Narrow Results

The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly geometric process and applications. Journal of the Operational Research Society, 69(1), 66–67] introduced the doubly geometric process (DGP) as an extension of the GP model, relaxing some of its assumptions. Due to its ability to overcome the limitations of the GP model, the DGP has gained significant popularity in recent times. This study focuses on the parameter estimation problem for the DGP when the distribution of the first interarrival time follows a lognormal distribution with parameters $\delta$ and $\tau$. We employ the maximum likelihood method to obtain estimates for both the model parameters and the distribution parameters. Additionally, we investigate the asymptotic joint distribution and statistical properties such as asymptotic unbiasedness and consistency of the estimators. Furthermore, we propose a novel test procedure to distinguish between the GP and DGP models. To assess the performance of the estimators and the proposed test procedure, we conduct a simulation study involving various sample sizes and parameter values. Finally, we present an application of the developed methods in fitting data from bladder cancer patients.

We have developed a hyperspectral deconvolution algorithm that sharpens the spectral dimension in addition to the more usual across-track and along-track dimensions. Using an individual three-dimensional model for each pixel's point spread function, the algorithm iteratively applies maximum likelihood criteria to reveal previously hidden features in the spatial and spectral dimensions. Of necessity, our solution is adaptive to unreported across-track and along-track vibrations with amplitudes smaller than the ground sampling distance. We sense and correct these vibrations using a combination of maximum likelihood deconvolution and gradient descent registration that maximizes statistical correlations over many bands. Test panels in real hyperspectral imagery show significant improvement when locations are corrected. Tests on simulated imagery show that the precision of relative corrected positions improves by about a factor of two.

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

University ranking arouses widespread interest among the society and the scientific community. It can cause resources to be allocated to the entity which has a higher ranking to make tremendous uneven distribution of resources such as funds, faculty, students and so on. Every year various controversial university rankings are issued by different institutions or individuals. However, they have to deal with a huge amount of data and cumbersome computing in their research. Furthermore, during the process of calculation, some key indicators are unreliable, subjective, and difficult to obtain or compute so that their results are easily questioned. An accurate and objective university ranking is important and necessary, but it still remains to be solved. In 2015, Clauset et al. creatively studied university rankings based on faculty hiring network with graduation-employment flow data. They used the minimum violation ranking (MVR) method to get a university ranking which has a high correlation with U.S. News & World Report (USN) and National Research Council (NRC) Ranking, implying a strong consistency between them. This method costs less and is also objective. Inspired by this thought, this paper proposed a new ranking algorithm with minimum weighted violation rankings derived through maximum likelihood estimation. This assumption is more reasonable, and the results are commendably consistent with the rankings of renowned agencies. This more general method is more flexible than non-weighted calculation. More importantly, this work revealed the essential mechanism of MVR by deriving maximum likelihood.

Finding a universal method of crystal structure solution and proving the Riemann hypothesis are two outstanding challenges in apparently unrelated fields. For centro-symmetric crystals however, a connection arises as the result of a statistical approach to the inverse phase problem. It is shown that parameters of the phase distribution are related to the non-trivial Riemann zeros by a Mellin transform.

In remote sensing the intensities from a multispectral image are used in a classification scheme to distinguish different ground cover from each other. An example is given where different soil types are classified. A digitized complete scene from a satellite sensor consists of a large amount of data and in future image sensors the resolution and the number of spectral bands will increase even further. Data parallel computers are therefore well-suited for these types of classification algorithms. This article will focus on three supervised classified algorithms: the Maximum Likelihood, the K-Nearest Neighbor and the Backpropagation algorithm, together with their parallel implementations. They are implemented on the Connection Machine/200 in the high-level language C*. The algorithms are finally tested and compared on an image registered over western Estonia.

We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.

In this study, we compare the performance of four different imputation strategies ranging from the commonly used Listwise Deletion to model based approaches such as the Maximum Likelihood on enhancing completeness in incomplete software project data sets. We evaluate the impact of each of these methods by implementing them on six different real-time software project data sets which are classified into different categories based on their inherent properties. The reliability of the constructed data sets using these techniques are further tested by building prediction models using stepwise regression. The experimental results are noted and the findings are finally discussed.

