High-level primitives for linear estimation

It is known that when the maximum likelihood estimator (MLE) algorithm passes a certain point, it produces images that begin to deteriorate. We propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins. The MLE algorithm searches for the image that has the maximum probability to generate the projection data. The underlying assumption of the algorithm is a Poisson distribution of the data. Therefore, the best image, according to the MLE algorithm, is the one that results in projection means which are as close to the data as possible. It is shown that this goal conflicts with the assumption that the data are Poisson-distributed. We test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration. The acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate. We show that the best MLE images, which pass the test, result in somewhat lower noise in regions of high activity than the filtered back-projection results and much improved images in low activity regions. The applicability of the proposed stopping rule to other iterative schemes is discussed.

Fusion of diverse data sources for flood extent mapping and risk assessment in Sindh: A comparative study of inundation mapping approaches

The authors present polynomial-based Newton algorithms for maximum likelihood estimation (MLE) of the parameters of multiple exponential signals in noise. This formulation can be used in the estimation, for example, of the directions of arrival of multiple noise-corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise-corrupted complex sine waves. The algorithms offer rapid convergence and exhibit the computation efficiency associated with the polynomial approach. Compact, closed-form expressions are presented for the gradients and Hessians. Various model assumptions concerning the statistics of the underlying signals are considered. Numerical simulations are presented to demonstrate the algorithms' performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The restricted EM algorithm under inequality restrictions on the parameters

One typical use of sensor networks is monitoring targets. The sensor networks classify, detect, locate, and track targets. The ML (Maximum likelihood) algorithm is one of the estimation algorithms of target location and has high accuracy to estimate target location. However, the calculation amount of the ML estimation algorithm is large. Energy-Ratios Source Localization Nonlinear Least Square (ER-NLS) is proposed to realize the ML algorithm. ER-NLS is the algorithm of estimating source location by using the ratio of sensors' receiving energies. However, ER-NLS has to search all the areas, so that the calculation amount of ER-NLS is large. In this paper we propose a method of reducing search area for localization. The proposed method uses the ratio of sensors' receiving energies. It can be used with the ML algorithm. We show that the proposed method with the ML algorithm can reduce the search areas to estimate the target location and thus reduce the complexity, while achieving the RMSE (root mean square error) close to that of the ML algorithm.

In this correspondence, we propose a fast maximum likelihood detection and estimation algorithm, called a multiple-mostlikely-replacement (MMLR) detector, for Bernoulli-Gaussian processes which are distorted by a linear time-invariant system and contaminated by a white Gaussian noise. This new detector works as well as the well-known single-most-likely-replacement (SMLR) detector. However, the former is computationally faster than the latter. We discuss two examples which demonstrate the computational advantage of the proposed algorithm using synthetic data.

: The basis for a method of modifying general nonlinear least squares algorithms for maximum likelihood estimation is developed. The resultant algorithm provides a direct general approach to maximum likelihood estimation. Only the likelihood function for a single observation need be specified. Neither second partial derivatives nor weights are required. First partial derivatives may be obtained numerically and are used to compute the covariance matrix of the estimated parameters.

Random processes of considerable importance in signal processing often exhibit short-term stationary statistical attributes although in the long term they appear to behave in a nonstationary manner. Image signals belong to this category. In this work we introduce a class of composite-source models as a means of representing consistently signals of this nature. A composite likelihood function is derived, the subsequent maximisation of which yields estimates of the parameters that are associated with the composite-source model. It is a fact, that maximisation of the composite likelihood function is almost intractable by analytical means. However, by introducing optimisation techniques based on dynamic programming, maximum-likelihood estimation of composite-source models is simplified drastically. A graph-theoretic approach is adopted to demonstrate how the principle of optimality enables efficient algorithms for recursive maximum-likelihood estimation to be developed. Algorithms applied for one-dimensional as well as two-dimensional signals are presented. In both cases it is shown that the estimation problem is equivalent to the problem of identifying the maximumlikelihood path which traverses a directed graph of specific structure. Finally, it is shown that composite source models so estimated can be used in image coding systems which require the least transmission rate for prespecified levels of average distortion of the transmitted image signals.

In this paper, we examine the problem of direction finding and detection of a moving source in a waveguide. Specifically, we are concerned with detecting a wide-band low signal power source moving through the ocean. Further, we desire an algorithm that is resistant to strong interferers (e.g. surface ships) that may also be moving within or on the boundary of the waveguide. The physical model that is given in this paper was derived from moving (constant velocity) sources traveling through a waveguide. The result can be considered to be a generalization of a result derived by Hawker (1979). The amplitude of the source signals and the variance of the noise are taken as unknown deterministic quantities. To determine the parameter estimates for the purpose of localization and detection, we use the maximum-likelihood (ML) estimation algorithm. For the detection algorithm, we use the generalized likelihood ratio test (GLRT).

