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Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.

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In this paper, we propose a new data-aided (DA) joint angle and delay (JADE) maximum likelihood (ML) estimator. The latter consists of a substantially modified and, hence, significantly improved gray wolf optimization (GWO) technique by fully integrating and embedding within it the powerful importance sampling (IS) concept. This new approach, referred to hereafter as GWOEIS (for "GWO embedding IS"), guarantees global optimality, and offers higher resolution capabilities over orthogonal frequency division multiplex (OFDM) (i.e., multi-carrier and multi-path) single-input multiple-output (SIMO) channels. The traditional GWO randomly initializes the wolfs' positions (angles and delays) and, hence, requires larger packs and longer hunting (iterations) to catch the prey, i.e., find the correct angles of arrival (AoAs) and time delays (TDs), thereby affecting its search efficiency, whereas GWOEIS ensures faster convergence by providing reliable initial estimates based on a simplified importance function. More importantly, and beyond simple initialization of GWO with IS (coined as IS-GWO hereafter), we modify and dynamically update the conventional simple expression for the convergence factor of the GWO algorithm that entirely drives its hunting and tracking mechanisms by accounting for new cumulative distribution functions (CDFs) derived from the IS technique. Simulations unequivocally confirm these significant benefits in terms of increased accuracy and speed Moreover, GWOEIS reaches the Cramér-Rao lower bound (CRLB), even at low SNR levels.

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In recent decades, many research studies have been conducted for the development of some new modifications of different baseline distributions to cope with real-world problems. This paper proposes a novel generalization of probability distributions, called modified type- II half-logistic distribution. We have derived the new family of probability distributions using T-X family with input as a type II variant of the half-logistic distribution. For the purpose of demonstration, the Weibull distribution is considered as a sub-model. Various algebraic properties of the suggested distribution have been discussed. For efficient parameter estimation, we have used the maximum likelihood principle. Additionally, two real-world data sets from the literature have been considered to illustrate the practical usefulness and significance of the suggested model.

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Problems of finding confidence intervals (CIs) and prediction intervals (PIs) for two-parameter negative binomial distributions are considered. Simple CIs for the mean of a two-parameter negative binomial distribution based on some large sample methods are proposed and compared with the likelihood CIs. Proposed CIs are not only simple to compute, but also better than the likelihood CIs for moderate sample sizes. Prediction intervals for the mean of a future sample from a two-parameter negative binomial distribution are also proposed and evaluated for their accuracy. The methods are illustrated using two examples with real life data sets.

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Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:•A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.•Goodness of fit test to test the spatial effects in GWMGGR model.•Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

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This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

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Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson-Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.

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The mixture of probabilistic regression models is one of the most common techniques to incorporate the information of covariates into learning of the population heterogeneity. Despite its flexibility, unreliable estimates can occur due to multicollinearity among covariates. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in the presence of multicollinearity. We evaluate the performance of our proposed methods via classification and stochastic versions of the expectation-maximization algorithm. We show using numerical simulations that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, we apply our methods to analyze the bone mineral data of women aged 50 and older.

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In this paper, we explore the coefficient signs in weighted logistic regression, a variation of logistic regression that includes positive weights and is commonly used for handling uneven data sets and reject inference in credit scoring. Initially, we examine simple weighted logistic regression. Assuming full rank and overlap, we demonstrate that the slope's sign matches the sign of the difference in weighted averages of the independent variable across two groups, 1 and 0. We extend this analysis to multiple weighted logistic regression by employing two vectors: one representing the slopes and the other the differences in weighted averages of the independent variables across the groups. We establish that if one vector is zero, the other must also be zero. Additionally, we prove that if the slope vector isn't zero, the angle between these vectors will be acute. Our theoretical results can serve as a preliminary step prior to feature selection, which is important in logistic regression. Our numerical analysis further illustrates how our theoretical results can be applied to the well-known German Credit Data for reject inference. Additionally, we provide a detailed explanation of feature selection in our analysis.

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Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly when the number of unknown model parameters is large. The aim of this study is to develop and test an efficient profile likelihood-based method, which takes advantage of the structure of the mathematical model being used. We do this by identifying specific parameters that affect model output in a known way, such as a linear scaling. We illustrate the method by applying it to three toy models from different areas of the life sciences: (i) a predator-prey model from ecology; (ii) a compartment-based epidemic model from health sciences; and (iii) an advection-diffusion reaction model describing the transport of dissolved solutes from environmental science. We show that the new method produces results of comparable accuracy to existing profile likelihood methods but with substantially fewer evaluations of the forward model. We conclude that our method could provide a much more efficient approach to parameter inference for models where a structured approach is feasible. Computer code to apply the new method to user-supplied models and data is provided via a publicly accessible repository.

