Maximum Likelihood Estimates Of Parameters Research Articles

A Copula-Based GLMM Model for Multivariate Longitudinal Data with Mixed-Types of Responses

We propose a copula-based generalized linear mixed model (GLMM) to jointly analyze multivariate longitudinal data with mixed types, including continuous, count and binary responses. The association of repeated measurements is modelled through the GLMM model, meanwhile a pair-copula construction (D-vine) is adopted to measure the dependency structure between different responses. By combining mixed models and D-vine copulas, our proposed approach could not only deal with unbalanced data with arbitrary margins but also handle moderate dimensional problems due to the efficiency and flexibility of D-vines. Based on D-vine copulas, algorithms for sampling mixed data and computing likelihood are also developed. Leaving the random effects distribution unspecified, we use nonparametric maximum likelihood for model fitting. Then an E-M algorithm is used to obtain the maximum likelihood estimates of parameters. Both simulations and real data analysis show that the nonparametric models are more efficient and flexible than the parametric models.

The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016

A new autoregressive model with seasonal dummy variables in which coefficients of seasonal dummies vary smoothly and deterministically over time is introduced. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed as in ARCH models. This variance is also allowed to be smoothly and deterministically time-varying. Under regularity conditions, consistency and asymptotic normality of the maximum likelihood estimators of parameters of this model is proved. The purpose of the model is to find out how the average monthly temperatures in the well-known central England temperature series have been varying during the period of more than 240 years. The main result is that warming has occurred but that there are notable differences between months. In particular, no warming is found for February, April, May and June.

PF715 THE IMPACT OF CRIZANLIZUMAB ON VOC‐RELATED MEDICAL FACILITY VISITS

Background:A major cause of morbidity among patients with sickle cell disease (SCD) is the intense, recurrent, unpredictable attacks, known as vaso‐occlusive crises (VOCs), which are responsible for >90% of hospital admissions in SCD. An important goal of pharmacological therapy is to prevent the occurrence of these painful episodes, and in turn, reduce the clinical and economic burden of the disease.In December 2018, the United States Food and Drug Administration granted crizanlizumab (SEG101) Breakthrough Therapy designation for the prevention of VOCs in patients with SCD. This designation was granted based on positive results from the Phase II SUSTAIN trial, in which 5 mg/kg crizanlizumab was associated with a 45.3% reduction in the median annual rate of VOCs leading to healthcare visits compared with placebo.Aims:The aim of the current analysis was to investigate the impact of crizanlizumab on VOC‐related medical facility visits.Methods:sing data from the SUSTAIN trial, analyses were conducted to determine the cumulative number of VOC events across all patients, medical facility visits and by medical facility type in the 5 mg/kg crizanlizumab and placebo arms. The total cumulative number of patient days in the study was considered in determining the event rate per year, which was calculated as follows:“[Total cumulative number of VOCs across all patients]/[Total number of days observed across all patients]” ∗ 365Incidence rate ratios (IRR) were derived using a Poisson regression model. Maximum likelihood parameter estimates were generated with standard errors to produce confidence intervals and p‐values. Effect modification over time by group was assessed by maximum likelihood.Results:The analyses showed a reduction in the overall rate of VOC events requiring a medical facility visit in the 5 mg/kg crizanlizumab group compared with the placebo group. Further examination of the impact of crizanlizumab on specific sites of care demonstrated a reduction in visits to outpatient care sites, largely driven by reduced visits to emergency care units and SCD crisis centers (Table 1). A trend to reduced inpatient admissions was also observed.Summary/Conclusion:Payers aim to reimburse treatments for SCD that reduce both the clinical and economic burden of the disease. In the SUSTAIN trial, patients treated with 5 mg/kg crizanlizumab experienced a 45.3% reduction in the median annual rate of VOCs leading to healthcare visits compared with those receiving placebo. The current analysis demonstrates that this reduction in VOCs leading to a healthcare visit was seen in most medical facility visits, largely driven by reduced visits to emergency care units and specialized SCD crisis centers. These findings suggest that patients treated with crizanlizumab will experience a substantial reduction in health care resource utilization and associated costs.image

Local influence of nonlinear mixed effects model based on M-estimation

In this work we mainly study the local influence in nonlinear mixed effects model with M-estimation. A robust method to obtain maximum likelihood estimates for parameters is presented, and the local influence of nonlinear mixed models based on robust estimation (M-estimation) by use of the curvature method is systematically discussed. The counting formulas of curvature for case weights perturbation, response variable perturbation and random error covariance perturbation are derived. Simulation studies are carried to access performance of the methods we proposed. We illustrate the diagnostics by an example presented in Davidian and Giltinan, which was analyzed under the non-robust situation.