The high level of human morbidity caused by E. coli O157:H7 necessitates an improved understanding of the infection dynamics of this bacterium within the bovine reservoir. Until recently, a degree of uncertainty surrounded the issue of whether these bacteria colonize the bovine gut and as yet, only incomplete in-vivo datasets are available. Such data typically consist of bacterial counts from fecal samples. The development of a deterministic model, which has been devised to make good use of such data, is presented. A partial differential equation, which includes advection, diffusion and growth terms, is used to model the (unobserved) passage of bacteria through the bovine gut. A set of experimentally-obtained fecal count data is used to parameterize the model. Between-animal variability is found to be greater than between-strain variability, with some results adding further weight to the hypothesis that E. coli O157:H7 can colonize the bovine gastrointestinal tract.

An accelerated life testing procedure can reduce the lifetime of a material by observing the material's behavior under higher levels of stress than what is normally encountered. Useful inference hinges on the selection of an appropriate lifetime distribution and the substitution of an acceleration model for a distribution parameter, such as the mean or scale. The (inverse) power-law model is one such acceleration model that has applications to fatigue studies in metals, where failure tends to be crack-induced. The Birnbaum–Saunders distribution was developed to model fatigue in materials where the failure of a specimen is due to the propagation of a dominant crack. This paper will compare two Birnbaum–Saunders type models from the literature (that have power-law accelerated features) with a new but distinctive model proposed here. The new model is an accelerated life model for a reparameterization of the baseline distribution. Comparison of the three models will be via the aluminum coupon data set from Birnbaum and Saunders⁵ and issues of accelerated testing will be discussed.

When software is tested according to the customer's operational profile, many techniques exist in the literature for using the resulting failure data to estimate the customer-perceived failure rate. Unfortunately, the overhead associated with defining and using the customer's operational profile during a system test can be significant. As a compromise, many projects test the software by executing it over a sustained period of time using simulated load scenarios that represent informed judgments of what the customer environment is likely to be. By itself, the load test data is suspect for estimating the customer-perceived failure rate since the load scenarios may not be accurate representations of the customer's usage patterns. Moreover, the load test data is limited by the relatively small amount of time that is set aside for load testing.

In some cases the release being tested is an evolution of a previous release already in the field. The field experience with the previous release along with a characterization of the difference between the two releases are natural sources of information for building a prior distribution of the failure rate of the new release. The load test data can then be used to obtain a posterior distribution of the failure rate of the new release. The posterior distribution inherently reflects the customer's operational profile through its dependence on the field data, and effectively enlarges the set of data from which inference about the failure rate of the new release is to be made. In this paper, we develop a model for the prior distribution of the failure rate, and obtain the corresponding posterior distribution. We illustrate our modeling approach using real data collected from one of our software products.

This paper proposes a method of estimating the lifetime distribution at use condition for constant stress accelerated life tests when an extrinsic failure mode as well as intrinsic one exists. A mixture of two distributions is introduced to describe these failure modes. It is assumed that the log lifetime of each failure mode follows a location-scale distribution and a linear relation exists between the location parameter and the stress. An estimation procedure using the expectation and maximization algorithm is proposed and specific formulas for Weibull distribution are obtained. Simulation studies are performed to investigate the properties of the estimates and the effects of stress level. Numerical comparisons with the masked data model are also performed.

In the presence of length-biasedness, a lifetime measure of interest may be estimated in two ways: (i) by modeling the data correctly using a length-biased distribution and using the resulting estimators in the original model as an adjustment, or (ii) by modeling the data correctly using a length-biased distribution, and obtaining the original lifetime measure of interest via a transformation, if one exists. Here we examine sufficiency in information context under transformations.

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

This paper presents a new four-parameter lifetime model by generalizing the Inverse Weibull (IW) distribution using Transmuted Kumaraswamy family of distributions. The proposed model explains the high probability at the tail effectively. The induction of additional parameters enhance the potentiality of the IW distribution and make it a pliant model that provides a vast range of existing distributions as special cases. Several probabilistic properties of the proposed model including moments, probability weighted moments, moment generating function, quantile function, reliability measures, and order statistics are discussed. The maximum likelihood (ML) procedure is adopted for the estimation of model parameters. The efficiency of ML estimates is to testify through simulation study. Four datasets from the field of reliability science are used to expound the competence of the proposed model.

