Non-unions are a common complication following fractures. Although fractures of the foot and ankle are frequent, reliable data on the incidence and epidemiology of non-unions in these regions are lacking. A nationwide retrospective analysis was conducted using inpatient data from the German Federal Statistical Office between 2014 and 2023. Fractures and non-unions of the foot and ankle were identified via ICD-10 coding, with two cohorts defined: fracture cases and non-union cases. Data were stratified by age and sex, and all co-coded secondary diagnoses were extracted and aggregated to identify the most frequent comorbidities. Temporal trends were assessed using linear regression, while age distributions were modelled with two-component Gaussian mixture models to capture distinct etiological subpopulations. Data processing, statistical analyses, and visualization were performed in R (Version 4.3) using Tidyverse packages. Between 2014 and 2023, 992,360 foot and ankle fractures and 20,268 non-unions of the foot and ankle were treated in hospitalized patients in German hospitals. Women were more frequently affected by both fractures and non-unions than men. The age distribution was bimodal, with peaks at 18–29 and 50–59 years in men, and at 50–79 years in women. The overall non-union rate was 2.0% and showed a declining trend over time. Age- and sex-specific differences were observed, with the highest non-union rate in women aged 40–49 years (3.2%). Comorbidities including obesity, allergies, depressive episodes, asthma, and sleep disorders were more prevalent in patients with non-unions compared to those with fractures. Non-unions following fractures of the foot and ankle remain rare and have declined steadily over the past decade. Age- and sex-specific differences underscore the need for targeted prevention strategies.

Understanding the complex microbial interactions and their implications for host health is a critical endeavor in biomedical research. In this paper, we propose a transformation-free Bayesian inference approach for estimating microbial and metabolomic association networks based on a latent Ising model. Our method addresses the challenges posed by the compositionality and zero-inflation of microbiome data, offering computational efficiency and versatility for mixed data types. By integrating two-component mixture models tailored to microbiome and metabolome data, along with spike-and-slab priors for sparse graph estimation and a pseudolikelihood approximation for efficient Bayesian computation, we provide a unified framework for joint microbial and metabolomic network inference. Simulation studies demonstrate the superior performance of our method compared to existing approaches, and an application to a real bacterial vaginosis microbiome-metabolome dataset reveals intriguing interaction patterns. Our proposed approach offers a promising avenue for uncovering biological insights from complex microbiome data and holds potential for advancing our understanding of microbiome-associated diseases and therapeutic interventions.

Maintaining proper nutrition is crucial for preserving health and preventing disease. However, what constitutes proper nutrition may vary among individuals; evidence indicates that the effects of diet and even single nutrients can differ considerably because of personal characteristics. This personal variability can be observed through blood markers, such as concentrations of plasma cholesterol and insulin, and captured using a hierarchical multivariate model. We leverage this variability and propose a conditional two-component Bayesian mixture model for generating personalized diet recommendations. The model uses the Nordic Nutrition Recommendations 2023 as a prior for healthy intake and infers individualized recommendations as posterior distributions. The first component identifies dietary options predicted to produce healthy levels across all considered blood markers, while the second selects, among these valid options, the diet closest to predefined personal preferences. The preference component is configurable and, in this study, was used to minimize dietary adjustments to support recommendation adherence while providing well-defined targets for nutrients less critical to concentration regulation. The method was evaluated using nutritional data from two studies: one in prediabetic individuals and one in patients with kidney dysfunction. Numerical simulations showed that the individualized diets could restore or approach normal plasma concentrations when the estimated personal nutrient effects indicated biological feasibility. As the results align with current nutritional literature, the Bayesian approach offers a principled way to leverage observational nutrition data. However, future clinical studies are needed to validate the results and modeling approach before these can be translated into evidence-based personalized nutritional counseling.