The competing risks analysis for parallel and series systems using Type-II progressive censoring

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach.

Investigation of parameter uncertainty in clustering using a Gaussian mixture model via jackknife, bootstrap and weighted likelihood bootstrap

Mixture models with (multivariate) Gaussian components are a popular tool in model-based clustering. Such models are often fitted by a procedure that maximizes the likelihood, such as the EM algorithm. At convergence, the maximum likelihood parameter estimates are typically reported, but in most cases little emphasis is placed on the variability associated with these estimates. In part this may be due to the fact that standard errors are not directly calculated in the model-fitting algorithm, either because they are not required to fit the model, or because they are difficult to compute. The examination of standard errors in model-based clustering is therefore typically neglected. Sampling based methods, such as the jackknife (JK), bootstrap (BS) and parametric bootstrap (PB), are intuitive, generalizable approaches to assessing parameter uncertainty in model-based clustering using a Gaussian mixture model. This paper provides a review and empirical comparison of the jackknife, bootstrap and parametric bootstrap methods for producing standard errors and confidence intervals for mixture parameters. The performance of such sampling methods in the presence of small and/or overlapping clusters requires consideration however; here the weighted likelihood bootstrap (WLBS) approach is demonstrated to be effective in addressing this concern in a model-based clustering framework. The JK, BS, PB and WLBS methods are illustrated and contrasted through simulation studies and through the traditional Old Faithful data set and also the Thyroid data set. The MclustBootstrap function, available in the most recent release of the popular R package mclust, facilitates the implementation of the JK, BS, PB and WLBS approaches to estimating parameter uncertainty in the context of model-based clustering. The JK, WLBS and PB approaches to variance estimation are shown to be robust and provide good coverage across a range of real and simulated data sets when performing model-based clustering; but care is advised when using the BS in such settings. In the case of poor model fit (for example for data with small and/or overlapping clusters), JK and BS are found to suffer from not being able to fit the specified model in many of the sub-samples formed. The PB also suffers when model fit is poor since it is reliant on data sets simulated from the model upon which to base the variance estimation calculations. However the WLBS will generally provide a robust solution, driven by the fact that all observations are represented with some weight in each of the sub-samples formed under this approach.

A Modeling Method of Stochastic Parameters’ Inverse Gauss Process Considering Measurement Error under Accelerated Degradation Test

To solve the problem that the individual differences and the measurement errors affect the accuracy of life estimation in accelerated degradation test, the inverse Gauss process with stochastic parameters is applied in the accelerated degradation test with the consideration of the influence of individual differences, and the analysis of measurement uncertainty is carried out. An inverse Gauss accelerated degradation model considering both individual differences and measurement errors is established. In the maximum likelihood estimation of parameters, Genetic Algorithm and Monte Carlo integral are used to solve the problems caused by complex integral and the unobservable measurement errors in the calculation process. Finally, the proposed method is verified by the Monte Carlo simulation under the constant accelerated stress and step accelerated stress and the illustrative example of electrical connectors under the constant acceleration stress, respectively. The results show that the modeling tool is useful for improving the accuracy of the life prediction and the reliability evaluation.

A New Two-Parameter Lifetime Distribution: Properties, Applications and Different Method of Estimations

In this paper, we introduce a new two-parameter distribution which is called new Odd Log-Logistic Half-Logistic (NOLL-HL) distribution. Theoretical properties of this model including the hazard function, survival function, asymptotic, extreme value, quantile function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes

High-Performance GLR Detector for Moving Target Detection in OFDM Radar-Based Vehicular Networks

Nowadays, orthogonal frequency division multiplexing (OFDM) radars have been used in many applications such as target detection and recognition in vehicular networks and surveillance systems, according to their frequency diversity property. The model of the received signal in an OFDM radar based on target’s parameters has a non-linear form with respect to unknown velocity and scattering coefficients, so there is no possibility of achieving a closed form solution for Maximum Likelihood Estimation of the unknown parameters and so the Neyman–Pearson detector. Therefore, in all published works, the generalized likelihood ratio (GLR) detector is obtained for the target with known velocity, or in case of simultaneous unknown velocity and scattering coefficients, only a wide two-dimensional grid search over all possible values of the unknown parameters is considered to maximize the Likelihood ratio. In this paper, a new method is proposed for simultaneous estimations of target velocity and scattering coefficients using a coordinate descent approach, which reduces the above nonlinear problem to two linear problems, and makes the implementation of GLR detector efficient. The simulation results confirm the efficiency of the proposed method.

