Approximate Maximum Likelihood Research Articles

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

Applying the Expectation-Maximization Algorithm to Multivariate Signal Extraction

Understanding time series signal extraction is vital for federal agencies, especially as data collection accelerates. One natural extension is moving from univariate to multivariate signal extraction, which offers the promise of reducing extraction error by exploiting cross-sectional relationships. However, such an extension ushers in new computational challenges, viz. larger parameter spaces and more complicated objective functions. The Expectation-Maximization (EM) algorithm provides a methodology to implicitly compute (or approximate) maximum likelihood estimates (MLEs). This paper provides methodology for applying the EM algorithm to a class of latent component multivariate time series models that allow for a nuanced specification of the unobserved signal. We derive an explicit formula for the maximization step, which facilitates computation speed while also improving the stability of the algorithm. Numerical studies demonstrate EM’s ability to efficiently compute MLEs in low-dimensional systems, while also providing feasible estimates in moderate-dimensional systems where MLEs are infeasible to compute. Applications to monthly housing starts and daily immigration are provided.

Enhanced Laplace approximation

The Laplace approximation has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators derived from the Laplace approximation are often biased for binary or temporally and/or spatially correlated data. Additionally, the corresponding Hessian matrix tends to underestimates the standard errors of these approximate maximum likelihood estimators. While higher-order approximations have been suggested, they are not applicable to complex models, such as correlated random effects models, and fail to provide consistent variance estimators. In this paper, we propose an enhanced Laplace approximation that provides the true maximum likelihood estimator and its consistent variance estimator. We study its relationship with the variational Bayes method. We also define a new restricted maximum likelihood estimator for estimating dispersion parameters and study their asymptotic properties. Enhanced Laplace approximation generally demonstrates how to obtain the true restricted maximum likelihood estimators and their variance estimators. Our numerical studies indicate that the enhanced Laplace approximation provides a satisfactory maximum likelihood estimator and restricted maximum likelihood estimator, as well as their variance estimators in the frequentist perspective. The maximum likelihood estimator and restricted maximum likelihood estimator can be also interpreted as the posterior mode and marginal posterior mode under flat priors, respectively. Furthermore, we present some comparisons with Bayesian procedures under different priors.

Exact selective inference with randomization

Summary We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce this problem to inference for a bivariate truncated Gaussian variable. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi & Taylor (2023). Yet our pivot always produces narrower confidence intervals than a closely related data-splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.

The complete mitochondrial genome of Hypsipetes amaurotis (Passeriformes: Pycnonotidae)

The brown-eared bulbul (Hypsipetes amaurotis) is a medium-sized songbird native to East Asia and characterized by its prominent reddish-brown ear-coverts. Previous studies on it have primarily been from the taxonomic and morphological aspects, with limited research in the realm of molecular biology. In this study, we sequenced and annotated the complete mitochondrial genome of H. amaurotis, which was the first reported complete mitogenome of the genus Hypsipetes. The mitogenome of H. amaurotis is 17,871 bp in length and was predicted to encode 37 typical mitochondrial genes, including 13 protein-coding genes (PCGs), 22 transfer RNA genes (tRNAs), two ribosomal RNA genes (rRNAs). Specifically, this mitogenome contains two D-loop control regions that are of similar length and sequencing pattern. A total of 8 Pycnonotidae and six outgroup taxa were used to determine the phylogenetic placement with two methods: Maximum Likelihood Approximation (IQ-TREE) and Bayesian inference (MrBayes). Our findings reveal that H. amaurotis is phylogenetically closely related to Ixos mcclellandii. The outcomes are generally consistent with the phylogenetic trees constructed in previous studies. The data gathered from this research provides valuable insights for future genomic investigations into the evolution, ecology, and conservation of this species.

Inference for compound truncated Poisson log-normal model with application to maximum precipitation data

The main objective of this paper is to propose a new general family of distributions, namely compound truncated Poisson log-normal distribution of which log-normal distribution is a special case. The proposed model has three unknown parameters, and it can take variety of shapes. It can be used effectively in analyzing maximum precipitation data during a particular period of time obtained from different stations. It is assumed that the number of stations operate follows a zero-truncated Poisson random variables, and the daily precipitation follows a log-normal random variable. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals can also be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model it is observed that the proposed model provides better fit than some of the existing models.