Response Time Threshold Methods (RTTMs) are widely used to identify rapid-guessing behavior (RG) in low-stakes assessments, yet face two key challenges: (a) inevitable misclassifications due to overlapping response time distributions of engaged and disengaged responses, and (b) lack of agreement on which method to use under varying conditions. This simulation study evaluated five RTTMs. Item responses and response times were generated from either a one-component model without RG or a two-component mixture model with RG in the population. Distribution, item, and person parameters were varied. Results showed that when the population contained RG, the mixture lognormal distribution-based method (MLN) was the most robust approach and estimated precise thresholds closest to the time points at which the misclassification rates were minimized, even when bimodality was more difficult to detect. The cumulative proportion method (CUMP) was less robust but also accurate when successful, though less precise. In addition, when the population did not include RG, CUMP was the only method to set thresholds for a notable proportion of cases. The methods were generally more conservative than liberal, though the mixture response time quantile method (MRTQ) was neither. The results are discussed in the light of prior RG research and the methods' characteristics, and future directions are suggested. Ultimately, for practical settings, we recommend a six-step process for RG identification that utilizes both a mixture modeling approach (MLN or MRTQ) and the CUMP method.

SUMMARY High-frequency induced polarization (HFIP) measurements enable quantification of ground ice content in frozen media by capturing ice relaxation within the frequency range of 1 to 100 kHz. Existing parametrized inversion approaches may bias results by imposing an ice relaxation signature where none exists, assuming a Cole-Cole-type response that may not reflect the true dielectric behaviour of ice, and neglecting low-frequency polarization. These limitations can lead to high data misfits and ambiguities in interpretation. This study presents an alternative approach that applies independent frequency inversion to directly derive complex resistivity spectra from field measurements, avoiding reliance on pre-defined models. The resulting inverted spectra provide a representation that more closely captures the true subsurface response. A second, petrophysical, inversion is then performed by fitting a two-component mixture model to the inverted spectra, weighted by the volumetric fractions of its components. One of these components is ice, allowing for the estimation of the volumetric ice content.The approach was applied at Heliport Mire (Abisko, Sweden), a permafrost peatland site, using two complementary profiles: a 50-m 2-D profile that captured broad lateral variations of frozen to unfrozen conditions, and an 8-m high-resolution 2-D profile that resolved the vertical transition between the upper unfrozen and underlying frozen layers. Independent frequency inversion, across 1 Hz to 57 kHz, successfully produced smooth, coherent spectral responses of true resistivity and phase shift across both profiles. Petrophysical inversion results show diverse conditions along the profile, identifying three distinct zones: ice-rich frozen peat (40−77 per cent ice content), a thawed or degraded peat region ($<$10 per cent ice content) and unfrozen forest ($<$5 per cent ice content, effectively representing ice-free conditions). HFIP-derived ice content values were consistent with those derived from laboratory measurements on a permafrost core extracted along the profile. The high-resolution profile distinctly identified the boundary between unfrozen and frozen ground, as confirmed by direct probing measurements. Additionally, the petrophysical model resolves parameters such as shape factor and matrix permittivity, offering further insight into subsurface properties. This methodology advances ground ice characterization by providing robust quantitative estimates of ice content while retaining spectral information with broader interpretative potential.

This study presents a drone-based method for assessing the condition of road markings from high-resolution imagery acquired by a UAV. A DJI Matrice 300 RTK (Real-Time Kinematic) equipped with a Zenmuse P1 camera (DJI, China) is flown over urban road corridors to capture images with centimeter-level ground sampling distance. In contrast to common approaches that rely on vehicle-mounted or street-view cameras, using a UAV reduces survey time and deployment effort while still providing views that are suitable for marking. The flight altitude, overlap, and corridor pattern are chosen to limit occlusions from traffic and building shadows while preserving the resolution required for condition assessment. From these images, the method locates individual markings, assigns a class to each marking, and estimates its level of deterioration. Candidate markings are first detected with YOLOv9 on the UAV imagery. The detections are cropped and segmented, which refines marking boundaries and thin structures. The condition is then estimated at the pixel level by modeling gray-level statistics with kernel density estimation (KDE) and a two-component Gaussian mixture model (GMM) to separate intact and distressed material. Subsequently, we compute a per-instance damage ratio that summarizes the proportion of degraded pixels within each marking. All results are georeferenced to map coordinates using a 3D reference model, allowing visualization on base maps and integration into road asset inventories. Experiments on unseen urban areas report detection performance (precision, recall, mean average precision) and segmentation performance (intersection over union), and analyze the stability of the damage ratio and processing time. The findings indicate that the drone-based method can identify road markings, estimate their condition, and attach each record to geographic space in a way that is useful for inspection scheduling and maintenance planning.