Estimating menarcheal age distribution from partially recalled data.

In a cross-sectional study, adolescent and young adult females were asked to recall the time of menarche, if experienced. Some respondents recalled the date exactly, some recalled only the month or the year of the event, and some were unable to recall anything. We consider estimation of the menarcheal age distribution from this interval-censored data. A complicated interplay between age-at-event and calendar time, together with the evident fact of memory fading with time, makes the censoring informative. We propose a model where the probabilities of various types of recall would depend on the time since menarche. For parametric estimation, we model these probabilities using multinomial regression function. Establishing consistency and asymptotic normality of the parametric maximum likelihood estimator requires a bit of tweaking of the standard asymptotic theory, as the data format varies from case to case. We also provide a non-parametric maximum likelihood estimator, propose a computationally simpler approximation, and establish the consistency of both these estimators under mild conditions. We study the small sample performance of the parametric and non-parametric estimators through Monte Carlo simulations. Moreover, we provide a graphical check of the assumption of the multinomial model for the recall probabilities, which appears to hold for the menarcheal data set. Our analysis shows that the use of the partially recalled part of the data indeed leads to smaller confidence intervals of the survival function.

Maximum likelihood estimation for the poly-Weibull distribution

The Weibull distribution has long been a popular choice for modeling lifetime data of various mechanical and biological phenomena when the associated hazard rate function is constant or monotone increasing or decreasing. However, nonmonotone hazard functions are common in reliability and survivability contexts where a system may undergo an initial “burn-in” prior to periods of useful life and eventual wear out. In these scenarios, the Weibull can only model a portion of the “bathtub” curve but is incapable of adequately modeling the entire failure process. Several modifications to the standard two-parameter Weibull distribution have therefore been introduced in the literature to effectively model and analyze lifetime data where the hazard rate function is bathtub-shaped. The performance of each modified distribution is typically assessed by its ability to fit a reference data set that is known to have a bathtub-shaped hazard rate function. The current article compares the performance of two recent contributions in this area to that of the poly-Weibull distribution with respect to several goodness-of-fit measures. In addition, numerical and analytical procedures are developed for obtaining the maximum likelihood parameter estimates, standard errors, and an equation to determine the moments for the generalized poly-Weibull distribution with arbitrary number of terms. Our results show that both the bi-Weibull and tri-Weibull distributions fit the reference data set better than the current best-fit models.

Physical Password Breaking via Thermal Sequence Analysis

The thermal camera can capture keyboard surface temperature change after a human’s touch. This phenomenon may be used to steal users’ passwords physically. In this paper, based on the study of thermal dynamics of keyboards, we design a password break system using an infrared thermal camera. First, we build a signal model to describe the dynamic process of temperature change on the keyboard using Newton’s law of cooling. Next, we develop a maximum likelihood parameter estimation algorithm to estimate the keystroke time instants. Then, by maximizing the probability of key order arrangement, a novel password breaking algorithm is developed. Our algorithm is tested using simulated data as well as real-world data. Experiment results show that our algorithm is effective for physical password breaking using thermal characteristics. Based on our results, we discuss strategies for password protection at the end.

Inference for Weibull generalized exponential distribution based on generalized order statistics

In this paper, the authors have derived relations for marginal and joint moment generating function of Weibull Generalized exponential distribution (WGED) based on generalized order statistics (gos). These derived relations are further reduced to the sub models of gos such as order statistics and record values. The Maximum likelihood (ML) estimates of the unknown parameters of WGED are derived for gos. Further, characterization results of WGED are also carried out. Finally, a simulation study is conducted for order statistics and record values. Based on the simulation study, various moments and performances of derived ML estimates are reported in terms of their respective mean squared errors.

Mixing patterns and individual differences in networks.

We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been widely studied, but here we go further and examine how and to what extent nodes that are otherwise similar can have different preferences. Many individuals in a friendship network, for instance, may prefer friends who are roughly the same age as themselves, but some may display a preference for older or younger friends. We introduce a network model that captures this behavior and a method for fitting it to empirical network data. We propose metrics to characterize the mean and variation of mixing patterns and show how to infer their values from the fitted model, either using maximum-likelihood estimates of model parameters or in a Bayesian framework that does not require fixing any parameters.

Unified Statistical Channel Model for Turbulence-Induced Fading in Underwater Wireless Optical Communication Systems

A unified statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical communication (UWOC) channels in the presence of air bubbles and temperature gradient for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture exponential–generalized gamma (EGG) distribution. We use the expectation–maximization algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, we show that the application of the EGG model leads to closed-form and analytically tractable expressions for key UWOC system performance metrics such as the outage probability, the average bit-error rate, and the ergodic capacity. To the best of our knowledge, this is the first-ever comprehensive channel model addressing the statistics of optical beam irradiance fluctuations in underwater wireless optical channels due to both air bubbles and temperature gradient.