TDoA positioning with data-driven LoS inference in mmWave MIMO communications

Location awareness is an essential feature to support various mobile services, and cooperative positioning with channel state information (CSI) in millimeter wave multiple-input multiple-output (MIMO) networks is promising. Meanwhile, strong non-line of sight (NLoS) effects in outdoor scenarios severely reduce the model-based localization accuracy, and existing fingerprint-based methods have a critical requirement for labeled data and lack scalability. To overcome these shortcomings, we propose a hybrid data-and-model driven cooperative localization scheme using uplink wideband MIMO CSI at multiple base stations (BS) as measurements. First, we design a data-driven line of sight (LoS) inference module, realized by a transformer with an attention mechanism, to estimate the statistics of LoS arrival times. Each BS is equipped with a module, and the counterpart LoS inferences are simultaneously and distributedly performed. Second, we locate the mobile user by a model-driven approximate maximum likelihood time difference of arrival algorithm with the estimated statistics. Experiment results in urban scenarios show that the proposed localization scheme is extensible and also robust to varying number of channel paths and combination of BS measurements. Considering a small training dataset, the proposed scheme significantly outperforms the data- and model-driven baselines in NLoS scenarios, in terms of positioning accuracy.

Maximum likelihood estimation for discrete latent variable models via evolutionary algorithms

We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.

ПОРОГОВІ МОДЕЛІ ДЛЯ ПРОЦЕСІВ ЛЕВІ ТА ОЦІНКА НАБЛИЖЕНОЇ МАКСИМАЛЬНОЇ ПРАВДОПОДІБНОСТІ

Using the Levy process (the solution to the Ito–Skorokhod stochastic differential equation) we propose the construction of the model of the threshold process and the approximate maximum likelihood method based on approximation of the logarithmic function of the likelihood of observations. The estimates for the parameters of the two-mode threshold jump process with discretely sampled data are found. We show that by checking the likelihood ratio, determining the presence of threshold effects is possible. Keywords: threshold jump process, approximate maximum likelihood method, stochastic differential equation.

Approximate Maximum Likelihood Estimation in Fractional Stochastic Transport Equation

We estimate the drift of the fractional stochastic transport equation the by maximum likelihood and the minimum contrast methods. We show consistency and asymptotic normality of the estimators. We consider both continuous and discrete time observations.

Testing Data Cloning as the Basis of an Estimator for the Stochastic Volatility in Mean Model

Developed as a refinement of stochastic volatility (SV) models, the stochastic volatility in mean (SVM) model incorporates the latent volatility as an explanatory variable in both the mean and variance equations. It, therefore, provides a way of assessing the relationship between returns and volatility, albeit at the expense of complicating the estimation process. This study introduces a Bayesian methodology that leverages data-cloning algorithms to obtain maximum likelihood estimates for SV and SVM model parameters. Adopting this Bayesian framework allows approximate maximum likelihood estimates to be attained without the need to maximize pseudo likelihood functions. The key contribution this paper makes is that it proposes an estimator for the SVM model, one that uses Bayesian algorithms to approximate the maximum likelihood estimate with great effect. Notably, the estimates it provides yield superior outcomes than those derived from the Markov chain Monte Carlo (MCMC) method in terms of standard errors, all while being unaffected by the selection of prior distributions.

Interference Mitigation-Enabled Signal Detection in Diffusive Molecular Communications Systems With Molecular-Type Spreading

To accomplish complex tasks, several nano-machines may need to communicate via multiple-access channel with one access point, where information fusion is carried out. However, multiple-access Diffusive Molecular Communications (DMC) systems suffer from severe Multiple-Access Interference (MAI) and Inter-Symbol Interference (ISI), which should be effectively mitigated at receiver in order to achieve acceptable performance. Built on two fundamental single-user detection schemes, namely Threshold assisted Majority Vote Detection (TMVD) and Equal Gain Combination Detection (EGCD), we first propose three low-complexity interference cancellation schemes, which are the TMVD-assisted Iterative Interference Cancellation (TMVD-IIC), TMVD-based Minimum-Distance Decoding assisted Interference Cancellation (TMVD-MDDIC) and the EGCD-assisted N-order Iterative Interference Cancellation (EGCD-NIIC), for operation in the Molecular Type Spread assisted Molecular Shift Keying (MTS-MoSK) DMC systems. Then, following the principle of maximum likelihood detection, we propose a Simplified Approximate Maximum Likelihood (SAML) detection scheme. The error performance of the MTS-MoSK DMC systems employing respectively the considered detection schemes is comprehensively investigated and compared. Furthermore, the complexities of the detection schemes are analyzed and discussed in terms of the complexity-performance trade-off. Our studies and results show that, compared with the single-user TMVD and EGCD schemes, the proposed interference cancellation schemes are capable of mitigating efficiently the effect of MAI and enabling significant performance improvement at the slightly increased complexity.

