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Utilizing over 31   000 Lg waveforms from 136 crustal earthquakes recorded at 346 regional stations, we conduct detailed tomographic mappings of the Lg Q structure across Eastern Asia in a frequency range from 0.5 to 4.0 Hz. By improving the standard two-station (TS) method, we effectively correct non-unity site response ratios using site responses estimated at individual stations. This innovative approach combines the flexible recording geometry of the TS method with the precision of reversed two-station (RTS) and reversed two-event (RTE) methods, producing a comprehensive data set devoid of source and site effects for Q tomography. To address unsolvable 3-D structural effects in the Lg spectral amplitude modelling, we justify these as modelling errors with a Gaussian distribution. This approach supports our SVD-based tomographic method, allowing for effective inversion of attenuation parameters and quantitative assessment of model resolution and errors. Our results reveal a complex relationship between Lg Q and the tectonic characteristics of Eastern Asia. In well-resolved regions, low Q o (1-Hz Q) values correspond to areas with high heat flow, partial melt, thick sediment and recent tectonic-thermal activities, in contrast to high Q o values in stable, ancient crusts lacking recent tectonic activity. Rift basins are characterized by low Lg Q o, whereas flexural basins generally have high Q o basements. We also note that post-formation factors, such as sedimentation and crustal flow intrusion, significantly impact Q o values. Furthermore, Lg Q shows a complex frequency relationship, though the power-law approximation with positive power η remains useful. The frequency dependence power η is inversely related to Q o: the regions with low Q o typically have high η and vice versa. This study provides reliable attenuation tomographic and relative site response models for Lg waves in Eastern Asia, pertinent for relative geophysical studies. [ABSTRACT FROM AUTHOR]

We propose a model for interval-valued time series that specifies the conditional joint distribution of the upper and lower bounds as a mixture of truncated bivariate normal distributions. It preserves the interval natural order and provides great flexibility on capturing potential conditional heteroscedasticity and non-Gaussian features. The standard expectation maximization (EM) algorithm applied to truncated mixtures does not provide a closed-form solution in the M step. A new EM algorithm solves this problem. The model applied to the interval-valued IBM daily stock returns exhibits superior performance over competing models in-sample and out-of-sample evaluation. A trading strategy showcases the usefulness of our approach. [ABSTRACT FROM AUTHOR]

We reanalyse the recent compilation of distance measurements to M87 by collecting the data from published literature. Different from the traditional statistical methods, based on the principle of minimum information loss, we use a robust most frequent value (MFV) procedure to estimate the distance to M87, irrespective of the Gaussian or non-Gaussian distributions. The MFV-based robust estimate for the M87 distance modulus is given by |$31.09^{+0.04}_{-0.03}$| (statistical) |$^{+0.05}_{-0.07}$| (systematic) mag corresponding to a 68.27 per cent confidence interval, whereas the result of combining the two uncertainties in quadrature is |$31.09^{+0.06}_{-0.08}$|  mag. We also construct the error distributions of M87 distance moduli values according to the weighted mean, median, and MFV, which is non-Gaussian. This demonstrates that the MFV method offers a more accurate and robust estimate of the distance to M87 compared to methods that depend on the unfulfilled assumption of Gaussianity. [ABSTRACT FROM AUTHOR]

Homomorphic signature is an extremely important public key authentication technique for network coding to defend against pollution attacks. However, there are many problems with previous homomorphic signature schemes which require key escrow, cannot resist malicious key generation center (KGC), and are insecure in the post-quantum era. Therefore, we propose a lattice-based certificateless linearly homomorphic signature scheme. In our scheme, certificateless structure can avoid key escrow and malicious KGC. The lattice structure ensures that our scheme is secure in the post-quantum era. The bimodal Gaussian distribution is used to improve the security and the efficiency. Compared with the previous schemes, our scheme has smaller storage space (no key escrow), can avoid malicious KGC, is more secure in the post-quantum era, and has higher signature efficiency. At the same time, our scheme is more suitable for network coding. Finally, under random oracle model, we proved that our scheme is weakly context hiding and existentially unforgeable against adaptive chosen message attacks against external attackers and the internal KGC. [ABSTRACT FROM AUTHOR]

Motivated by applications in text mining and discrete distribution inference, we test for equality of probability mass functions of K groups of high-dimensional multinomial distributions. Special cases of this problem include global testing for topic models, two-sample testing in authorship attribution, and closeness testing for discrete distributions. A test statistic, which is shown to have an asymptotic standard normal distribution under the null hypothesis, is proposed. This parameter-free limiting null distribution holds true without requiring identical multinomial parameters within each group or equal group sizes. The optimal detection boundary for this testing problem is established, and the proposed test is shown to achieve this optimal detection boundary across the entire parameter space of interest. The proposed method is demonstrated in simulation studies and applied to analyse two real-world datasets to examine, respectively, variation among customer reviews of Amazon movies and the diversity of statistical paper abstracts. [ABSTRACT FROM AUTHOR]

Galaxy cluster masses derived from observations of weak lensing suffer from a number of biases affecting the accuracy of mass-observable relations calibrated from such observations. In particular, the choice of the cluster centre plays a prominent role in biasing inferred masses. In the past, empirical miscentring distributions have been used to address this issue. Using hydrodynamic simulations, we aim to test the accuracy of weak lensing mass bias predictions based on such miscentring distributions by comparing the results to mass biases computed directly using intracluster medium (ICM)-based centres from the same simulation. We construct models for fitting masses to both centred and miscentred Navarro–Frenk–White profiles of reduced shear, and model the resulting distributions of mass bias with normal and lognormal distributions. We find that the standard approach of using miscentring distributions leads to an overestimation of cluster masses at levels of between 2 per cent and 6 per cent when compared to the analysis in which actual simulated ICM centres are used, even when the underlying miscentring distributions match in terms of the miscentring amplitude. While we find that neither lognormal nor normal distributions are generally reliable for accurately modelling the shapes of the mass bias distributions, both models can serve as reasonable approximations in practice. [ABSTRACT FROM AUTHOR]

In recent studies of many-body localization in nonintegrable quantum systems, the distribution of the ratio of two consecutive energy level spacings, |$r_n=(E_{n+1}-E_n)/(E_{n}-E_{n-1})$| or |$\tilde{r}_n=\min (r_n,r_n^{-1})$|⁠ , has been used as a measure to quantify the chaoticity, alternative to the more conventional distribution of the level spacings, |$s_n=\bar{\rho }(E_n)(E_{n+1}-E_n)$|⁠ , as the former makes unnecessary the unfolding required for the latter. Based on our previous work on the Tracy–Widom approach to the Jánossy densities, we present analytic expressions for the joint probability distribution of two consecutive eigenvalue spacings and the distribution of their ratio for the Gaussian unitary ensemble (GUE) of random Hermitian |$N\times N$| matrices at |$N\rightarrow \infty$|⁠ , in terms of a system of differential equations. As a showcase of the efficacy of our results for characterizing an approach to quantum chaoticity, we contrast them to arguably the most ideal of all quantum-chaotic spectra: the zeroes of the Riemann |$\zeta$| function on the critical line at increasing heights. [ABSTRACT FROM AUTHOR]

