Variational Bayesian Learning and Semiparametric Models on the Double Exponential Family

In this paper, we focus on variational Bayesian learning deterministic optimization methods for inference in biparametric exponential models where the parameters follow semiparametric regression structures. This combination of data models and algorithms contributes to solving real-world problems and reduces the computation time. This allows both the rapid exploration of many data models and the accurate estimation of the mean and variance functions through the connection between generalized linear models and graph theory. A simulation study was carried out to assess the performance of the deterministic approximation. Finally, herein, we present an application using macroeconomic data to emphasize the benefits of the proposed approach.

Semiparametric Smoothing Spline in Joint Mean and Dispersion Models with Responses from the Biparametric Exponential Family: A Bayesian Perspective

This article extends the fusion among various statistical methods to estimate the mean and variance functions in heteroscedastic semiparametric models when the response variable comes from a two-parameter exponential family distribution. We rely on the natural connection among smoothing methods that use basis functions with penalization, mixed models and a Bayesian Markov Chain sampling simulation methodology. The significance and implications of our strategy lies in its potential to contribute to a simple and unified computational methodology that takes into account the factors that affect the variability in the responses, which in turn is important for an efficient estimation and correct inference of mean parameters without the requirement of fully parametric models. An extensive simulation study investigates the performance of the estimates. Finally, an application using the Light Detection and Ranging technique, LIDAR, data highlights the merits of our approach.

EXPRESS: Negative values and variance functions: Implications for statistical analysis

When reporting concentrations of substances in biological specimens it has been virtually universal practice to suppress negative results, initially by left-censoring negative results to zero and more recently by left-censoring to values such as Limit of Blank (LoB), Limit of Detection (LoD) or even Limit of Quantification (LoQ). Negative concentrations are obviously nonsensical and current reporting practices place proper emphasis on assisting the clinician. However, it is easily overlooked that negative concentrations are merely artefacts of data reduction and while adjusting them is sensible clinical practice there are potentially adverse consequences for statistical analysis, in particular for those parametric summaries and analyses which rely on reliable estimates of low-end uncertainty. This article puts a case for the availability of negative results, describes complications with respect to estimating variance functions and discusses practical workarounds.

Classification of Pain Event Related Potential for Evaluation of Pain Perception Induced by Electrical Stimulation

Variability in individual pain sensitivity is a major problem in pain assessment. There have been studies reported using pain-event related potential (pain-ERP) for evaluating pain perception. However, none of them has achieved high accuracy in estimating multiple pain perception levels. A major reason lies in the lack of investigation of feature extraction. The goal of this study is to assess four different pain perception levels through classification of pain-ERP, elicited by transcutaneous electrical stimulation on healthy subjects. Nonlinear methods: Higuchi’s fractal dimension, Grassberger-Procaccia correlation dimension, with auto-correlation, and moving variance functions were introduced into the feature extraction. Fisher score was used to select the most discriminative channels and features. As a result, the correlation dimension with a moving variance without channel selection achieved the best accuracies of 100% for both the two-level and the three-level classification but degraded to 75% for the four-level classification. The best combined feature group is the variance-based one, which achieved accuracy of 87.5% and 100% for the four-level and three-level classification, respectively. Moreover, the features extracted from less than 20 trials could not achieve sensible accuracy, which makes it difficult for an instantaneous pain perception levels evaluation. These results show strong evidence on the possibility of objective pain assessment using nonlinear feature-based classification of pain-ERP.

Research methodology

Given the diversity of psychiatric research, having a statistically rigorous set of methodological tools for the design and analysis is critically important. The field of psychiatry has, in and of itself, inspired several advances in research methodology that have led to widespread use across all areas of medicine and, more generally, throughout the biological, social, and physical sciences. This chapter reviews statistical and methodological contributions to the analysis of longitudinal data, inter-rater agreement, item response theory (IRT), and computerized adaptive testing (CAT), as well as the joint modelling of both the mean and variance functions in intensive longitudinal data (location-scale models). It is written for a general psychiatric research audience, but lays out areas for future study and development for quantitative scientists as well.

Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families

The Rao-Blackwell theorem has had a fundamental role in statistical theory. However, as opposed to what seems natural, Rao and Blackwell did not investigate and write the theorem jointly. In fact, they both published the same result independently, two years apart. Indeed, as C.R. Rao writes in Wikipedia: ”the result on one parameter case was published by Rao (1945) in the Bulletin of the Calcutta Mathematical Society and by Blackwell (1947) in The Annals of Mathematical Statistics. Only Lehmann and Sche ´e (1950) called the result as Rao-Blackwell theorem”. Forty years later, a situation very similar to the previous one seems to have happened. Tweedie (1984) in a paper published in a proceedings to a conference held in Calcutta and Bar-Lev and Enis (1986) in a paper published in The Annals of Statistics both presented for the first time, albeit two years apart, independently and in di erent contexts, the class of natural exponential families having power variance functions (NEF-PVFs). Tweedie’s results were then mentioned by Jorgensen (1987) in his fundamental paper on exponential dispersion models published in the Journal of the Royal Statistical Society, Series B. Jorgensen, however, mentioned also other researchers, including Bar-Lev and Enis, as dealt with the same problem. Nonetheless, Jorgensen (1987) stated in his paper that ”The most complete study” of NEF-PVFs was given by Tweedie (1984), a statement which has led to naming the class of NEF-PVFs as the Tweedie class. This statement of Jorgensen is entirely and utterly incorrect. Accordingly, one of the goals of this note is to 'prove' such incorrectness. Based on this 'proof' it will be evident, so I trust, that both Bar-Lev and Enis should have received the appropriate credit by re-naming the class of NEF-PVFs via the exploitation of the names of Tweedie, Bar-Lev and Enis. This would resemble the dignified and elegant manner Lehmann and Sche ´e acted on the Rao-Blackwell Theorem. Notwithstanding, the main aim of the note is to encourage young researchers to present their results with self-confidence and to get the credit they deserve.