The pharmaceutical industry is currently interested in the population approach and population models, also known as mixed effects models and random effects models depending on the precise form. Population models are useful in that they can account for both withinand between-individual sources of variability and serial correlation within individual observations when analyzing unbalanced repeated measures data. The modelling of population pharmacodynamic or pharmacokinetic profiles typically involves nonlinear random effects models. Each individual's observations are modelled by identical (up to unknown parameter values) nonlinear regression models, with the distribution of the observations, or a transformation of the observations, about expected responses taken to be normal, with the degree of variability described by a variance model. Between-individual variability is modelled by a population distribution for the individual regression parameter values (random effects). In a parametric analysis the population distribution is taken to be normal, the parameters of which, along with the parameters of the variance model, are known as the population parameters. Maximum likelihood estimation of the population parameters for nonlinear random effects models was pioneered by Beal and Sheiner (1979), and since then a number of algorithms have appeared for approximate maximum likelihood, including Steimer et al. (1984), Lindstrom and Bates (1990), Beal and Sheiner (1992), and Mentre and Gomeni (1995). All of these algorithms are approximate in some way. For a summary see Beal and Sheiner (1992), Wolfinger (1993), Pinheiro and Bates (1994), and Davidian and Giltinan (1995). In this paper an EM algorithm for exact maximum likelihood estimation is introduced. An EM algorithm obtaining maximum likelihood estimates for linear random effects models was introduced by Dempster, Laird, and Rubin (1977). Laird and Ware (1982), Lindstrom and Bates (1988), Jennrich and Schluchter (1986), and Liu and Rubin (1994) all describe hybrid EM algorithms for the linear random effects model. A true EM algorithm for the linear model is described by Jamshidian and Jennrich (1993). Mentre and Gomeni (1995) describe an approximate EM algorithm for nonlinear random effects models and, from the algorithm given in this paper, it can be seen clearly how their approximations arise. The present algorithm uses Monte Carlo methods to perform the E step, a strategy previously adopted in an altogether different model by Guo and Thompson (1994). Guo and Thompson require a Gibbs sampler, that is, a Markov chain Monte Carlo method for their E step, but the present algorithm uses independent samples. In Section 2 of this paper the nonlinear random effects model is described. Section 3 gives the EM algorithm without random effect covariates, while Section 4 gives the modified algorithm in the

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

Remaining useful life (RUL) prediction of machinery plays a significant role for predictive maintenance, thus attracting more and more attentions in recent years. Stochastic process model-based methods are widely used in the RUL prediction of machinery. One of the major issues in the stochastic process model-based methods is that how to deal with the unit-to-unit variability during the RUL prediction process. Traditional methods generally handle this issue by introducing a unit-to-unit variability parameter into the model expression and estimate the parameter using the maximum likelihood estimation (MLE) algorithm. There exist two major limitations in the traditional methods. 1) The degradation processes are assumed to be dependent on only the age, which restricts their implementation in the cases of the state-dependent degradation processes. 2) They do not discuss the influence of the unit-to-unit variability in the RUL prediction processes systematically. To deal with these two limitations, a new RUL prediction method based on age- and state-dependent stochastic process models is proposed in this paper. In the proposed method, a generalized expression of the age- and stage-dependent stochastic process models is generated. An enhanced MLE algorithm is developed to estimate the model parameters according to the measurements of the available training units. And the unit-to-unit variability parameter is updated according to the real-time measurements of the testing unit. The effectiveness of the proposed method is demonstrated using a numerical simulation dataset of fatigue crack-growth.

Improved SPECT reconstructions have been obtained by the use of an Inverse Monte Carlo (IMOC) reconstruction algorithm. Monte Carlo solution to the photon transport equation for SPECT generates an accurate system response model for use in an iterative Maximum Likelihood estimation (MLE) algorithm. Reconstruction from simulated projections demonstrate that the MLE algorithm continues to converge at 1000 iterations for noise free data. Reconstruction from experimentally acquired projections reveals superior RMS noise and resolution recovery when compared with filtered backprojection for simple phantoms. Compensation for scatter and attenuation is provided by including these effects in the Monte Carlo simulation.

Computation: Expectation-Maximization Algorithm

Matrix-variate data analysis by two-way factor model with replicated observations