For multivariate non-Gaussian involving copulas, likelihood inference is dominated by the data in the middle, and fitted models might not be very good for joint tail inference, such as assessing the strength of tail dependence. When preliminary data and likelihood analysis suggest asymmetric tail dependence, a method is proposed to improve extreme value inferences based on the joint lower and upper tails. A prior that uses previous information on tail dependence can be used in combination with the likelihood. With the combination of the prior and the likelihood (which in practice has some degree of misspecification) to obtain a tilted log-likelihood, inferences with suitably transformed parameters can be based on Bayesian computing methods or with numerical optimization of the tilted log-likelihood to obtain the posterior mode and Hessian at this mode.

Measurement errors occur very commonly in practice. After fitting the model, influence diagnostics is an important step in statistical data analysis. The most frequently used diagnostic method for measurement error models is the local influence. However, this methodology may fail to detect masked influential observations. To overcome this limitation, we propose the use of the conformal normal curvature with the forward search algorithm. The results are presented through easy to interpret plots considering different perturbation schemes. The proposed methodology is illustrated with three real data sets and one simulated data set, two of which have been previously analyzed in the literature. The third data set deals with the stability of the hygroscopic solid dosage in pharmaceutical processes to ensure the maintenance of product safety quality. In this application, the analytical mass balance is subject to measurement errors, which require attention in the modeling process and diagnostic analysis.

The estimation and visualization of process states are important for process control in chemical and industrial plants. Since industrial processes are related to Gaussian distributions theoretically, this study focused on Gaussian process latent variable models. Process state estimation and visualization methods are proposed using two latent variables based on the Bayesian Gaussian process latent variable model (BGPLVM), infinite warped mixture model (iWMM), and Gaussian process dynamical models (GPDM). The Tennessee Eastman process dataset was analyzed and it was confirmed that the performance of estimating the process states was highest in the order of GPDM, iWMM, and BGPLVM. Moreover, time-delayed process variables were added to the process variables to consider the process dynamics, which further improved the performance of estimating the process states. Particularly in the case of GPDM, only two latent variables could estimate the process states, with approximately 100% accuracy for four process states. Additionally, even 10 process states could be estimated with approximately 90% accuracy, and it was confirmed that the process state estimation and process state visualization could be achieved simultaneously.

The hypothesis implicit in the rating scale design is that the categories reflect increasing levels of the latent variable. Rasch models for ordered polytomous items include parameters, called thresholds, that allow for empirically testing this hypothesis. Failure of the thresholds to advance monotonically with the categories (a condition that is referred to as \"threshold disordering\") provides evidence that the rating scale is not functioning as intended. This work focuses on scales consisting of rather large numbers of categories, whose use is often recommended in the literature. Threshold disordering is observed in both an extended 8-point scale specially developed for the Patient Health Questionnaire-9 and the original 10-point scale of the Behavioral Religiosity Scale. The results of this work prompt practitioners not to take the functioning of the rating scale for granted, but to verify it empirically.

The sum score on a psychological test is, and should continue to be, a tool central in psychometric practice. This position runs counter to several psychometricians\' belief that the sum score represents a pre-scientific conception that must be abandoned from psychometrics in favor of latent variables. First, we reiterate that the sum score stochastically orders the latent variable in a wide variety of much-used item response models. In fact, item response theory provides a mathematically based justification for the ordinal use of the sum score. Second, because discussions about the sum score often involve its reliability and estimation methods as well, we show that, based on very general assumptions, classical test theory provides a family of lower bounds several of which are close to the true reliability under reasonable conditions. Finally, we argue that eventually sum scores derive their value from the degree to which they enable predicting practically relevant events and behaviors. None of our discussion is meant to discredit modern measurement models; they have their own merits unattainable for classical test theory, but the latter model provides impressive contributions to psychometrics based on very few assumptions that seem to have become obscured in the past few decades. Their generality and practical usefulness add to the accomplishments of more recent approaches.

In 2015 the US federal government sponsored a dengue forecasting competition using historical case data from Iquitos, Peru and San Juan, Puerto Rico. Competitors were evaluated on several aspects of out-of-sample forecasts including the targets of peak week, peak incidence during that week, and total season incidence across each of several seasons. our team was one of the winners of that competition, outperforming other teams in multiple targets/locales. In this paper we report on our methodology, a large component of which, surprisingly, ignores the known biology of epidemics at large-for example, relationships between dengue transmission and environmental factors-and instead relies on flexible nonparametric nonlinear Gaussian process (GP) regression fits that \"memorize\" the trajectories of past seasons, and then \"match\" the dynamics of the unfolding season to past ones in real-time. Our phenomenological approach has advantages in situations where disease dynamics are less well understood, or where measurements and forecasts of ancillary covariates like precipitation are unavailable, and/or where the strength of association with cases are as yet unknown. In particular, we show that the GP approach generally outperforms a more classical generalized linear (autoregressive) model (GLM) that we developed to utilize abundant covariate information. We illustrate variations of our method(s) on the two benchmark locales alongside a full summary of results submitted by other contest competitors.

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via the Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent variables to assign zero to some of the basis function coefficients with a positive probability. This procedure allows for an adaptive basis selection since it can determine the number of bases and which ones should be selected to represent functional data. Moreover, the proposed procedure measures the uncertainty of the selection process and can be applied to multiple curves simultaneously. The methodology developed can deal with observed curves that may differ due to experimental error and random individual differences between subjects, which one can observe in a real dataset application involving daily numbers of COVID-19 cases in Brazil. Simulation studies show the main properties of the proposed method, such as its accuracy in estimating the coefficients and the strength of the procedure to find the true set of basis functions. Despite having been developed in the context of functional data analysis, we also compared the proposed model via simulation with the well-established LASSO and Bayesian LASSO, which are methods developed for non-functional data.

Evaluating correlations between disease biomarkers and clinical outcomes is crucial in biomedical research. During the early stages of many chronic diseases, changes in biomarkers and clinical outcomes are often subtle. A major challenge to detecting subtle correlations is that studies with large sample sizes are usually needed to achieve sufficient statistical power. This challenge is even greater when biofluid and imaging biomarker data are used because the required procedures are burdensome, perceived as invasive, and/or expensive, limiting sample sizes in individual studies. Combining data across multiple studies may increase statistical power, but biomarker data may be generated using different assay platforms, scanner types, or processing protocols, which may affect measured biomarker values. Therefore, harmonizing biomarker data is essential to combining data across studies. Bridging studies involve re-processing of a subset of samples or imaging scans to evaluate how biomarker values vary by studies. This presents an analytic challenge on how to best harmonize biomarker data across studies to allow unbiased and optimal estimates of their correlations with standardized clinical outcomes. We conceptualize that a latent biomarker underlies the observed biomarkers across studies, and propose a novel approach that integrates the data in the bridging study with the study-specific biomarker data for estimating the biological correlations between biomarkers and clinical outcomes. Through extensive simulations, we compare our method to several alternative methods/algorithms often used to estimate the correlations. Finally, we demonstrate the application of this methodology to a real-world multi-center Alzheimer\'s disease biomarker study to correlate cerebrospinal fluid biomarker concentrations with cognitive outcomes.

Recent approaches aim to represent the dimensional structure of psychopathology, but relatively little research has rigorously tested sub-dimensions within internalizing psychopathology. This study tests pre-registered models of the dimensional structure of internalizing psychopathology, and their relations with current and lifetime depressive and anxiety disorders diagnostic data, in adult samples harmonized across three sites (n=427). Across S-1 bifactor and hierarchical models, we found converging evidence for both general and specific internalizing dimensions. Depression, generalized anxiety disorder (GAD), social anxiety disorder (SAD), and panic attacks were all associated with a general internalizing factor that we posit primarily represents motivational anhedonia. GAD was also associated with a specific anxious apprehension factor, and SAD with specific anxious apprehension and low positive affect factors. We suggest that dimensional approaches capturing shared and specific internalizing symptom facets more accurately describe the structure of internalizing psychopathology and provide useful alternatives to categorical diagnoses to advance clinical science.

Response process data from computer-based problem-solving items describe respondents\' problem-solving processes as sequences of actions. Such data provide a valuable source for understanding respondents\' problem-solving behaviors. Recently, data-driven feature extraction methods have been developed to compress the information in unstructured process data into relatively low-dimensional features. Although the extracted features can be used as covariates in regression or other models to understand respondents\' response behaviors, the results are often not easy to interpret since the relationship between the extracted features, and the original response process is often not explicitly defined. In this paper, we propose a statistical model for describing response processes and how they vary across respondents. The proposed model assumes a response process follows a hidden Markov model given the respondent\'s latent traits. The structure of hidden Markov models resembles problem-solving processes, with the hidden states interpreted as problem-solving subtasks or stages. Incorporating the latent traits in hidden Markov models enables us to characterize the heterogeneity of response processes across respondents in a parsimonious and interpretable way. We demonstrate the performance of the proposed model through simulation experiments and case studies of PISA process data.