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference that allows latent variables and model misspecification. Concretely, we show a Bernstein–von Mises (BvM) theorem for the variational distribution from MF under possible model misspecification, which implies the distributional convergence of MF variational approximation to a normal distribution centring at the maximal likelihood estimator. Motivated by the BvM theorem, we propose a model selection criterion using the evidence lower bound (ELBO), and demonstrate that the model selected by ELBO tends to asymptotically agree with the one selected by the commonly used Bayesian information criterion (BIC) as the sample size tends to infinity. Compared to BIC, ELBO tends to incur smaller approximation error to the log-marginal likelihood (a.k.a. model evidence) due to a better dimension dependence and full incorporation of the prior information. Moreover, we show the geometric convergence of the coordinate ascent variational inference algorithm, which provides a practical guidance on how many iterations one typically needs to run when approximating the ELBO. These findings demonstrate that variational inference is capable of providing a computationally efficient alternative to conventional approaches in tasks beyond obtaining point estimates. [ABSTRACT FROM AUTHOR]

In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a |$2048^3$| mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour. [ABSTRACT FROM AUTHOR]

Background: mammography is the gold standard in the early detection of breast cancer. Due to the increase in the rate of women suffering from this malignancy all over the world, this imaging modality has been widely used. Considering the side effects caused by ionizing radiation to measure the carcinogenic risk of mammography X-rays, mean glandular dose (MGD) is the best parameter to evaluate the dose received by patients undergoing mammography. The aims of this study were to measure MGD in mammography in mammographic craniocaudal (CC) and mediolateral oblique (MLO) projections and investigate the relationship of MGD with compressed breast thickness (CBT), body mass index, age of the patient, and device exposure conditions. Materials and methods: this cross-sectional analytical study was conducted on women aged 30–70 referring to the mammography unit of Shahid Sadoughi Hospital in Yazd city from May to August 2022. The TLD-GR 200 (thermoluminescence dosimeter) was placed on the breast of the patients for CC and MLO projections, and then the MGD was obtained by multiplying the entrance surface dose and the normalized glandular dose. Analysis of data (such as demographic information of patients, CBT, kVp, and mAs) was done by SPSS 23 software. The normality of the data was checked using Shapiro–Wilk tests. It was found that except for age, other variables did not have a normal distribution; therefore, equivalent parametric and nonparametric tests were used. In this regard, Spearman's correlation was used to assess the correlation between variables. P -value < .05 was considered as level of significance. Results: The mean ± standard deviation (SD) age of patients was 47.3 ± 7.1 years. The median ± IQR (the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. It is defined as the difference between the 75th and 25th percentiles of the data.) (mean ± SD) value of MGD per woman was 1.2 ± 0.4 mGy (1.3 ± 0.3 mGy). The median ± IQR MGD in the MLO and CC projections was 1.6 ± 0.6 mGy and 0.9 ± 0.4 mGy, respectively. Significant relationships (P -value ≤ .001) were observed between MGD with CBT (R  = 0.62) and age (R  = −0.85). Conclusion: The results showed that the mammography unit at Shahid Sadoughi Hospital in Yazd is functioning properly. The calculated median ± IQR MGD per woman referring to this unit (1.2 ± 0.4 mGy) was clearly below the dose limit recommended by American College of Radiology and International Commission on Radiological Protection (3 mGy). Moreover, among the factors affecting MGD, the highest correlation was seen between MGD and age (R  = −0.85). [ABSTRACT FROM AUTHOR]

The article discusses a Bayesian meta-analysis framework for estimating penetrance for cancer risk, focusing on a hierarchical random-effects model. The authors demonstrate the framework's effectiveness in estimating age-adjusted penetrance for carriers of pathogenic mutations in a susceptibility gene for moderate breast cancer risk. The article highlights the challenges of synthesizing uncertainty estimates from individual studies and suggests further methodological investigations in this area. The text also explores the potential use of Bayesian machine learning methods for meta-analysis in clinical studies. [Extracted from the article]

OBJECTIVES Ascending aortic aneurysms pose a different risk to each patient. We aim to provide personalized risk stratification for such patients based on sex, age, body surface area and aneurysm location (root versus ascending). METHODS Root and ascending diameters, and adverse aortic events (dissection, rupture, death) of ascending thoracic aortic aneurysm patients were analysed. Aortic diameter was placed in context vis-a-vis the normal distribution in the general population with similar sex, age and body surface area, by conversion to z scores. These were correlated of major adverse aortic events, producing risk curves with 'hinge points' of steep risk, constructed separately for the aortic root and mid-ascending aorta. RESULTS A total of 1162 patients were included. Risk curves unveiled generalized thresholds of z  = 4 for the aortic root and z  = 5 for the mid-ascending aorta. These correspond to individualized thresholds of less than the standard criterion of 5.5 cm in the vast majority of patients. Indicative results include a 75-year-old typical male with 2.1 m2 body surface area, who was found to be at increased risk of adverse events if root diameter exceeds 5.15 cm, or mid ascending exceeds 5.27 cm. An automated calculator is presented, which identifies patients at high risk of adverse events based on sex, age, height, weight, and root and ascending size. CONCLUSIONS This analysis exploits a large sample of aneurysmal patients, demographic features of the general population, pre-dissection diameter, discrimination of root and supracoronary segments, and statistical tools to extract thresholds of increased risk tailor-made for each patient. [ABSTRACT FROM AUTHOR]

Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multicenter trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survival responses. We demonstrate how the common normal assumption for reaction times can be relaxed in the sleep deprivation benchmark data set and report marginal odds ratios for the notoriously difficult toe nail data. We furthermore discuss the analysis of two clinical trials aiming at the estimation of marginal treatment effects. In the first trial, pain was repeatedly assessed on a bounded visual analog scale and marginal proportional-odds models are presented. The second trial reported disease-free survival in rectal cancer patients, where the marginal hazard ratio from Weibull and Cox models is of special interest. An empirical evaluation compares the performance of the novel approach to general estimation equations for binary responses and to conditional mixed-effects models for continuous responses. An implementation is available in the tram add-on package to the R system and was benchmarked against established models in the literature. [ABSTRACT FROM AUTHOR]

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalizing this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications. [ABSTRACT FROM AUTHOR]

Background: Parametric statistical methods are generally better than nonparametric, but require that data follow a known, usually normal, distribution. One important application is finding reference limits and detection limits. Parametric analyses yield better estimates and measures of their uncertainty than nonparametric approaches, which rely solely on a few extreme values. Some reference data follow normal distributions; some can be transformed to normal; some are normal or transformable to normal apart from a few extreme values; and detection and quantitation limits can lead to data censoring. Methods: A quantile–quantile (QQ) toolbox provides powerful general methodology for all these settings. Results: QQ methodology leads to a family of simple methods for finding optimal power transformations, testing for normality before and after transformation, estimating reference limits, and constructing confidence intervals. Conclusions: These parametric methods have a particular appeal to clinical laboratorians because, while statistically rigorous, they do not require specialized software or statistical expertise, but can be implemented even in spreadsheets. We conclude with an exploration of reference values for amyloid beta proteins associated with Alzheimer disease. [ABSTRACT FROM AUTHOR]