This paper considers optimal designs of step-stress accelerated life tests in which each lognormally-distributed test item is first run at low stress, and if it does not fail for a specified time, then it is run at high stress until a predetermined censoring time. It is assumed that a log-linear relation exists between the lognormal location parameter and stress, and that a cumulative exposure model for the effect of changing stress holds. The optimum stress change point minimizes the asymptotic variance of maximum likelihood estimator of a specified percentile at design stress. For selected values of the design parameters, the optimum plans are tabulated. Designs of high-to-low step-stress accelerated life tests (ALTs) in which each item is first run at high stress and then at low stress, and the optimality criterion of minimizing the generalized asymptotic variance of maximum likelihood estimators of model parameters, are also considered. The effects of the incorrect pre-estimates of the design parameters are investigated.

We use minimum relative entropy (MRE) methods to estimate univariate probability density functions for a varied set of financial and economic variables, including S&P500 index returns, individual stock returns, power price returns and a number of housing-related economic variables. Some variables have fat tail distributions, others have finite support. Some variables have point masses in their distributions and others have multimodal distributions. We indicate specifically how the MRE approach can be tailored to the stylized facts of the variables that we consider and benchmark the MRE approach against alternative approaches. We find, for a number of variables, that the MRE approach outperforms the benchmark methods.

In order to reduce the estimation uncertainty for the wind energy output, the accurate assessment of the wind speed distribution plays an important role. Due to the influence of the complex terrain, the wind speed data in mountainous area may show the heavy tail. The tail has an important effect on the annual energy production of the wind turbine because of the power output being the cubic of the wind speed. Hence the heavy tail should be highlighted before choosing the proper distributions. To characterize the heavy tail, the box plot, QQ plot and conditional mean exceedance are used. In addition, the wind climate in the mountainous area is very complicated and typically mixed by local storms and large-scale wind flows. The distribution of the wind speed is prone to exhibit bimodal or even multi-modal nature. The conventional unimodal distributions such as Weibull may not well portray these distributions. The mixture distribution has more flexibilities to handle this challenge. Both generalized extreme value distribution and generalized Pareto distribution are considered to formulate the mixture distribution in modeling the tail. The maximum likelihood method and the constrained maximum likelihood method are used to estimate distribution parameters. The comprehensive evaluation criteria are adopted to determine the most appropriate distribution of four sets of wind speed in the mountainous area of Yunnan, China. Graphical tools, such as histogram density curve and QQ plot, are also used for evaluation. Results show that heavy tail distribution should be considered for the wind data in mountainous areas and the proposed mixture model with the constrained maximum likelihood method for the parameter estimation will be superior for the wind energy potential estimation.

This paper discusses the use of the Beta-binomial distribution to estimate the matching performance of a biometric identification device. Specifically, the Beta-binomial distribution can be used to assess the variability in estimates of the false match and the false non-match rates when multiple users are tested more than once. This method accounts for the extraneous variability in this scenario and allows for the creation of confidence intervals under certain regularity conditions. The Beta-binomial differs from the binomial in that it models the extra-variation that is due to a lack of marginal independence among the observations. The Beta-binomial also has the flexibility to model the correlation of observations by the same individual that the binomial does not possess. This paper discusses maximum likelihood methodology for estimating the parameters of the Beta-binomial distribution. Finally, examples are given for simulated data that explicate this methodology.

We present a noise-injected version of the expectation–maximization (EM) algorithm: the noisy expectation–maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary results give special cases when noise improves the EM algorithm. We demonstrate these noise benefits on EM algorithms for three data models: the Gaussian mixture model (GMM), the Cauchy mixture model (CMM), and the censored log-convex gamma model. The NEM positivity condition simplifies to a quadratic inequality in the GMM and CMM cases. A final theorem shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse.