Tractable Bayes of skew-elliptical link models for correlated binary data.

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models, the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior. The new methodology is illustrated by an application to COVID-19 data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides a better fit to our highly imbalanced dataset.

Nonparametric trend estimation in functional time series with application to annual mortality rates.

We address the problem of trend estimation for functional time series. Existing contributions either deal with detecting a functional trend or assuming a simple model. They consider neither the estimation of a general functional trend nor the analysis of functional time series with a functional trend component. Similarly to univariate time series, we propose an alternative methodology to analyze functional time series, taking into account a functional trend component. We propose to estimate the functional trend by using a tensor product surface that is easy to implement, to interpret, and allows to control the smoothness properties of the estimator. Through a Monte Carlo study, we simulate different scenarios of functional processes to show that our estimator accurately identifies the functional trend component. We also show that the dependency structure of the estimated stationary time series component is not significantly affected by the error approximation of the functional trend component. We apply our methodology to annual mortality rates in France.

HLIBCov: Parallel hierarchical matrix approximation of large covariance matrices and likelihoods with applications in parameter identification.

We provide more technical details about the HLIBCov package, which is using parallel hierarchical (H-) matrices to: •Approximate large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement.•Compute matrix-vector product, Cholesky factorization and inverse with a log-linear complexity.•Identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These unknown parameters are estimated by maximizing the joint Gaussian log-likelihood function. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.

Bayesian modeling of air pollution extremes using nested multivariate max-stable processes.

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max-stable processes. Our proposed model admits a hierarchical tree-based formulation, in which the data are conditionally independent given some latent nested positive stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max-stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.

Diagonal likelihood ratio test for equality of mean vectors in high-dimensional data.

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

A scalable multi-resolution spatio-temporal model for brain activation and connectivity in fMRI data.

Functional Magnetic Resonance Imaging (fMRI) is a primary modality for studying brain activity. Modeling spatial dependence of imaging data at different spatial scales is one of the main challenges of contemporary neuroimaging, and it could allow for accurate testing for significance in neural activity. The high dimensionality of this type of data (on the order of hundreds of thousands of voxels) poses serious modeling challenges and considerable computational constraints. For the sake of feasibility, standard models typically reduce dimensionality by modeling covariance among regions of interest (ROIs)-coarser or larger spatial units-rather than among voxels. However, ignoring spatial dependence at different scales could drastically reduce our ability to detect activation patterns in the brain and hence produce misleading results. We introduce a multi-resolution spatio-temporal model and a computationally efficient methodology to estimate cognitive control related activation and whole-brain connectivity. The proposed model allows for testing voxel-specific activation while accounting for non-stationary local spatial dependence within anatomically defined ROIs, as well as regional dependence (between-ROIs). The model is used in a motor-task fMRI study to investigate brain activation and connectivity patterns aimed at identifying associations between these patterns and regaining motor functionality following a stroke.

Spherical Process Models for Global Spatial Statistics.

Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis.

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. We extend these propriety results to cases where the response variables are censored. The latter scenario is of interest in the context of accelerated failure time models, which are relevant in survival analysis. We present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors. This study also sheds some light on the trade-off between increased model flexibility and the risk of over-fitting. We illustrate the performance of the proposed models with real data. Although we focus on models with univariate response variables, we also present some extensions to the multivariate case in the Supporting Information. Copyright © 2016 John Wiley & Sons, Ltd.

An exploratory data analysis of electroencephalograms using the functional boxplots approach.

Many model-based methods have been developed over the last several decades for analysis of electroencephalograms (EEGs) in order to understand electrical neural data. In this work, we propose to use the functional boxplot (FBP) to analyze log periodograms of EEG time series data in the spectral domain. The functional bloxplot approach produces a median curve-which is not equivalent to connecting medians obtained from frequency-specific boxplots. In addition, this approach identifies a functional median, summarizes variability, and detects potential outliers. By extending FBPs analysis from one-dimensional curves to surfaces, surface boxplots are also used to explore the variation of the spectral power for the alpha (8-12 Hz) and beta (16-32 Hz) frequency bands across the brain cortical surface. By using rank-based nonparametric tests, we also investigate the stationarity of EEG traces across an exam acquired during resting-state by comparing the spectrum during the early vs. late phases of a single resting-state EEG exam.