An Approximate Maximum Likelihood Method for the Joint Estimation of Range and Doppler of Multiple Targets in OFDM-Based Radar Systems

An Approximate Maximum Likelihood Method for the Joint Estimation of Range and Doppler of Multiple Targets in OFDM-Based Radar Systems

Source Localization Based on Hybrid AOA, TDOA, and RSS Measurements

In this paper, a constrained weighted least squares (CWLS) problem with two quadratic constraints for hybrid AOA, TDOA, and RSS localization is formulated. The Lagrange multiplier method cannot be efficiently used in this situation, so we provide four methods to solve the CWLS problem: 1) weighted least squares (WLS); 2) iterative constrained weighted least squares (ICWLS); 3) Lagrange multiplier method combined with Newton’s method (LMM+NM); 4) semidefinite programming (SDP). Furthermore, in order to obtain a good balance between accuracy and computational burden, we develop a fixed point iteration (FPI)-based algorithm that is derived from an approximate maximum likelihood estimator (MLE). Simulation results show that the accuracy of the proposed FPI method is better than the other four methods; besides, its computational burden is one in ten of the SDP algorithm.

Regression of binary network data with exchangeable latent errors

AbstractUndirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

Subspace-based distributed target detection in compound-Gaussian clutter

This paper investigates the problem of radar detection of distributed targets embedded in unknown compound-Gaussian clutter. To solve the problem, we first derive two detectors for fixed covariance matrix according to Rao and Wald tests with the use of order statistics theory. Then, the unknown covariance matrix is estimated by the approximate maximum likelihood (AML) estimation. Numerical examples through simulated and real data show that the Wald test-based detector has a higher probability of detection (PD) than existing detectors.

Semiparametric approach to estimation of marginal mean effects and marginal quantile effects

We consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance, and we apply the new tool to analyze a Swiss non-labor income data and discover a new interesting predictor.

A Statistical Dependence Framework Based on a Multivariate Normal Copula Function and Stochastic Differential Equations for Multivariate Data in Forestry

Stochastic differential equations and Copula theories are important topics that have many advantages for applications in almost every discipline. Many studies in forestry collect longitudinal, multi-dimensional, and discrete data for which the amount of measurement of individual variables does not match. For example, during sampling experiments, the diameters of all trees, the heights of approximately 10% of the trees, and the tree crown base height and crown width for a significantly smaller number of trees are measured. In this study, for estimating five-dimensional dependencies, we used a normal copula approach, where the dynamics of individual tree variables (diameter, potentially available area, height, crown base height, and crown width) are described by a stochastic differential equation with mixed-effect parameters. The approximate maximum likelihood method was used to obtain parameter estimates of the presented stochastic differential equations, and the normal copula dependence parameters were estimated using the pseudo-maximum likelihood method. This study introduced the normalized multi-dimensional interaction information index based on differential entropy to capture dependencies between state variables. Using conditional copula-type probability density functions, the exact form equations defining the links among the diameter, potentially available area, height, crown base height, and crown width were derived. All results were implemented in the symbolic algebra system MAPLE.

Approximate maximum likelihood time-delay estimation for two closely spaced sources

The study of ground reflections of Global Navigation Satellite System (GNSS) signals, as in GNSS Reflectometry (GNSS-R) can lead to the receiver height estimation. The latter is estimated by comparing the time of arrival difference between the direct and reflected signals, also called path separation. In ground-based scenarios, this path separation can be very small, inducing important interference between paths, which makes it difficult to correctly obtain altimetry products. The path separation estimation can be obtained by a brute force dual source maximum likelihood estimator (2S-MLE), but this solution has a large computational cost. On the other hand, the path separation is so small that a number of approximations can be done. In this study, a third order Taylor approximation of the dual source likelihood criterion is proposed to reduce its complexity. The proposed algorithm performance is compared to the non approximated 2S-MLE for the estimation of the path separation, and to a standard single source processing for the estimation of the direct signal time-delay. These results, along with the corresponding lower bounds, prove that the proposed approach may be of interest for two applications: ground-based GNSS-R altimetry (or radar with low elevation targets) and GNSS multipath mitigation.

Unsupervised mixture estimation via approximate maximum likelihood based on the Cramér - von Mises distance

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cramér - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.