Phase separation in bilayers composed of a few lipid species is widely used as a model for exploring the lateral heterogeneity of complex cell membranes. Molecular dynamics (MD) simulations offer atomistic insights into coexisting lipid phases. But identifying these phases from trajectories remains challenging. Here, we present an unsupervised method for lipid phase recognition in phase-separated bilayers. In this method, the membrane plane is first discretized into pixels. For each pixel, the local lipid packing degree, which is defined as the atomic density within that pixel, is calculated and assigned to the corresponding pixel. A threshold is then determined by fitting a two-component Gaussian mixture model (GMM) to the distribution of lipid packing degree, enabling phase state assignment to pixels and subsequent mapping back to lipids. Our method is applicable to different systems, regardless of their compositions or temperatures, thus minimizing potential artifacts. Tests on bilayers with diverse lipid compositions and temperatures show that our method outperforms the commonly used hidden Markov model (HMM) in both accuracy and robustness. Notably, in this method, phase recognition relies solely on bilayer-intrinsic properties (lipid packing degree), without requiring temporal information, labeled data, or assumptions about the local lipid environment. This makes our method broadly applicable to various tasks, including characterizing the phase transformation process before the system reaches equilibration and identifying coexisting phases in protein-containing bilayers. In summary, we provide a robust and accurate framework for identifying coexisting phases in bilayers and tracking their dynamic transitions in simulations.

Abstract A common peculiarity of large-scale applied studies is that the relevant features (signals) are sparse and it is of interests to shrink down the focus toward a much smaller subset in a systematic way. This line of inquiry is of special interest for parsimonious modeling in high-dimensional settings where the goal is to balance model complexity, interpretability, and predictive accuracy. Motivated by microbiome and metagenomic research where high dimensionality is combined with an inherently compositional nature of the data, we formulate an innovative, data-driven framework for selection of sparse, signal-bearing segments ( subcompositions ) hidden in a long sequence of compositional data. Operating with subcompositions as analysis units, the proposed framework is furnished with a broad class of integral probability metrics (IPMs) to quantify a subcomposition’s signal strength, which in turn reflects its influence on the association between the subcomposition’s microbial community and a host phenotype, or any other health/disease-related factor of interest. This class of IPMs is general enough to allow for the incorporation of structural information underlying the data, such as phylogenetic relationships among microbial communities. At the heart of our framework is a threshold-based Selector of Influential Subcompositions (), an algorithm which works as a screen-and-clean scheme outputting the set of influential subcompositions: the data is subject to screening based on empirical signal strength, and threshold cleaning to filter out the subcompositions that contain no signals. sets the selection threshold in a data-driven fashion by adapting the recent notion of CsCsHM statistic, proposed as an optimal signal detection procedure in a sparse, two-component mixture model. We validate the proposed framework through extensive numerical experiments, including challenging cases with sparse, high-dimensional real-world datasets, and demonstrate its effectiveness in identifying clinically relevant influential subcompositions for differentiation of the vaginal microbiome taxonomic profiles in a cohort of Swedish women. The code is available at https://github.com/annti71/Selins .