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Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

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Function and structure are strongly coupled in obligated oligomers such as Triosephosphate isomerase (TIM). In animals and fungi, TIM monomers are inactive and unstable. Previously, we used ancestral sequence reconstruction to study TIM evolution and found that before these lineages diverged, the last opisthokonta common ancestor of TIM (LOCATIM) was an obligated oligomer that resembles those of extant TIMs. Notably, calorimetric evidence indicated that ancestral TIM monomers are more structured than extant ones. To further increase confidence about the function, structure, and stability of the LOCATIM, in this work, we applied two different inference methodologies and the worst plausible case scenario for both of them, to infer four sequences of this ancestor and test the robustness of their physicochemical properties. The extensive biophysical characterization of the four reconstructed sequences of LOCATIM showed very similar hydrodynamic and spectroscopic properties, as well as ligand-binding energetics and catalytic parameters. Their 3D structures were also conserved. Although differences were observed in melting temperature, all LOCATIMs showed reversible urea-induced unfolding transitions, and for those that reached equilibrium, high conformational stability was estimated (ΔGTot = 40.6-46.2 kcal/mol). The stability of the inactive monomeric intermediates was also high (ΔGunf = 12.6-18.4 kcal/mol), resembling some protozoan TIMs rather than the unstable monomer observed in extant opisthokonts. A comparative analysis of the 3D structure of ancestral and extant TIMs shows a correlation between the higher stability of the ancestral monomers with the presence of several hydrogen bonds located in the "bottom" part of the barrel.

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Mendelian randomization (MR) utilizes genome-wide association study (GWAS) summary data to infer causal relationships between exposures and outcomes, offering a valuable tool for identifying disease risk factors. Multivariable MR (MVMR) estimates the direct effects of multiple exposures on an outcome. This study tackles the issue of highly correlated exposures commonly observed in metabolomic data, a situation where existing MVMR methods often face reduced statistical power due to multicollinearity. We propose a robust extension of the MVMR framework that leverages constrained maximum likelihood (cML) and employs a Bayesian approach for identifying independent clusters of exposure signals. Applying our method to the UK Biobank metabolomic data for the largest Alzheimer disease (AD) cohort through a two-sample MR approach, we identified two independent signal clusters for AD: glutamine and lipids, with posterior inclusion probabilities (PIPs) of 95.0% and 81.5%, respectively. Our findings corroborate the hypothesized roles of glutamate and lipids in AD, providing quantitative support for their potential involvement.

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Crashes are frequently disproportionally observed in disadvantaged areas. Despite the evident disparities in transportation safety, there has been limited exploration of quantitative approaches to incorporating equity considerations into road safety management. This study proposes a novel concept of equity-aware safety performance functions (SPFs), enabling a distinct treatment of equity-related variables such as race and income. Equity-aware SPFs introduce a fairness distance and integrate it into the log-likelihood function of the negative binomial regression as a form of partial lasso regularization. A parameter λ is used to control the importance of the regularization term. Equity-aware SPFs are developed for pedestrian-involved crashes at the census tract level in Virginia, USA, and then employed to compute the potential for safety improvement (PSI), a prevalent metric used in hotspot identification. Results show that equity-aware SPFs can diminish the effects of equity-related variables, including poverty ratio, black ratio, Asian ratio, and the ratio of households without vehicles, on the expected crash frequencies, generating higher PSIs for disadvantaged areas. Based on the results of Wilcoxon signed-rank tests, it is evident that there are significant differences in the rankings of PSIs when equity awareness is considered, especially for disadvantaged areas. This study adds to the literature a new quantitative approach to harmonize equity and effectiveness considerations, empowering more equitable decision-making in safety management, such as allocating resources for safety enhancement.