For herbivorous insects with a broad diet breadth, host plant identity can influence larval development by either accelerating or delaying growth. For some species of Lepidoptera, the number of larval instars varies depending on the host plant's identity. Fall webworm (Hyphantria cunea , Drury) is a polyphagous herbivore that feeds on over 450 host plants worldwide. Of the 2 morphotypes (red- and black-head) of fall webworm, the number of instars for the red-head fall webworms has not been characterized. Given its broad diet breadth, fall webworm developmental stages may vary with plant identity. We investigated whether host plant identity affected the number of instars observed during red-head fall webworm development. We measured the head capsules of over 6,000 fall webworm larvae reared on 6 different plants commonly eaten by fall webworms in Colorado. We modeled head capsule widths as Gaussian mixture models, with a Gaussian distribution that corresponded to each instar. We show that our red-head fall webworms varied in number of instars depending on the identity of their host plant upon which they fed. We found that red-head fall webworm exhibited 7 instars on 5 of the host plants and 8 instars on 1 host plant that we studied. Our results for the number of instars for red-head fall webworm are consistent with reports of the number of instars for black-head fall webworm. Our research provides insight into the influence of host plant identity on fall webworm development, which can be used to advance lab and field research of this species. [ABSTRACT FROM AUTHOR]

In order to investigate the potential Hubble tension, we compile a catalogue of 216 measurements of the Hubble–Lemaître constant H 0 between 2012 and 2022, which includes 109 model-independent measurements and 107 ΛCDM model-based measurements. Statistical analyses of these measurements show that the deviations of the results with respect to the average H 0 are far larger than expected from their error bars if they follow a Gaussian distribution. We find that x σ deviation is indeed equivalent in a Gaussian distribution to x eqσ deviation in the frequency of values, where x eq = 0.72 x 0.88. Hence, a tension of 5σ, estimated between the Cepheid-calibrated type Ia supernovae and cosmic microwave background (CMB) data, is indeed a 3σ tension in equivalent terms of a Gaussian distribution of frequencies. However, this recalibration should be independent of the data whose tension we want to test. If we adopt the previous analysis of data of 1976–2019, the equivalent tension is reduced to 2.25σ. Covariance terms due to correlations of measurements do not significantly change the results. None the less, the separation of the data into two blocks with H 0 < 71 and H 0 ≥ 71 km s−1 Mpc−1 finds compatibility with a Gaussian distribution for each of them without removing any outlier. These statistical results indicate that the underestimation of error bars for H 0 remain prevalent over the past decade, dominated by systematic errors in the methodologies of CMB and local distance ladder analyses. [ABSTRACT FROM AUTHOR]

A chemodynamical model of our Galaxy is fitted to data from DR17 of the APOGEE survey supplemented with data from the StarHorse catalogue and Gaia DR3. Dynamically, the model is defined by action-based distribution functions for dark matter and six stellar components plus a gas disc. The gravitational potential jointly generated by the model's components is used to examine the Galaxy's chemical composition within action space. The observational data probably cover all parts of action space that are populated by stars. The overwhelming majority of stars have angular momentum J ϕ > 0 implying that they were born in the Galactic disc. High-α stars dominate in a region that is sharply bounded by |$J_\phi \lesssim J_\phi (\hbox{solar})$|⁠. Chemically the model is defined by giving each stellar component a Gaussian distribution in ([Fe/H],[Mg/Fe]) space about a mean that is a linear function of the actions. The model's 47 dynamical parameters are chosen to maximize the likelihood of the data given the model in 72 three-dimensional velocity spaces while its 70 chemical parameters are similarly chosen in five-dimensional chemodynamical space. The circular speed falls steadily from |$237\, \mathrm{km\, s}^{-1}$| at |$R=4\, \mathrm{kpc}$| to |$218\, \mathrm{km\, s}^{-1}$| at |$R=20\, \mathrm{kpc}$|⁠. Dark matter contributes half the radial force on the Sun and has local density |$0.011\, {\rm M}_\odot \, \mathrm{pc}^{-3}$|⁠ , there being |$24.5\, {\rm M}_\odot \, \mathrm{pc}^{-2}$| in dark matter and |$26.5\, {\rm M}_\odot \, \mathrm{pc}^{-2}$| in stars within |$1.1\, \mathrm{kpc}$| of the plane. [ABSTRACT FROM AUTHOR]

We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for two-dimensional random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential, being Gaussian, the eigenvalue fields are distinctly non-Gaussian. We extend the Doroshkevich formula for the joined distribution of eigenvalues to two-dimensional fields and evaluate the two- and three-point correlation functions. In addition, we assess the number densities of singular points of the eigenvalue fields and find their corresponding two- and three-point correlation functions. The incentive for the present study is based on our interest in developing a fully analytical theory for the structure and dynamics of the cosmic web. The tidal forces and the resulting mass element deformation shape the prominent anisotropic wall-like and filamentary components of the cosmic web. Less well-known is that the web-like spatial pattern is already recognizable in the primordial tidal and deformation eigenvalue field. Against the full phase-space assessment of structure formation in the Universe, the caustic skeleton theory entails an analytical framework for the non-linear evolution of the cosmic web. It accomplishes this by describing the folding of the dark matter sheet and quantifying the emerging caustic singularities, which are fully specified by the spatial properties of the deformation eigenvalues and eigenvectors. Finally, the eigenvalues of the primordial tidal tensor are crucial in the generation of the angular momentum of galaxies. Understanding their spatial distribution is a critical element in predicting the resulting rotation amplitude and orientation. [ABSTRACT FROM AUTHOR]

Urgency is a key element of provisional measures. In its substantive meaning, it is a conditio sine qua non for their grant. In the procedural sense, it signifies a swift way of processing the request by the Court. The manner in which the International Court of Justice manages those proceedings remains insufficiently explored. If the Court were to delay them, irreparable prejudice might have already occurred. To fill the gap in the literature, this article aims at elaborating on the management of interim relief proceedings. To this end, it employs methods of statistical analysis to assess the Court's past practice. It argues that those proceedings lack predictability, based on an analysis of parameters such as minimum, maximum, mean, standard deviation, Pearson correlation coefficient, normal distribution (Gaussian), skewness coefficient, coefficient of variation and kurtosis. [ABSTRACT FROM AUTHOR]

As in random matrix theories, eigenvector/value distributions are important quantities of random tensors in their applications. Recently, real eigenvector/value distributions of Gaussian random tensors have been explicitly computed by expressing them as partition functions of quantum field theories with quartic interactions. This procedure to compute distributions in random tensors is general, powerful, and intuitive, because one can take advantage of well-developed techniques and knowledge of quantum field theories. In this paper we extend the procedure to the cases that random tensors have mean backgrounds and eigenvector equations have random deviations. In particular, we study in detail the case that the background is a rank-one tensor, namely, the case of a spiked tensor. We discuss the condition under which the background rank-one tensor has a visible peak in the eigenvector distribution. We obtain a threshold value, which agrees with a previous result in the literature. [ABSTRACT FROM AUTHOR]

Motivation Microbes are essential components in the ecosystem and participate in most biological procedures in environments. The high-throughput sequencing technologies help researchers directly quantify the abundance of microbes in a natural environment. Microbiome studies explore the construction, stability, and function of microbial communities with the aid of sequencing technology. However, sequencing technologies only provide relative abundances of microbes, and this kind of data is called compositional data in statistics. The constraint of the constant-sum requires flexible statistical methods for analyzing microbiome data. Current statistical analysis of compositional data mainly focuses on one compositional vector such as bacterial communities. The fungi are also an important component in microbial communities and are always measured by sequencing internal transcribed spacer instead of 16S rRNA genes for bacteria. The different sequencing methods between fungi and bacteria bring two compositional vectors in microbiome studies. Results We propose a novel statistical method, called gmcoda, based on an additive logistic normal distribution for estimating the partial correlation matrix for cross-domain interactions. A majorization–minimization algorithm is proposed to solve the optimization problem involved in gmcoda. Through simulation studies, gmcoda is demonstrated to work well in estimating partial correlations between two compositional vectors. Gmcoda is also applied to infer cross-domain interactions in a real microbiome dataset and finds potential interactions between bacteria and fungi. Availability and implementation Gmcoda is open source and freely available from https://github.com/huayingfang/gmcoda under GNU LGPL v3. [ABSTRACT FROM AUTHOR]

Based on the Apache Point Observatory Galactic Evolution Experiment survey we conducted a search for carbon-deficient red giants (CDGs). We found 103 new CDGs, increasing the number in the literature by more than a factor of 3. CDGs are very rare, representing 0.03 per cent of giants. They appear as an extended tail off the normal carbon distribution. We show that they are found in all components of the Galaxy, contrary to previous findings. The location of CDGs in the Hertzsprung–Russell diagram (HRD) shows that they are primarily intermediate-mass stars (⁠|$2-4~\rm {M}_{\odot }$|⁠). Their extended distribution may indicate that CDGs can also sometimes have |$M \lt 2.0~\rm {M}_{\odot }$|⁠. We attempted to identify the evolutionary phases of the CDGs using stellar model tracks. We found that the bulk of the CDGs are likely in the subgiant branch or red clump phase, whereas other CDGs may be in the red giant branch or early asymptotic giant branch phases. Degeneracy in the HRD makes exact identification difficult. We examined their C, N, and O compositions and confirmed previous studies showing that the envelope material has undergone extensive hydrogen burning through the CN(O) cycle. The new-CDGs have [C+N+O/Fe] that generally sum to zero, indicating that they started with scaled-solar composition. However, the previously known-CDGs generally have [C+N+O/Fe] > 0.0, indicating that some He-burning products were added to their envelopes. As to the site(s) in which this originally occurred, we do not find a convincing solution. [ABSTRACT FROM AUTHOR]

We obtain the median-, the arithmetic mean–, and the weighted mean–based central estimates for the distance to M87 using all the measurements collated in literature. We then reconstruct the error distribution for the residuals of the combined measurements and also split them based on the tracers used. We then check for consistency with a Gaussian distribution and other symmetric distributions such as Cauchy, Laplacian, and Student's- t distributions. We find that when we analyze the combined data, the weighted mean–based estimates show a poor agreement with the Gaussian distribution, indicating that there are unaccounted systematic errors in some of the measurements. Therefore, the median-based estimate for the distance to M87 would be the most robust. This median-based distance modulus to M87 is given by 31.08 ± 0.09 mag and 31.07 ± 0.09 mag, with and without considering measurements categorized as "averages," respectively. [ABSTRACT FROM AUTHOR]

While the probability density function of the cosmic microwave background (CMB) convergence field approximately follows a Gaussian distribution, primordial non-Gaussianities, and small contributions from structures at low redshifts make the overall distribution slightly non-Gaussian. Some of the late-time component can be modelled using the distribution of galaxies and subtracted off from the original CMB lensing map to produce a map of matter distribution at high redshifts. Using this high-redshift mass map, we are able to directly study the early phases of structure formation. In this work, we forecast the detectability of signatures of non-Gaussianity due to non-linear structure formation at z > 1.2. Assuming the optimal case of no systematics, we find that it is challenging to detect such signatures in current surveys, but future experiments such as the deep field of CMB-S4 will be able to make detections of ∼7σ. [ABSTRACT FROM AUTHOR]

How much genome differences between species reflect neutral or adaptive evolution is a central question in evolutionary genomics. In humans and other mammals, the presence of adaptive versus neutral genomic evolution has proven particularly difficult to quantify. The difficulty notably stems from the highly heterogeneous organization of mammalian genomes at multiple levels (functional sequence density, recombination, etc.) which complicates the interpretation and distinction of adaptive versus neutral evolution signals. In this study, we introduce mixture density regressions (MDRs) for the study of the determinants of recent adaptation in the human genome. MDRs provide a flexible regression model based on multiple Gaussian distributions. We use MDRs to model the association between recent selection signals and multiple genomic factors likely to affect the occurrence/detection of positive selection, if the latter was present in the first place to generate these associations. We find that an MDR model with two Gaussian distributions provides an excellent fit to the genome-wide distribution of a common sweep summary statistic (integrated haplotype score), with one of the two distributions likely enriched in positive selection. We further find several factors associated with signals of recent adaptation, including the recombination rate, the density of regulatory elements in immune cells, GC content, gene expression in immune cells, the density of mammal-wide conserved elements, and the distance to the nearest virus-interacting gene. These results support the presence of strong positive selection in recent human evolution and highlight MDRs as a powerful tool to make sense of signals of recent genomic adaptation. [ABSTRACT FROM AUTHOR]

Motivation Learning low-dimensional representations of single-cell transcriptomics has become instrumental to its downstream analysis. The state of the art is currently represented by neural network models, such as variational autoencoders, which use a variational approximation of the likelihood for inference. Results We here present the Deep Generative Decoder (DGD), a simple generative model that computes model parameters and representations directly via maximum a posteriori estimation. The DGD handles complex parameterized latent distributions naturally unlike variational autoencoders, which typically use a fixed Gaussian distribution, because of the complexity of adding other types. We first show its general functionality on a commonly used benchmark set, Fashion-MNIST. Secondly, we apply the model to multiple single-cell datasets. Here, the DGD learns low-dimensional, meaningful, and well-structured latent representations with sub-clustering beyond the provided labels. The advantages of this approach are its simplicity and its capability to provide representations of much smaller dimensionality than a comparable variational autoencoder. Availability and implementation scDGD is available as a python package at https://github.com/Center-for-Health-Data-Science/scDGD. The remaining code is made available here: https://github.com/Center-for-Health-Data-Science/dgd. [ABSTRACT FROM AUTHOR]