Abstract We investigate the relationship between disc winds, radio jets, accretion rates and black hole masses of a sample of ∼100k quasars at z ≈ 2. Combining spectra from the 17th data release of the Sloan Digital Sky Survey (SDSS) with radio fluxes from the 2nd data release of the Low Frequency ARray (LOFAR) Two-Meter Sky Survey (LoTSS), we statistically characterise a radio loud and radio quiet population using a two-component Gaussian Mixture model, and perform population matching in black hole mass and Eddington fraction. We determine how the fraction of radio loud sources changes across this parameter space, finding that jets are most efficiently produced in quasars with either a very massive central black hole (MBH > 109M⊙) or one that is rapidly accreting (λEdd > 0.3). We also show that there are differences in the blueshift of the $\textrm {C}\, \rm \small {IV}$ λ1549Å line and the equivalent width of the $\rm {He}\, \rm \small {II}$ λ1640Å line in radio loud and radio quiet quasars that persist even after accounting for differences in the mass and accretion rate of the central black hole. Generally, we find an anti-correlation between the inferred presence of disc winds and jets, which we suggest is mediated by differences in the quasars’ spectral energy distributions. The latter result is shown through the close coupling between tracers of wind kinematics and the ionising flux– which holds for both radio loud and radio quiet sources, despite differences between their emission line properties– and is hinted at by a different Baldwin effect in the two populations.

Two-component mixture models have proved powerful tools for modeling heterogeneity in various clustering scenarios. However, traditional models often assume constant mixture weights, which can be unsuitable for some applications. In this paper, we relax this assumption and allow the mixture weights to vary dynamically with the data index, making the model adaptable to diverse data sets. We introduce an efficient Gibbs sampling algorithm that jointly estimates the mixture component parameters and dynamic weights. We propose a wavelet-based version of data augmentation to assess the dynamic behavior of the mixture weights, exploiting the advantageous properties of wavelet bases in curve estimation. We validate the method through Monte Carlo simulations and real-world applications, including flood detection in a river in southern Brazil and the identification of chromosomal anomalies in DNA samples. The results align with existing findings, demonstrating the robustness of our method.

Eye movements are predictive of successful episodic memory encoding and retrieval, but it is unclear whether they reflect the precision of retrieved memory content. Here, we examined relationships between eye fixations, memory precision and fMRI BOLD activity. At study, participants were presented with object images, each placed at a random location on an invisible circle. At test, both studied and new images were presented. Participants were instructed to make a covert recognition memory judgment to each image, recall and then signal its studied location, guessing if necessary. Simultaneous fMRI and eye-tracking data were acquired during the test phase. For correctly recognized images, the trial-wise angular distance between the studied and reported locations was fitted to a two-component mixture model. Based on the model-derived parameters, correctly recognized images were categorized as those associated with successful location retrieval (location hits) or guesses. Location hits were further divided into high- and low precision trials. At retrieval, fixations predicted both successful retrieval and the precision of the retrieved location memory. Additionally, across-trial fixation patterns were more similar for location hits than for guesses, and for high- than for low-precision trials. The association between retrieval success and eye fixation precision was evident across almost the entire recall phase, whereas memory precision effects emerged around 1–1.5s after image onset. Fixation precision and fixation pattern similarity each predicted trial-wise memory precision independently of hippocampal BOLD activity, which also predicted precision. These findings suggest that eye fixations during retrieval track the fidelity of mnemonic content.

The black soil region in Northeast China is an important grain-producing area and ecological barrier in our country, and changes in its soil quality are directly related to national food security and ecological sustainability. This study systematically analyzes the temporal and spatial evolution of soil organic carbon (SOC), bulk density, pH, and total nitrogen (TN) in black soils over the past four decades (1980–2021) using soil profile data from the Hailun area of Heilongjiang, China. It quantitatively evaluated three key degradation issues: acidification, thinning, and hardening. To reconstruct and validate historical data gaps, the study employed a dual-carbon-pool vertical-attenuation model, a two-component mixture model, a geochemical equilibrium and migration model, and a process-data fusion model. The results show that SOC content in surface soils decreased by 42.3%, TN decreased by 31.4%, pH declined by an average of 0.23 units, and bulk density increased by 12.5%. The patterns of soil degradation differed significantly among soil types, with meadow soils showing the most severe degradation, while paddy soils remained relatively stable. The study further revealed the cascade degradation mechanism of carbon reduction, soil acidification, nitrogen loss, and soil compaction, providing a scientific basis for protecting and sustainably utilizing black soil. 

