flock (culling) and genetic selection for SL due to their low sampling variability, moderate heritability and ease of location.