We study the class of first-order locally balanced Metropolis–Hastings algorithms introduced in Livingstone & Zanella (2022). To choose a specific algorithm within the class, the user must select a balancing function |$g:{\mathbb{R}}_+ \to {\mathbb{R}}_+$| satisfying |$g(t) = tg(1/t)$| and a noise distribution for the proposal increment. Popular choices within the class are the Metropolis-adjusted Langevin algorithm and the recently introduced Barker proposal. We first establish a general limiting optimal acceptance rate of 57 |$\%$| and scaling of |$n^{-1/3}$|⁠ , as the dimension |$n$| tends to infinity among all members of the class under mild smoothness assumptions on |$g$| and when the target distribution for the algorithm is of product form. In particular, we obtain an explicit expression for the asymptotic efficiency of an arbitrary algorithm in the class, as measured by expected squared jumping distance. We then consider how to optimize this expression under various constraints. We derive an optimal choice of noise distribution for the Barker proposal, an optimal choice of balancing function under a Gaussian noise distribution, and an optimal choice of first-order locally balanced algorithm among the entire class, which turns out to depend on the specific target distribution. Numerical simulations confirm our theoretical findings, and in particular, show that a bimodal choice of noise distribution in the Barker proposal gives rise to a practical algorithm that is consistently more efficient than the original Gaussian version. [ABSTRACT FROM AUTHOR]

Identification of taxa can significantly be assisted by statistical classification based on trait measurements either individually or by phylogenetic (clustering) methods. In this article, we present a general Bayesian approach for classifying species individually based on measurements of a mixture of continuous and ordinal traits, and any type of covariates. The trait vector is derived from a latent variable with a multivariate Gaussian distribution. Decision rules based on supervised learning are presented that estimate model parameters through blocked Gibbs sampling. These decision regions allow for uncertainty (partial rejection), so that not necessarily one specific category (taxon) is output when new subjects are classified, but rather a set of categories including the most probable taxa. This type of discriminant analysis employs reward functions with a set-valued input argument, so that an optimal Bayes classifier can be defined. We also present a way of safeguarding against outlying new observations, using an analogue of a p -value within our Bayesian setting. We refer to our Bayesian set-valued classifier as the Karlsson–Hössjer method, and it is illustrated on an original ornithological data set of birds. We also incorporate model selection through cross-validation, exemplified on another original data set of birds. [ABSTRACT FROM AUTHOR]

Affordable light detection and ranging sensors are becoming available for tasks such as simultaneous localization and mapping (SLAM) in robotics and autonomous driving; however, these sensors offer less quality data of lower resolution that hinders the performance of registration methods. The deep learning based approaches seem to be sensitive to these data flaws. Specifically, a state-of-the-art deep learning-based approach failed to produce meaningful results after several attempts to carry out transfer learning over a dataset collected indoors with one such affordable sensors. The paper introduces a hybrid approach combining two well-established registration techniques, the iterative closest point algorithm and the normal distributions transform that achieves good performance on the SLAM task over the same dataset. [ABSTRACT FROM AUTHOR]

We propose a model‐based clustering method for high‐dimensional longitudinal data via regularization in this paper. This study was motivated by the Trial of Activity in Adolescent Girls (TAAG), which aimed to examine multilevel factors related to the change of physical activity by following up a cohort of 783 girls over 10 years from adolescence to early adulthood. Our goal is to identify the intrinsic grouping of subjects with similar patterns of physical activity trajectories and the most relevant predictors within each group. The previous analyses conducted clustering and variable selection in two steps, while our new method can perform the tasks simultaneously. Within each cluster, a linear mixed‐effects model (LMM) is fitted with a doubly penalized likelihood to induce sparsity for parameter estimation and effect selection. The large‐sample joint properties are established, allowing the dimensions of both fixed and random effects to increase at an exponential rate of the sample size, with a general class of penalty functions. Assuming subjects are drawn from a Gaussian mixture distribution, model effects and cluster labels are estimated via a coordinate descent algorithm nested inside the Expectation‐Maximization (EM) algorithm. Bayesian Information Criterion (BIC) is used to determine the optimal number of clusters and the values of tuning parameters. Our numerical studies show that the new method has satisfactory performance and is able to accommodate complex data with multilevel and/or longitudinal effects. [ABSTRACT FROM AUTHOR]

We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed-form solutions for the error distributions of individual bins in 3d-power spectra for two estimators currently in use in the field, which we designate as 'straight-square' and 'cross-multiply' estimators. We then demonstrate when the corresponding spherically binned power spectra should (and should not) have Gaussian error distributions, which requires appealing to non-standard statements of the central limit theorem. This has important implications for how upper limits are reported, as well as how cosmological inferences are performed based on power spectrum measurements. Specifically, assuming a Gaussian error distribution can over- or underestimate the upper limit depending on the type of estimator and produces overly compact likelihood functions for the power spectrum. [ABSTRACT FROM AUTHOR]

Motivation Three-way data structures, characterized by three entities, the units, the variables and the occasions, are frequent in biological studies. In RNA sequencing, three-way data structures are obtained when high-throughput transcriptome sequencing data are collected for n genes across p conditions at r occasions. Matrix variate distributions offer a natural way to model three-way data and mixtures of matrix variate distributions can be used to cluster three-way data. Clustering of gene expression data is carried out as means of discovering gene co-expression networks. Results In this work, a mixture of matrix variate Poisson-log normal distributions is proposed for clustering read counts from RNA sequencing. By considering the matrix variate structure, full information on the conditions and occasions of the RNA sequencing dataset is simultaneously considered, and the number of covariance parameters to be estimated is reduced. We propose three different frameworks for parameter estimation: a Markov chain Monte Carlo-based approach, a variational Gaussian approximation-based approach, and a hybrid approach. Various information criteria are used for model selection. The models are applied to both real and simulated data, and we demonstrate that the proposed approaches can recover the underlying cluster structure in both cases. In simulation studies where the true model parameters are known, our proposed approach shows good parameter recovery. Availability and implementation The GitHub R package for this work is available at https://github.com/anjalisilva/mixMVPLN and is released under the open source MIT license. [ABSTRACT FROM AUTHOR]