HighlightsWhat are the main findings?The proposed Adaptive Pseudo Text Augmentation framework effectively identifies noisy image–text correspondence in text-to-image person re-identification using a Gaussian mixture model and recovers valuable data through pseudo-text generation with a multimodal large language model.The model achieves state-of-the-art or competitive performance on CUHK-PEDES, ICFG-PEDES, and RSTPReid datasets, demonstrating superior robustness under noisy supervision.What are the implications of the main findings?The proposed method improves the reliability of cross-modal alignment in real-world T2I-ReID datasets that contain coarse or mismatched text descriptions.It provides a general and extensible strategy for noise-resilient learning in other multimodal tasks involving imperfect annotations.Text-to-image person re-identification (T2I-ReID) aims to retrieve pedestrians from images/videos based on textual descriptions. However, most methods implicitly assume that training image–text pairs are correctly aligned, while in practice, issues such as under-correlated and falsely correlated image–text pairs arise due to coarse-grained text annotations and erroneous textual descriptions. To address this problem, we propose a T2I-ReID method based on noise identification and pseudo-text generation. We first extracts image–text features using the Contrastive Language–Image Pre-Training model (CLIP), then employs the token fusion model to select and fuse informative local token features, resulting in token fusion embedding (TFE) for fine-grained representations. To identify noisy image–text pairs, we apply the two-component Gaussian mixture model (GMM) to fit the per-sample loss distributions computed by the predictions of basic feature embedding (BFE) and TFE. Finally, when the noise identification tends to stabilize, we employ a multimodal large language model (MLLM) to generate pseudo-texts that replace the noisy text, facilitating learning more reliable visual–semantic associations and cross-modal alignment under noisy conditions. Extensive experiments on the CUHK-PEDES, ICFG-PEDES, and RSTPReid datasets demonstrate the effectiveness of our proposed model and the good compatibility with other baselines.

Context . Observational studies are identifying stars thought to be remnants from the earliest stages of the Milky Way’s hierarchical mass assembly, referred to as the proto-Galaxy. Aims . We used red giant stars with kinematics from Gaia DR3 RVS data and [ α /M] and [M/H] estimates from low-resolution Gaia XP spectra to investigate the relationship between azimuthal velocity and metallicity. Our aim is to understand the transition from a chaotic proto-Galaxy to a well-ordered rotating (high- α ) disc-like population. Methods . To analyze the structure of the data in [M/H]−v ϕ space for both high- and low- α samples with carefully defined α -separation, we developed a model with two Gaussian components in v ϕ , one representing a disc-like population and the other a halo-like population. This model is designed to capture the conditional distribution P(v ϕ |[M/H]) with a two-component Gaussian mixture model with fixed means and standard deviations in the azimuthal velocities. To quantify the spin-up of the high- α disc population, we extended this two-component model by allowing the mean velocity and velocity dispersion to vary between the spline knots across the metallicity range used. We also compared our findings with existing literature using traditional Gaussian mixture modelling in bins of [M/H] and investigated using orbital circularity instead of azimuthal velocity. Results . Our findings show that the metal-poor high- α disc gradually spins up across [M/H] ∼−1.7 to −1, while the low- α sample exhibits a sharp transition at [M/H] ≍−1. This latter result is due to the accreted (mostly Gaia -Enceladus-Sausage) debris dominating the metal-poor end, underscoring the critical role of [ α /M] selection in studying the Milky Way’s (old, high- α ) disc evolution. Conclusions . These results indicate that the proto-Galaxy underwent a slow, monotonic spin-up phase over increasing metallicities rather than a rapid, dramatic spin-up at [M/H] ∼−1, as previously inferred in the literature.

