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.

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.

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.

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.

Range size-abundance relationships in Australian passerines

Aim  To investigate the relationship between geographical range size and abundance (population density) in Australian passerines.
Location  Australia (including Tasmania).
Methods   We analysed the relationship between range size and local abundance for 272 species of Australian passerines, across the whole order and within families. We measured abundance as mean and maximum abundance, and used a phylogenetic generalized least-squares regression method within a maximum-likelihood framework to control for effects of phylogeny. We also analysed the relationship within seven different habitat types.
Results  There was no correlation between range size and abundance for the whole set of species across all habitats. Analyses within families revealed some strong correlations but showed no consistent pattern. Likewise we found little evidence for any relationship or conflicting patterns in different habitats, except that woodland/forest habitat species exhibit a negative correlation between mean abundance and range size, whilst species in urban habitats exhibit a significant positive relationship between maximum abundance and range size. Despite the general lack of correlation, the raw data plots of range size and abundance in this study occupied a triangular space, with narrowly distributed species exhibiting a greater variation in abundances than widely distributed species. However, using a null model analysis, we demonstrate that this was due to a statistical artefact generated by the frequency distributions for the individual variables.
Conclusions   We find no evidence for a positive range size-abundance relationship among Australian passerines. This absence of a relationship cannot be explained by any conflicting effects introduced by comparing across different habitats, nor is it explained by the fact that large proportions of Australia are arid. We speculate that the considerable isolation and evolutionary age of Australian passerines may be an explanatory factor.

Software reliability growth models based on local polynomial modeling with kernel smoothing

Software reliability growth models (SRGMs) are extensively employed in software engineering to assess the reliability of software before their release for operational use. These models are usually parametric functions obtained by statistically fitting parametric curves, using Maximum Likelihood estimation or Least–squared method, to the plots of the cumulative number of failures observed N(t) against a period of systematic testing time t. Since the 1970s, a very large number of SRGMs have been proposed in the reliability and software engineering literature and these are often very complex, reflecting the involved testing regime that often took place during the software development process. In this paper we extend some of our previous work by adopting a nonparametric approach to SRGM modeling based on local polynomial modeling with kernel smoothing. These models require very few assumptions, thereby facilitating the estimation process and also rendering them more relevant under a wide variety of situations. Finally, we provide numerical examples where these models will be evaluated and compared.

AdaBoost.MRF: boosted Markov random forests and application to multilevel activity recognition

Activity recognition is an important issue in building intelligent monitoring systems. We address the recognition of multilevel activities in this paper via a conditional Markov random field (MRF), known as the dynamic conditional random field (DCRF). Parameter estimation in general MRFs using maximum likelihood is known to be computationally challenging (except for extreme cases), and thus we propose an efficient boosting-based algorithm AdaBoost.MRF for this task. Distinct from most existing work, our algorithm can handle hidden variables (missing labels) and is particularly attractive for smarthouse domains where reliable labels are often sparsely observed. Furthermore, our method works exclusively on trees and thus is guaranteed to converge. We apply the AdaBoost.MRF algorithm to a home video surveillance application and demonstrate its efficacy.

AdaM : adaptive-maximum imputation for neighborhood-based collaborative filtering

In the context of collaborative filtering, the well known data sparsity issue makes two like-minded users have little similarity, and consequently renders the k nearest neighbour rule inapplicable. In this paper, we address the data sparsity problem in the neighbourhood-based CF methods by proposing an Adaptive-Maximum imputation method (AdaM). The basic idea is to identify an imputation area that can maximize the imputation benefit for recommendation purposes, while minimizing the imputation error brought in. To achieve the maximum imputation benefit, the imputation area is determined from both the user and the item perspectives; to minimize the imputation error, there is at least one real rating preserved for each item in the identified imputation area. A theoretical analysis is provided to prove that the proposed imputation method outperforms the conventional neighbourhood-based CF methods through more accurate neighbour identification. Experiment results on benchmark datasets show that the proposed method significantly outperforms the other related state-of-the-art imputation-based methods in terms of accuracy.