In vitro structure-toxicity relationship of chalcones in human hepatic stellate cells.

Xanthohumol (XN), the major prenylated chalcone from hops (Humulus lupulus L.), has received much attention within the last years, due to its multiple pharmacological activities including anti-proliferative, anti-inflammatory, antioxidant, pro-apoptotic, anti-bacterial and anti-adhesive effects. However, there exists a huge number of metabolites and structurally-related chalcones, which can be expected, or are already known, to exhibit various effects on cells. We have therefore analyzed the effects of XN and 18 other chalcones in a panel, consisting of multiple cell-based assays. Readouts of these assays addressed distinct aspects of cell-toxicity, like proliferation, mitochondrial health, cell cycle and other cellular features. Besides known active structural elements of chalcones, like the Michael system, we have identified several moieties that seem to have an impact on specific effects and toxicity in human liver cells in vitro. Based on these observations, we present a structure-toxicity model, which will be crucial to understand the molecular mechanisms of wanted effects and unwanted side-effects of chalcones.

Surface boxplots.

In this paper, we introduce a surface boxplot as a tool for visualization and exploratory analysis of samples of images. First, we use the notion of volume depth to order the images viewed as surfaces. In particular, we define the median image. We use an exact and fast algorithm for the ranking of the images. This allows us to detect potential outlying images that often contain interesting features not present in most of the images. Second, we build a graphical tool to visualize the surface boxplot and its various characteristics. A graph and histogram of the volume depth values allow us to identify images of interest. The code is available in the supporting information of this paper. We apply our surface boxplot to a sample of brain images and to a sample of climate model outputs.

On Kolmogorov Asymptotics of Estimators of the Misclassification Error Rate in Linear Discriminant Analysis.

We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.

Variogram estimation in the presence of trend.

Estimation of covariance function parameters of the error process in the presence of an unknown smooth trend is an important problem because solving it allows one to estimate the trend nonparametrically using a smoother corrected for dependence in the errors. Our work is motivated by spatial statistics but is applicable to other contexts where the dimension of the index set can exceed one. We obtain an estimator of the covariance function parameters by regressing squared differences of the response on their expectations, which equal the variogram plus an offset term induced by the trend. Existing estimators that ignore the trend produce bias in the estimates of the variogram parameters, which our procedure corrects for. Our estimator can be justified asymptotically under the increasing domain framework. Simulation studies suggest that our estimator compares favorably with those in the current literature while making less restrictive assumptions. We use our method to estimate the variogram parameters of the short-range spatial process in a U.S. precipitation data set.

Semiparametric location estimation under non-random sampling.

We study a class of semiparametric skewed distributions arising when the sample selection process produces non-randomly sampled observations. Based on semiparametric theory and taking into account the symmetric nature of the population distribution, we propose both consistent estimators, i.e. robust to model mis-specification, and efficient estimators, i.e. reaching the minimum possible estimation variance, of the location of the symmetric population. We demonstrate the theoretical properties of our estimators through asymptotic analysis and assess their finite sample performance through simulations. We also implement our methodology on a real data example of ambulatory expenditures to illustrate the applicability of the estimators in practice.

Who's asking? Patients may under-report postoperative pain scores to nurses (or over-report to surgeons) following surgery of the female reproductive tract.

OBJECTIVE: To determine if postoperative pain reporting via standardised visual analogue scale (VAS) is affected by which member of the healthcare team collects the information. MATERIALS AND METHODS: A standardised ten-point VAS measured postsurgical pain level among patients (n = 60) undergoing laparotomy via Pfannenstiel incision. All study patients received the same patient-controlled analgesia and uniform post-operative orders were used. VAS data were gathered from patients by surgeons (MD) and nurses (RN) 6 h and 24 h after surgery; RNs and MDs independently recorded patients' VAS pain scores in variable order. RESULTS: When assessed 6 h after surgery, the average pain level reported by patients to RNs was significantly lower than that reported to MDs (3.3 +/- 2.8 vs. 4.0 +/- 2.4; P = 0.02). Average patient pain levels remained lower when reported to RNs 24 h post-operatively compared to that reported to MDs, although this difference was not significant (1.9 +/- 2.1 vs. 2.1 +/- 2.1; P = 0.39). Whenever post-surgical patients provided different VAS scores for pain level to RNs and MDs, the higher pain reading was always reported to the MD. CONCLUSION: This study identified important variances in subjective pain reporting by patients that appeared to be influenced by who sampled the data. We found patients gave lower VAS pain scores to RNs compared to MDs; the reverse pattern was never observed. Post-surgical patients may communicate pain information differently depending on who asks them, particularly in the early post-operative period. Accordingly, patient pain data gathered over time by a care team with a heterogeneous composition (i.e., RNs, MDs) may not be fully interchangeable. Patient projections of pain severity and/or intensity appear to vary as a function of who evaluates the patient.

Clinical features and reproductive outcomes for embryos undergoing dual freeze-thaw sequences followed by blastocyst transfer: critique of 14 consecutive cases in IVF.

These data suggest that the physiologic stress associated with two consecutive freeze-thaw processes is likely minor. Dual freeze-thaw of embryos does not appear to adversely impact delivery rate in IVF; a livebirth delivery rate of 35.7% per transfer was observed in our population.

Nonparametric autocovariance estimation from censored time series by Gaussian imputation.

One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.

Ovarian hyperstimulation syndrome and prophylactic human embryo cryopreservation: analysis of reproductive outcome following thawed embryo transfer.

OBJECTIVE: To review utilisation of elective embryo cryopreservation in the expectant management of patients at risk for developing ovarian hyperstimulation syndrome (OHSS), and report on reproductive outcome following transfer of thawed embryos. MATERIALS AND METHODS: Medical records were reviewed for patients undergoing IVF from 2000-2008 to identify cases at risk for OHSS where cryopreservation was electively performed on all embryos at the 2 pn stage. Patient age, total number of oocytes retrieved, number of 2 pn embryos cryopreserved, interval between retrieval and thaw/transfer, number (and developmental stage) of embryos transferred (ET), and delivery rate after IVF were recorded for all patients. RESULTS: From a total of 2892 IVF cycles undertaken during the study period, 51 IVF cases (1.8%) were noted where follicle number exceeded 20 and pelvic fluid collection was present. Elective embryo freeze was performed as OHSS prophylaxis in each instance. Mean (+/- SD) age of these patients was 32 +/- 3.8 yrs. Average number of oocytes retrieved in this group was 23 +/- 8.7, which after fertilisation yielded an average of 14 +/- 5.7 embryos cryopreserved per patient. Thaw and ET was performed an average of 115 +/- 65 d (range 30-377 d) after oocyte retrieval with a mean of 2 +/- 0.6 embryos transferred. Grow-out to blastocyst stage was achieved in 88.2% of cases. Delivery/livebirth rate was 33.3% per initiated cycle and 43.6% per transfer. Non-transferred blastocysts remained in cryostorage for 24 of 51 patients (46.1%) after ET, with an average of 3 +/- 3 blastocysts refrozen per patient. CONCLUSION: OHSS prophylaxis was used in 1.8% of IVF cycles at this institution; no serious OHSS complications were encountered during the study period. Management based on elective 2 pn embryo cryopreservation with subsequent thaw and grow-out to blastocyst stage for transfer did not appear to compromise embryo viability or overall reproductive outcome. For these patients, immediate elective embryo cryopreservation and delay of ET by as little as 30 d allowed for satisfactory conclusion of the IVF sequence, yielding a livebirth-delivery rate (per ET) >40%.

A multivariate two-sample mean test for small sample size and missing data.

We develop a new statistic for testing the equality of two multivariate mean vectors. A scaled chi-squared distribution is proposed as an approximating null distribution. Because the test statistic is based on componentwise statistics, it has the advantage over Hotelling's T2 test of being applicable to the case where the dimension of an observation exceeds the number of observations. An appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments. Monte Carlo studies indicate good power compared to Hotelling's T2 and a recently proposed test by Srivastava (2004, Technical Report, University of Toronto). The test is applied to drug discovery data.