Research Type Level 4 – Case series Introduction/Purpose When evaluating ankle arthritis and a patient’s candidacy for total ankle replacement (TAR), it is critical to understand the patient’s pattern of deformity. Broadly, deformity is categorized as varus or valgus. However, as our understanding of deformity and TAR techniques have advanced, we have come to recognize that varus is not uniform. Varus ankles require careful preoperative assessment and intraoperative balancing to achieve deformity correction. Although various classification systems for categorizing varus ankle arthritis exist, one of their primary limitations is that they are defined by one measurement in the coronal plane. Thus, this study sought to define new criteria to classify varus ankle arthritis using multiple radiographic parameters. We hypothesized that we would be able to discern phenotypic clusters of varus ankle arthritis. Methods Patients were identified from a prospective single-institution registry of TAR. Ankles with pre-operative varus ankle arthritis (defined as coronal tibiotalar angle > 5 degrees) between 2015-2021 were included. Five surgeons contributed patients. Patient demographics and intraoperative concomitant procedures were recorded. The following radiographic measurements were collected: coronal tibiotalar alignment (angle between the tibial axis and the articular surface of the talar dome), coronal intra-articular alignment (angle between the tibial plafond and the articular surface of the talar dome), medial distal tibial angle (MDTA), talar center of migration (TCM), lateral talo-first metatarsal (Meary’s) angle, anterior distal tibial angle (ADTA), and hindfoot alignment angle. To identify phenotype clusters, data were rescaled and a principal components analysis was conducted. Then, various cluster analyses, including agglomerative clustering, t-distributed Stochastic Neighbor Embedding (t-SNE), and a two-component Gaussian mixture model, were performed. All analyses were performed using Python 3.12. Results The 184-patient cohort consisted of 61.4% males with mean age 63.6 ± 9.0 years and mean BMI 29.3 ± 4.5 kg/m2. In each method of statistical analysis (principal components, T-SNE, agglomerative clustering, two-component Gaussian mixture model), radiographic parameters had a diffuse pattern without clear signs of clustering. In evaluation of a two-cluster candidate solution, the silhouette score was < 0.2, supporting weak evidence of a clustered structure. Intraoperatively, concomitant procedures were varied: tendo-Achilles lengthening (TAL) or gastrocnemius recession 68.48% (126/184), medializing calcaneal osteotomy (MCO) 3.80% (7/184), lateral ligament stabilization [Brostrom] 29.35% (54/184), medial cuneiform dorsal opening wedge [Cotton] osteotomy 1.09% (2/184), first metatarsal dorsiflexion osteotomy 13.04% (24/184), subtalar fusion 2.72% (5/184), first tarsometatarsal (TMT) joint fusion 2.72% (5/184), and lateralizing calcaneal osteotomy (LCO) 3.80% (7/184). Conclusion Varus ankles are not uniform and prove challenging to organize into rigid categories. Each measurement included independent information such that a lower-dimensional representation would omit pertinent details regarding the underlying deformity. Thus, reliance on rudimentary classifications of varus may be inadequate for characterizing varus ankle arthritis. During TAR, the surgeon must evaluate all components of the deformity, and a diverse array of intraoperative procedures may be needed to balance a varus ankle. Future analysis may explore how these radiographic variables are associated with preoperative PROMIS scores, and if certain thresholds of these variables can predict intraoperative decision-making for concomitant procedures.

Water is the predominant component of living systems, and its regulation and movement in response to stimuli is a critical feature of homeostasis. While many techniques report relative changes in the water content of cells, measuring the absolute water content in live cells is difficult. In this work, we introduce methodologies for quantifying the absolute intracellular water content using holotomography, which can be applied to unlabeled live cells of arbitrary shape. Using the volumetric and mass-sensitive nature of holotomography, we treat the cell as a two-component mixture model of solid and aqueous materials and solve for the absolute water content. We apply these techniques to quantify absolute intracellular water content of cells undergoing mitosis and responding to external stressors, including osmotic shock and pulsed electric fields, which induce rapid osmotic change. These techniques will aid in elucidating biological, chemical, and physical mechanisms of water transport.