This work focuses on the gas chemical composition of CGCG007-025. This compact dwarf is undergoing a galaxy wide star-forming burst, whose spatial behaviour has been observed by VLT/MUSE. We present a new line measurement library to treat almost 7800 voxels. The direct method chemical analysis is limited to 484 voxels with good detection of the |$[\mathrm{S}\, {\small III}]6312\, \mathring{\rm A}$| temperature diagnostic line. The recombination fluxes are corrected for stellar absorption via a population synthesis. Additionally, we discuss a new algorithm to fit photoionization models via neural networks. The eight ionic abundances analysed show a spatial normal distribution with a |$\sigma \sim 0.1\, {\rm dex}$|⁠ , where only half this value can be explained by the uncertainty in the measurements. The oxygen abundance distribution is 12 + log(O/H) = 7.88 ± 0.11. The |${\it T}_{e}[\mathrm{S}\, {\small III}]$| and ne[S  ii ] are also normally distributed. However, in the central and brightest region, the ne[S  ii ] is almost thrice the mean galaxy value. This is also reflected in the extinction measurements. The ionization parameter has a distribution of |${\rm log}(U) = -2.52^{0.17}_{0.19}$|⁠. The parameter spatial behaviour agrees with the S2+/S+ map. Finally, the discrepancies between the direct method and the photoionization model fitting are discussed. In the latter technique, we find that mixing lines with uneven uncertainty magnitudes can impact the accuracy of the results. In these fittings, we recommend overestimating the minimum flux uncertainty one order below the maximum line flux uncertainty. This provides a better match with the direct method. [ABSTRACT FROM AUTHOR]

A popular design for clinical trials assessing targeted therapies is the two‐stage adaptive enrichment design with recruitment in stage 2 limited to a biomarker‐defined subgroup chosen based on data from stage 1. The data‐dependent selection leads to statistical challenges if data from both stages are used to draw inference on treatment effects in the selected subgroup. If subgroups considered are nested, as when defined by a continuous biomarker, treatment effect estimates in different subgroups follow the same distribution as estimates in a group‐sequential trial. This result is used to obtain tests controlling the familywise type I error rate (FWER) for six simple subgroup selection rules, one of which also controls the FWER for any selection rule. Two approaches are proposed: one based on multivariate normal distributions suitable if the number of possible subgroups, k, is small, and one based on Brownian motion approximations suitable for large k. The methods, applicable in the wide range of settings with asymptotically normal test statistics, are illustrated using survival data from a breast cancer trial. [ABSTRACT FROM AUTHOR]

Measuring plant heights one by one is an important way to explore the height structure of grassland plant communities, and can be used to analyze the universal rules and regional variations of vegetation growth under environmental change. We chose grasslands in three plateaus, namely Tibetan Plateau (TP), Mongolian Plateau (MP) and Loess Plateau (LP), and set up three grassland transects along the precipitation gradients from meadow, steppe to desert. The mean height of grassland vegetation was 30.38 ± 22.44 cm, and the mean height from TP, MP to LP increased significantly. The aggregation of grassland vegetation exhibited a positive skew distribution (0.91, 3.60), and the community aggregation from TP, MP to LP tended to a normal distribution (0, 3). However, for TP, there was an exponential distribution in community aggregation of meadows, and a uniform distribution in that of desert. The explanatory effect of climate and soil nutrients on the variation of mean height in each region was more than 70%, while the explanatory effect on the community aggregation was the highest at TP, only 29%. From TP, MP to LP, response intensity of mean height to environmental changes increased significantly, and the influence of temperature and precipitation gradually increased, the influence of radiation, wind speed, and nutrients gradually weakened, and the synergy among environmental factors strengthened. Our study shows that normal distribution is a universal rule of grassland height construction, and that the synergy of environmental factors varies from region to region. [ABSTRACT FROM AUTHOR]

The Šeba billiard, a rectangular torus with a point scatterer, is a popular model to study the transition between integrability and chaos in quantum systems. Whereas such billiards are classically essentially integrable, they may display features such as quantum ergodicity [ 11 ], which are usually associated with quantum systems whose classical dynamics is chaotic. Šeba proposed that the eigenfunctions of toral point scatterers should also satisfy Berry's random wave conjecture, which implies that the value distribution of the eigenfunctions ought to be Gaussian. However, Keating, Marklof, and Winn formulated a conjecture that suggested that Šeba billiards with irrational aspect ratio violate the random wave conjecture, and we show that this is indeed the case. More precisely, for tori having diophantine aspect ratio, we construct a subsequence of the set of new eigenfunctions having even/even symmetry, of essentially full density, and show that its 4th moment is not consistent with a Gaussian value distribution. In fact, given any set |$\Lambda $| interlacing with the set of unperturbed eigenvalues, we show non-Gaussian value distribution of the Green's functions |$G_{\lambda }$|⁠ , for |$\lambda $| in an essentially full density subsequence of |$\Lambda $|⁠. [ABSTRACT FROM AUTHOR]

The progress of single-cell RNA sequencing (scRNA-seq) has led to a large number of scRNA-seq data, which are widely used in biomedical research. The noise in the raw data and tens of thousands of genes pose a challenge to capture the real structure and effective information of scRNA-seq data. Most of the existing single-cell analysis methods assume that the low-dimensional embedding of the raw data belongs to a Gaussian distribution or a low-dimensional nonlinear space without any prior information, which limits the flexibility and controllability of the model to a great extent. In addition, many existing methods need high computational cost, which makes them difficult to be used to deal with large-scale datasets. Here, we design and develop a depth generation model named Gaussian mixture adversarial autoencoders (scGMAAE), assuming that the low-dimensional embedding of different types of cells follows different Gaussian distributions, integrating Bayesian variational inference and adversarial training, as to give the interpretable latent representation of complex data and discover the statistical distribution of different types of cells. The scGMAAE is provided with good controllability, interpretability and scalability. Therefore, it can process large-scale datasets in a short time and give competitive results. scGMAAE outperforms existing methods in several ways, including dimensionality reduction visualization, cell clustering, differential expression analysis and batch effect removal. Importantly, compared with most deep learning methods, scGMAAE requires less iterations to generate the best results. [ABSTRACT FROM AUTHOR]

Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of ∼109 M⊙ and below to be detected. We test commonly used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a ∼1013 M⊙ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the baryon dominated region. To remove particle noise, we represent the projected galaxy mass distribution by a series of Gaussian profiles which precisely capture the features of the projected galaxy. We first model the lens mass as a (broken) power-law density profile and then search for small haloes. Of the two projections, one has a regular elliptical shape, while the other has distinct deviations from an elliptical shape. For the former, the broken power-law model gives no false positives and correctly recovers the mass of the superposed small halo; however, for the latter we find false positives and the inferred halo mass is overestimated by ∼4–5 times. We then use a more complex model in which the lens mass is decomposed into stellar and dark matter components. In this case, we show that we can capture the simulated galaxy's complex projected structures and correctly infer the input small halo. [ABSTRACT FROM AUTHOR]