The Odd Log-Logistic Generalized Gompertz Distribution: Properties, Applications and Different Methods of Estimation

We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential, generalized exponential and generalized Gompertz distributions, among others. We obtain explicit expressions for the moments, moment-generating function, asymptotic distribution, quantile function, mean deviations and distribution of order statistics. The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study. The applicability of the new model is illustrated by means of a real data set.

Estimating Multiscale Direct Causality Graphs in Neural Spike-Field Networks

Neural representations span various spatiotemporal scales of brain activity, from the spiking activity of single neurons to field activity measuring large-scale networks. The simultaneous analyses of spikes and fields to uncover causal interactions in multiscale networks could help understand neural mechanisms. However, assessing causality within spike-field networks is challenging as spikes are binary-valued with a fast time-scale while fields are continuous-valued with slower time-scales. Current causality measures are largely not applicable to mixed discrete-continuous network activity. Here, in this paper, we develop a novel multiscale causality estimation algorithm for spike-field networks. We construct a likelihood function comprised of point process models for spikes and linear Gaussian models for fields. For spikes, firing rates are modeled as a function of the history of both field signals and binary spike events within the network. For fields, to make their linear models consistent with biophysical findings, we use the history of field signals and the history of the latent log-firing rates of neurons as predictors. To resolve the challenge of estimating the network model parameters in the presence of latent firing rates, we develop a sequential maximum-likelihood parameter estimation procedure that extends to large networks. Once models are estimated, we compute directed information as our measure of multiscale causality and devise two statistical tests to assess its significance. Using extensive simulations, we show that the algorithm can accurately reconstruct the true causality graphs of random spike-field networks. Moreover, the algorithm is robust to the number of connections, connection strengths, or exact topology of the network. This multiscale causality estimation algorithm has important implications for studying neural mechanisms and for future neurotechnology design.

Parameter and reliability estimation of inverted Maxwell mixture model

In present study the probability density function of mixture is derived for inverse Maxwell density. The main distributional properties and reliability characteristics are studied. Maximum likelihood estimation of the pertinent parameters along with failure rate functions and reliability are obtained. The Bayesian study of anonymous parameters of inverse Maxwell mixture model, assuming three priors is considered employed distinct loss functions. The prior reliance of mixture density is characterized by the inverted gamma, uniform and Jeffreys prior. The efficiencies of the considered set of estimates of mixture distribution parameters are studied through simulation. To scrutinize the response of prior reliance and loss functions posterior risks of the Bayes estimators are figured out and differentiated. Bayes estimator assuming the informative have been observed performing better.

Small-Target Detection between SAR Images Based on Statistical Modeling of Log-Ratio Operator.

The log-ratio (LR) operator is well suited for change detection in synthetic aperture radar (SAR) amplitude or intensity images. In applying the LR operator to change detection in multi-temporal SAR images, a crucial problem is how to develop precise models for the LR statistics. In this study, we first derive analytically the probability density function (PDF) of the LR operator. Subsequently, the PDF of the LR statistics is parameterized by three parameters, i.e., the number of looks, the coherence magnitude, and the true intensity ratio. Then, the maximum-likelihood (ML) estimates of parameters in the LR PDF are also derived. As an example, the proposed statistical model and corresponding ML estimation are used in an operational application, i.e., determining the constant false alarm rate (CFAR) detection thresholds for small target detection between SAR images. The effectiveness of the proposed model and corresponding ML estimation are verified by applying them to measured multi-temporal SAR images, and comparing the results to the well-known generalized Gaussian (GG) distribution; the usefulness of the proposed LR PDF for small target detection is also shown.

A Fay–Herriot model when auxiliary variables are measured with error

The Fay–Herriot model is an area-level linear mixed model that is widely used for estimating the domain means of a given target variable. Under this model, the dependent variable is a direct estimator calculated by using the survey data and the auxiliary variables are true domain means obtained from external data sources. Administrative registers do not always give good auxiliary variables so that statisticians sometimes take them from alternative surveys and therefore they are measured with error. We introduce a variant of the Fay–Herriot model that takes into account the measurement error of the auxiliary variables and give two fitting algorithms that calculate maximum and residual maximum likelihood estimates of the model parameters. Based on the new model, empirical best predictors of domain means are introduced and an approximation of its mean squared error is derived. We finally give an application to estimate poverty proportions in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.