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BACKGROUND: Chemoreception is crucial for insect fitness, underlying for instance food-, host-, and mate finding. Chemicals in the environment are detected by receptors from three divergent gene families: odorant receptors (ORs), gustatory receptors (GRs), and ionotropic receptors (IRs). However, how the chemoreceptor gene families evolve in parallel with ecological specializations remains poorly understood, especially in the order Coleoptera. Hence, we sequenced the genome and annotated the chemoreceptor genes of the specialised ambrosia beetle Trypodendron lineatum (Coleoptera, Curculionidae, Scolytinae) and compared its chemoreceptor gene repertoires with those of other scolytines with different ecological adaptations, as well as a polyphagous cerambycid species. RESULTS: We identified 67 ORs, 38 GRs, and 44 IRs in T. lineatum ('Tlin'). Across gene families, T. lineatum has fewer chemoreceptors compared to related scolytines, the coffee berry borer Hypothenemus hampei and the mountain pine beetle Dendroctonus ponderosae, and clearly fewer receptors than the polyphagous cerambycid Anoplophora glabripennis. The comparatively low number of chemoreceptors is largely explained by the scarcity of large receptor lineage radiations, especially among the bitter taste GRs and the 'divergent' IRs, and the absence of alternatively spliced GR genes. Only one non-fructose sugar receptor was found, suggesting several sugar receptors have been lost. Also, we found no orthologue in the 'GR215 clade', which is widely conserved across Coleoptera. Two TlinORs are orthologous to ORs that are functionally conserved across curculionids, responding to 2-phenylethanol (2-PE) and green leaf volatiles (GLVs), respectively. CONCLUSIONS: Trypodendron lineatum reproduces inside the xylem of decaying conifers where it feeds on its obligate fungal mutualist Phialophoropsis ferruginea. Like previous studies, our results suggest that stenophagy correlates with small chemoreceptor numbers in wood-boring beetles; indeed, the few GRs may be due to its restricted fungal diet. The presence of TlinORs orthologous to those detecting 2-PE and GLVs in other species suggests these compounds are important for T. lineatum. Future functional studies should test this prediction, and chemoreceptor annotations should be conducted on additional ambrosia beetle species to investigate whether few chemoreceptors is a general trait in this specialized group of beetles.

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To optimize colorectal cancer (CRC) surveillance, accurate information on the risk of developing CRC from premalignant lesions is essential. However, directly observing this risk is challenging since precursor lesions, i.e., advanced adenomas (AAs), are removed upon detection. Statistical methods for multistate models can estimate risks, but estimation is challenging due to low CRC incidence. We propose an outcome-dependent sampling (ODS) design for this problem in which we oversample CRCs. More specifically, we propose a three-state model for jointly estimating the time distributions from baseline colonoscopy to AA and from AA onset to CRC accounting for the ODS design using a weighted likelihood approach. We applied the methodology to a sample from a Norwegian adenoma cohort (1993-2007), comprising 1, 495 individuals (median follow-up 6.8 years [IQR: 1.1 - 12.8 years]) of whom 648 did and 847 did not develop CRC. We observed a 5-year AA risk of 13% and 34% for individuals having non-advanced adenoma (NAA) and AA removed at baseline colonoscopy, respectively. Upon AA development, the subsequent risk to develop CRC in 5 years was 17% and age-dependent. These estimates provide a basis for optimizing surveillance intensity and determining the optimal trade-off between CRC prevention, costs, and use of colonoscopy resources.

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Profile mixture models capture distinct biochemical constraints on the amino acid substitution process at different sites in proteins. These models feature a mixture of time-reversible models with a common matrix of exchangeabilities and distinct sets of equilibrium amino acid frequencies known as profiles. Combining the exchangeability matrix with each profile generates the matrix of instantaneous rates of amino acid exchange for that profile. Currently, empirically estimated exchangeability matrices (e.g. the LG matrix) are widely used for phylogenetic inference under profile mixture models. However, these were estimated using a single profile and are unlikely optimal for profile mixture models. Here, we describe the GTRpmix model that allows maximum likelihood estimation of a common exchangeability matrix under any profile mixture model. We show that exchangeability matrices estimated under profile mixture models differ from the LG matrix, dramatically improving model fit and topological estimation accuracy for empirical test cases. Because the GTRpmix model is computationally expensive, we provide two exchangeability matrices estimated from large concatenated phylogenomic-supermatrices to be used for phylogenetic analyses. One, called Eukaryotic Linked Mixture (ELM), is designed for phylogenetic analysis of proteins encoded by nuclear genomes of eukaryotes, and the other, Eukaryotic and Archaeal Linked mixture (EAL), for reconstructing relationships between eukaryotes and Archaea. These matrices, combined with profile mixture models, fit data better and have improved topology estimation relative to the LG matrix combined with the same mixture models. Starting with version 2.3.1, IQ-TREE2 allows users to estimate linked exchangeabilities (i.e. amino acid exchange rates) under profile mixture models.

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Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test.

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Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.

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Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.

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