Objectives: Rezafungin EUCAST MIC testing has been associated with notable inter-laboratory variation, which prevented ECOFF setting for C. albicans. We assessed in vitro susceptibility and reproducibility for a modified EUCAST methodology and established associated wild-type upper limits (WT-ULs).Methods: MICs against 150 clinical Candida isolates (six species), molecularly characterized fks mutants (n = 13), and QC strains (n = 6) were determined at six laboratories according to E.Def 7.3 but using Tween 20 supplemented medium. WT-ULs were determined using the derivatization method, the ECOFFinder programme and visual inspection. Consensus WT-ULs were determined.Results: The laboratory- and species-specific MIC distributions were Gaussian with >99.5% MICs within four 2-fold dilutions except for C. parapsilosis (92.8%). The following consensus WT-UL were determined: C. albicans 0.008 mg/L; C. dubliniensis and C. glabrata 0.016 mg/L; C. krusei and C. tropicalis 0.03 mg/L; and C. parapsilosis 4 mg/L. Adopting these WT-UL, six clinical isolates were non-wild-type, five of which harboured Fks alterations. For 11/13 mutants, all 670 MICs were categorized as non-wild-type whereas MICs for C. glabrata Fks2 D666Y and C. tropicalis Fks1 R656R/G overlapped with the corresponding wild-type distributions. Repeat testing of six reference strains yielded 98.3%-100% of MICs within three 2-fold dilutions except for C. albicans CNM-CL-F8555 (96%) and C. parapsilosis ATCC 22019 (93.3%).Conclusions: The modified EUCAST method significantly improved inter-laboratory variation, identified wild-type populations and allowed perfect separation of wild-type and fks mutants except for two isolates harbouring weak mutations. These consensus WT-UL have been accepted as ECOFFs and will be used for rezafungin breakpoint setting. [ABSTRACT FROM AUTHOR]

Single-cell RNA-sequencing (scRNAseq) data contain a high level of noise, especially in the form of zero-inflation, that is, the presence of an excessively large number of zeros. This is largely due to dropout events and amplification biases that occur in the preparation stage of single-cell experiments. Recent scRNAseq experiments have been augmented with unique molecular identifiers (UMI) and External RNA Control Consortium (ERCC) molecules which can be used to account for zero-inflation. However, most of the current methods on graphical models are developed under the assumption of the multivariate Gaussian distribution or its variants, and thus they are not able to adequately account for an excessively large number of zeros in scRNAseq data. In this article, we propose a single-cell latent graphical model (scLGM)—a Bayesian hierarchical model for estimating the conditional dependency network among genes using scRNAseq data. Taking advantage of UMI and ERCC data, scLGM explicitly models the two sources of zero-inflation. Our simulation study and real data analysis demonstrate that the proposed approach outperforms several existing methods. [ABSTRACT FROM AUTHOR]

Eigenvalue distributions are important dynamic quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric order-three random tensors with a Gaussian distribution as the simplest case. We first rewrite this problem as the computation of a partition function of a four-fermi theory with R replicated fermions. The partition function is exactly computed for some small- N,R cases, and is shown to precisely agree with Monte Carlo simulations. For large- N , it seems difficult to compute it exactly, and we apply an approximation using a self-consistency equation for two-point functions and obtain an analytic expression. It turns out that the real tensor eigenvalue distribution obtained by taking R = 1/2 is simply the Gaussian within this approximation. We compare the approximate expression with Monte Carlo simulations, and find that, if an extra overall factor depending on N is multiplied to the the expression, it agrees well with the Monte Carlo results. It is left for future study to improve the approximation for large- N to correctly derive the overall factor. [ABSTRACT FROM AUTHOR]

Using four mixed bivariate distributions (Normal distribution, Skew-Normal distribution, Student distribution, Skew-Student distribution) and bootstrap re-sampling analysis. We analyse the samples of CGRO/BATSE , Swift/BAT , and Fermi/GBM gamma-ray bursts in detail on the T 90–HR (Hardness Ratio) plane. The Bayesian information criterion is used to judge the goodness of fit for each sample, comprehensively. It is found that all the three samples show a symmetric (either Normal or Student) distribution. It is also found that the existence of three classes of gamma-ray bursts is preferred by the three samples, but the strength of this preference varies with the sample size: when the sample size of the data set is larger, the preference of three classes scheme becomes weaker. Therefore, the appearance of an intermediate class may be caused by a small sample size and the possibility that there are only two classes of gamma-ray bursts still cannot be expelled yet. A further bootstrap re-sampling analysis also confirms this result. [ABSTRACT FROM AUTHOR]

We develop a new analysis method that allows us to compare multidimensional observables to a theoretical model. The method is based on unsupervised clustering algorithms which assign the observational and simulated data to clusters in high dimensionality. From the clustering result, a goodness of fit (the p-value) is determined with the Fisher–Freeman–Halton test. We first show that this approach is robust for 2D Gaussian distributions. We then apply the method to the observed MW satellites and simulated satellites from the fiducial model of our semi-analytic code a-sloth  . We use the following five observables of the galaxies in the analysis: stellar mass, virial mass, heliocentric distance, mean stellar metallicity [Fe/H], and stellar metallicity dispersion σ[Fe/H]. A low p-value returned from the analysis tells us that our a-sloth  fiducial model does not reproduce the mean stellar metallicity of the observed MW satellites well. We implement an ad hoc improvement to the physical model and show that the number of dark matter merger trees which have a p-value > 0.01 increases from 3 to 6. This method can be extended to data with higher dimensionality easily. We plan to further improve the physical model in a-sloth  using this method to study elemental abundances of stars in the observed MW satellites. [ABSTRACT FROM AUTHOR]

Statistical analyses of measurements of the Hubble–Lemaître constant H 0 (163 measurements between 1976 and 2019) show that the statistical error bars associated with the observed parameter measurements have been underestimated – or the systematic errors were not properly taken into account – in at least 15–20 per cent of the measurements. The fact that the underestimation of error bars for H 0 is so common might explain the apparent discrepancy of values, which is formally known as the Hubble tension. Here we have carried out a recalibration of the probabilities with this sample of measurements. We find that the x σ deviation is indeed equivalent in a normal distribution to the x eqσ deviation in the frequency of values, where x eq = 0.83 x 0.62. Hence, a tension of 4.4σ, estimated between the local Cepheid–supernova distance ladder and cosmic microwave background (CMB) data, is indeed a 2.1σ tension in equivalent terms of a normal distribution of frequencies, with an associated probability P (> x eq) = 0.036 (1 in 28). This can be increased up to a equivalent tension of 2.5σ in the worst of the cases of claimed 6σ tension, which may occur anyway as a random statistical fluctuation. [ABSTRACT FROM AUTHOR]

Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed in recent literature, bypassing such a trade-off is still an open problem even in routine binary regression models, and there is limited theory on the quality of variational approximations in high-dimensional settings. To address this gap, we study the approximation accuracy of routinely used mean-field variational Bayes solutions in high-dimensional probit regression with Gaussian priors, obtaining novel and practically relevant results on the pathological behaviour of such strategies in uncertainty quantification, point estimation and prediction. Motivated by these results, we further develop a new partially factorized variational approximation for the posterior distribution of the probit coefficients that leverages a representation with global and local variables but, unlike for classical mean-field assumptions, it avoids a fully factorized approximation, and instead assumes a factorization only for the local variables. We prove that the resulting approximation belongs to a tractable class of unified skew-normal densities that crucially incorporates skewness and, unlike for state-of-the-art mean-field solutions, converges to the exact posterior density as |$p \rightarrow \infty$|⁠. To solve the variational optimization problem, we derive a tractable coordinate ascent variational inference algorithm that easily scales to |$p$| in the tens of thousands, and provably requires a number of iterations converging to |$1$| as |$p \rightarrow \infty$|⁠. Such findings are also illustrated in extensive empirical studies where our novel solution is shown to improve the approximation accuracy of mean-field variational Bayes for any |$n$| and |$p$|⁠ , with the magnitude of these gains being remarkable in those high-dimensional |$p>n$| settings where state-of-the-art methods are computationally impractical. [ABSTRACT FROM AUTHOR]