The value of visual fleece assessment in addition to objective measurements in identifying Angora goats of greater clean mohair production

Visual assessment of the fleece of Merino sheep is an accepted method to aid genetic improvement but there is little evidence to support the use of visual assessment for improving mohair production. This paper examines the extent that visual traits, including staple length, character (staple crimp), staple definition, tippiness, style and staple entanglement, are related to clean fleece weight in animals of similar live weight and mean fibre diameter (MFD) from the same flock. Measurements were made over 9 shearing periods on a population of castrated Angora males (wethers) goats representing the current range and diversity of genetic origins in Australia, including South African, Texan and interbred admixtures of these and Australian sources (these different genetic origins are defined as Breed in this work). Data on genetic origin, sire, dam, lifetime characteristics (date of birth, dam age, birth weight, birth parity (single or twin), weaning weight), live weight, fleece growth and visual fleece attributes were recorded. A restricted maximum likelihood (REML) model was developed to relate clean fleece weight with age, MFD, average fleece-free live weight, lifetime characteristics and visual fleece attributes. There were separate linear responses of clean fleece weight to MFD and staple length for each age group, a quadratic response to the square root of average fleece-free live weight, an effect of sire breed and linear responses to dam age, staple definition score and character. Depending on age at shearing, the increase in clean fleece weight was between about 50 and 80. g for each increase of 1. μm in MFD. At similar MFD, clean fleece weight was generally greater at summer shearings compared with winter shearings. There was a strong increase in clean fleece weight with average fleece-free live weight up to around 50. kg but little response in clean fleece weight for animals larger than 50. kg. There was some evidence of a smaller increase in clean fleece weight as the age of dam increased. There was an effect of Breed in the model but this effect disappeared when a random sire effect was included in the model. There was a positive response to staple length at some age groups but the response did not differ from zero in other age groups. This response varied from negligible to about 70. g per 1. cm increase in staple length. Clean fleece weight increased about 40. g per unit increase in staple definition score and increased about 30. g for every 4 units increase in the number of staple crimps. There was no evidence that clean fleece weight was affected by staple style, staple tip score or staple entanglement score or lifetime factors such as birth weight, date of birth, birth parity, or weaning weight. The results show that using a combination of measuring MFD and visually assessing the fleece for staple length, staple definition and crimps can help identify the most profitable Angora goats. In this process, the objective measurement of MFD appears essential. Visual assessment will provide some extra benefit in identifying these animals above that provided by measuring MFD alone. Animal size should be considered by mohair producers when identifying more productive mohair producing animals. © 2014 Elsevier B.V.

Internet traffic classification using constrained clustering

Statistics-based Internet traffic classification using machine learning techniques has attracted extensive research interest lately, because of the increasing ineffectiveness of traditional port-based and payload-based approaches. In particular, unsupervised learning, that is, traffic clustering, is very important in real-life applications, where labeled training data are difficult to obtain and new patterns keep emerging. Although previous studies have applied some classic clustering algorithms such as K-Means and EM for the task, the quality of resultant traffic clusters was far from satisfactory. In order to improve the accuracy of traffic clustering, we propose a constrained clustering scheme that makes decisions with consideration of some background information in addition to the observed traffic statistics. Specifically, we make use of equivalence set constraints indicating that particular sets of flows are using the same application layer protocols, which can be efficiently inferred from packet headers according to the background knowledge of TCP/IP networking. We model the observed data and constraints using Gaussian mixture density and adapt an approximate algorithm for the maximum likelihood estimation of model parameters. Moreover, we study the effects of unsupervised feature discretization on traffic clustering by using a fundamental binning method. A number of real-world Internet traffic traces have been used in our evaluation, and the results show that the proposed approach not only improves the quality of traffic clusters in terms of overall accuracy and per-class metrics, but also speeds up the convergence.

Stochastic optimization models for energy management in carbonization process of carbon fiber production

Industrial producers face the task of optimizing production process in an attempt to achieve the desired quality such as mechanical properties with the lowest energy consumption. In industrial carbon fiber production, the fibers are processed in bundles containing (batches) several thousand filaments and consequently the energy optimization will be a stochastic process as it involves uncertainty, imprecision or randomness. This paper presents a stochastic optimization model to reduce energy consumption a given range of desired mechanical properties. Several processing condition sets are developed and for each set of conditions, 50 samples of fiber are analyzed for their tensile strength and modulus. The energy consumption during production of the samples is carefully monitored on the processing equipment. Then, five standard distribution functions are examined to determine those which can best describe the distribution of mechanical properties of filaments. To verify the distribution goodness of fit and correlation statistics, the Kolmogorov-Smirnov test is used. In order to estimate the selected distribution (Weibull) parameters, the maximum likelihood, least square and genetic algorithm methods are compared. An array of factors including the sample size, the confidence level, and relative error of estimated parameters are used for evaluating the tensile strength and modulus properties. The energy consumption and N2 gas cost are modeled by Convex Hull method. Finally, in order to optimize the carbon fiber production quality and its energy consumption and total cost, mixed integer linear programming is utilized. The results show that using the stochastic optimization models, we are able to predict the production quality in a given range and minimize the energy consumption of its industrial process.