Fault identification in Printed Circuit Board Assembly (PCBA) testing is essential for assuring product quality; nevertheless, conventional methods still have difficulties due to the lack of labeled faulty data and the “black box” nature of advanced models. This study introduces a label-free, interpretable self-supervised framework that uses two pretext tasks: (i) an autoencoder (reconstruction error and two latent features) and (ii) isolation forest (faulty score) to form a four-dimensional representation of each test sequence. A two-component Gaussian Mixture Model is used, and the samples are clustered into normal and fault groups. The decision is explained with cluster mean differences, SHAP (LinearSHAP or LinearExplainer on a logistic-regression surrogate), and a shallow decision tree that generated if–then rules. On real PCBA data, internal indices showed compact and well-separated clusters (Silhouette 0.85, Calinski–Harabasz 50,344.19, Davies–Bouldin 0.39), external metrics were high (ARI 0.72; NMI 0.59; Fowlkes–Mallows 0.98), and the clustered result used as a fault predictor reached 0.98 accuracy, 0.98 precision, and 0.99 recall. Explanations show that the IForest score and reconstruction error drive most decisions, causing simple thresholds that can guide inspection. An ablation without the self-supervised tasks results in degraded clustering quality. The proposed approach offers accurate, label-free fault prediction with transparent reasoning and is suitable for deployment in industrial test lines.

Abstract In small area estimation, different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models such as the linear mixed effects model or M-quantile regression are often used to improve the precision of survey sample estimates by leveraging auxiliary information for which means or totals are known at the area level. In many applications, the unit-level linkage of records from different sources is probabilistic and potentially error-prone. In this article, we present adjustments of the small area predictors that are based on either the linear mixed effects model or M-quantile regression to account for the presence of linkage error. These adjustments are developed from a two-component mixture model that hinges on the assumption of independence of the target and auxiliary variable given incorrect linkage. Estimation and inference is based on composite likelihoods and machinery revolving around the Expectation-Maximization Algorithm. For each of the two regression methods, we propose modified small area predictors and approximations for their mean squared errors. The empirical performance of the proposed approaches is studied in both design-based and model-based simulations that include comparisons to a variety of baselines.

A statistical description of the sea surface is necessary for solving a wide range of fundamental and applied problems. Modeling the probability density function of sea surface elevations is one of the main components of this description. This paper considers two approaches to calculate the parameters of the probability density function in the form of a two-component Gaussian mixture. The first one is based on the use of an incomplete system of Pearson equations, which is due to the fact that when measuring sea waves, the fifth statistical moment is usually not determined. In the second approach, an additional empirical relationship between the third and fifth statistical moments is used to close the system of Pearson equations. It is shown that the first approach is preferable, since it makes it possible to construct the probability density function in almost all ranges of the measured statistical moments of the third and fourth orders. Taking into account the fifth statistical moment significantly limits the area in which solutions of the considered system of equations exist.

The diagnostic cut-off values for IgG antibodies against recombinant Aspergillus fumigatus (rAsp) antigens in allergic bronchopulmonary aspergillosis (ABPA) remain unclear. To derive and validate diagnostic cut-offs for IgG antibodies against rAsp f 1, f 2 and f 4 in ABPA and assess their diagnostic performance in distinguishing ABPA from asthma. In this case-control study, we prospectively enrolled consecutive subjects with asthma and ABPA. We measured serum IgG levels against rAsp f 1, rAsp f 2 and rAsp f 4 using a fluorescent enzyme immunoassay. Subjects were randomly split into derivation (50%) and validation (50%) cohorts. Cut-offs were derived using receiver operating characteristic (ROC) curves and Youden's index. Additionally, we performed Bayesian latent class analysis (BLCA) using two-component Gaussian mixture models to derive unbiased cut-offs. Diagnostic performance was assessed using sensitivity, specificity and the area under the ROC curve (AUROC). Of 375 participants, 261 had ABPA and 114 had asthma. ROC-derived AUROC values for rAsp f 1, f 2 and f 4-IgG were 0.63, 0.47 and 0.52, while the cut-off values were 10.1 mgA/L, 10.3 mgA/L and 10.5 mgA/L, respectively. Sensitivity was ≤ 42% for all antigens, while specificity exceeded 89%. BLCA yielded cut-offs of 18.6, 14.9 and 13.7 mgA/L for f 1, f 2 and f 4, respectively, with similarly poor sensitivity and high specificity. IgG antibodies against rAsp f 1, f 2 and f 4 exhibit high specificity but poor sensitivity in identifying ABPA, limiting their utility as standalone diagnostic markers.