When disaggregation of national estimates in several domains or areas is required, direct survey estimators, which use only the domain‐specific survey data, are usually design‐unbiased even under complex survey designs (at least approximately) and require no model assumptions. Nevertheless, they are appropriate only for domains or areas with sufficiently large sample size. For example, when estimating poverty in a domain with a small sample size (small area), the volatility of a direct estimator might make that area seems like very poor in one period and very rich in the next one. Small area (or indirect) estimators have been developed in order to avoid such undesired instability. Small area estimators borrow strength from the other areas so as to improve the precision and therefore obtain much more stable estimators. However, the usual model‐based assumptions, which include some kind of area homogeneity, may not hold in real applications. A more flexible model based on multivariate mixtures of normal distributions that generalises the usual nested error linear regression model is proposed for estimation of general parameters in small areas. This flexibility makes the model adaptable to more general situations, where there may be areas with a different behaviour from the other ones, making the model less restrictive (hence, more close to nonparametric) and more robust to outlying areas. An expectation‐maximisation (E‐M) method is designed for fitting the proposed mixture model. Under the proposed mixture model, two different new predictors of general small area indicators are proposed. A parametric bootstrap method is used to estimate the mean squared errors of the proposed predictors. Small sample properties of the new predictors and of the bootstrap procedure are analysed by simulation studies and the new methodology is illustrated with an application to poverty mapping in Palestine. [ABSTRACT FROM AUTHOR]

The objective of this study was to evaluate the effect of corn silage particle size on beef quality and expression of gluconeogenic and lipogenic genes in feedlot-finished Nellore heifers. Nellore heifers (n = 94), with an initial body weight (BW) of 249.71 ± 34.62, were allotted into 32 pens (three animals per pen) in a completely randomized design, with 2 treatments and 16 repetitions. The treatments were corn silage with a particle size of 13 mm (short) or 24 mm (long). The feeding period lasted 101 d, with the first 15 d for diet adaptation. After slaughter, samples of the longissimus thoracis muscle (LT) from the left side of the half carcass and liver were taken for beef quality and gene expression analyses. The chemical composition of the beef was analyzed using near infrared according to the AOAC method 2007-04, using the FoodScanTM equipment (AOAC method: 2007-04; FOSS, Hillerod, Denmark). RT-qPCR analyses of each gene investigated were carried out using cDNA from 16 biological replicates per treatment (1 heifer chosen randomly in each pen), with each biological replicate subjected to 2 technical replicates. Relative gene expression analyses were calculated using the delta delta ct method and the reference genes used were ACTB and GAPDH. The normality of all experimental data was checked using the Shapiro-Wilk test in SAS software. When the data did not present a normal distribution, transformation was performed using PROC RANK. The model included particle size as a fixed effect and pen as a random effect. There was no treatment effect on collagen, moisture, and mineral content (P > 0.10), but muscles from heifers fed short particle sizes tended to have greater protein content (23.3 versus 22.9; P = 0.098), while muscles from heifers fed with long particles had greater intramuscular fat content (2.62 versus 3.28; P = 0.05). For liver gene expression, heifers fed short particle sizes tended to have greater expression of the PC gene (1.00 versus 0.82; P = 0.06), while PEPCK2 had higher expression in heifers fed long particles (1.00 versus 1.18; P = 0.04). In addition, the long particle size of corn silage affected the expression of PPARA (P = 0.001), and there was no effect of diets (P > 0.05) on PPARG and SREBF1 expressions (Table 1). Expression of LPL, FABP4, SCD1, CPT2 (P < 0.001), and ACACA (P = 0.017) genes increased in the muscle of heifers fed long particle size. Therefore, it is concluded that the use of corn silage with long particle size in feedlot diets has the potential to increase the expression of genes involved in lipogenesis and then increase intramuscular fat in Nellore heifers. [ABSTRACT FROM AUTHOR]

By mapping the molecular fraction of the Galactic Centre (GC), we quantitatively address the question of how much molecular and central the CMZ (central molecular zone) is. For this purpose, we analyse the CO and H  i -line archival data, and determine the column- (surface-) and volume-molecular fractions, |$f_{\rm mol}^\Sigma$| and |$f_{\rm mol}^\rho$|⁠ , which are the ratio of column-mass density of H2 projected on the sky to that of total gas (H2 + H  i) from the line intensities, and the ratio of volume-mass densities of H2 to total gas from the brightness temperature, respectively. It is shown that |$f_{\rm mol}^\Sigma$| is as high as ∼0.9–0.95 in the CMZ, and |$f_{\rm mol}^\rho$| is 0.93–0.98 in the GC Arms I and II attaining the highest value of ∼0.98 toward Sgr B2. The expanding molecular ring (EMR, or the parallelogram) has a slightly smaller |$f_{\rm mol}^\rho$| as ∼0.9–0.93. We define the CMZ as the region with |$f_{\rm mol}^\Sigma \ge 0.8\rm {-\!\!-}0.9$| between the shoulders of plateau-like distribution of H2 column density from l  = −1 |${_{.}^{\circ}}$| 1 to +1 |${_{.}^{\circ}}$| 8 having Gaussian vertical distribution with a half thickness of ±0 |${_{.}^{\circ}}$| 2. The CMZ is embedded in the Central H  i Zone (CHZ), which is defined as an H  i disc between l ∼ −2° and +2 |${_{.}^{\circ}}$| 5, b  = −0 |${_{.}^{\circ}}$| 5 and +0 |${_{.}^{\circ}}$| 5. Based on the analysis, we discuss the origin of CMZ and interstellar physics such as the volume filling factors of molecular and H  i gases inferred from the difference between |$f_{\rm mol}^\Sigma$| and |$f_{\rm mol}^\rho$|⁠. [ABSTRACT FROM AUTHOR]

In this article, we discuss the pricing performances of a large collection of GARCH models by questioning the global synergy between the choice of the affine/nonaffine GARCH specification, the use of competing alternatives to the Gaussian distribution, the selection of an appropriate pricing kernel, and the choice of different estimation strategies based on several sets of financial information. Furthermore, the study answers an important question in relation to the correlation between the performance of a pricing scheme and its ability to forecast VIX dynamics. VIX analysis clearly appears as a parsimonious first-stage filter to discard the worst GARCH option pricing models. [ABSTRACT FROM AUTHOR]