Statistical analysis of data sets with missing values is a pervasive problem for which standard methods are of limited value. The first edition of Statistical Analysis with Missing Data has been a standard reference on missing-data methods. Now, reflecting extensive developments in Bayesian methods for simulating posterior distributions, this Second Edition by two acknowledged experts on the subject offers a thoroughly up-to-date, reorganized survey of current methodology for handling missing-data problems.

Statistical Analysis with Missing Data

<h2>Abstract</h2> Beta oscillations are linked to the control of goal-directed processing of sensory information and the timing of motor output. Recent evidence demonstrates they are not sustained but organized into intermittent high-power bursts mediating timely functional inhibition. This implies there is a considerable moment-to-moment variation in the neural dynamics supporting cognition. Beta bursts thus offer new opportunities for studying how sensory inputs are selectively processed, reshaped by inhibitory cognitive operations and ultimately result in motor actions. Recent method advances reveal diversity in beta bursts that provide deeper insights into their function and the underlying neural circuit activity motifs. We propose that brain-wide, spatiotemporal patterns of beta bursting reflect various cognitive operations and that their dynamics reveal nonlinear aspects of cortical processing. 

Beta: bursts of cognition

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability.

The advantages of a simulation-based approach are highlighted, giving a full predictive distribution, which is used to estimate risk margins under Solvency II and risk adjustments under IFRS 17. We discuss methods for obtaining capital requirements in a cost-of-capital risk margin, and methods for estimating risk adjustments using risk measures applied to a simulated distribution of the outstanding liabilities over their lifetime.

/pdf/on-the-lifetime-and-one-year-views-of-reserve-risk-with-54io5my4rs.pdf

On the Lifetime and One-Year Views of Reserve Risk, with Application to IFRS 17 and Solvency II Risk Margins

This article presents the results of a case study from one professor’s experience teaching an introductory statistics course. The goal of this study was to better understand student perceptions of ...

Student Perceptions of Engagement in an Introductory Statistics Course.

/pdf/on-the-lifetime-and-one-year-views-of-reserve-risk-with-88fye9yi1p.pdf

On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins

This is the first study to derive closed-form analytical expressions for multi-year non-life insurance risk in the chain ladder model. Extending on previous research on the additive reserving model, we define multi-year risk via prediction errors of multi-year claims development results including both observed and future accident years. A resampling argument and a first-order Taylor approximation address the quantification of estimation errors and multiplicative dependencies in the chain ladder framework, respectively. From our generalized multi-year approach, we deduce estimators for reserve and premium risks in multi-year view and their implicit correlation. We reproduce well-known results from literature for the special cases of one-year and ultimo view. Further, we comment on how to obtain estimators for generalized versions of the chain ladder method. A case study demonstrates the applicability of our analytical formulae.

Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

In this paper, we describe an in-class experiment that is easy to implement with large groups of students. The experiment takes approximately 15-20 minutes to run and involves each student completing one of four types of Sudoku puzzles and recording the time it takes to completion. The resulting data set can be used as a teaching tool at an introductory level right through to an advanced level of statistics. Basic methods for describing and displaying data as well as the intricacies that arise with real data may be discussed in an introductory course. The range of more sophisticated analyses that can be taught with the data set include chi-squared tests for independence, ANOVA, t- and F-tests, logistic regression and survival analysis. We describe and provide the tools to implement the experiment and illustrate several potential teaching topics using a collected data set.

Engaging Students in a Large Lecture: An Experiment Using Sudoku Puzzles.

https://doi.org/10.1016/j.pneurobio.2022.102372

Oscillations without cortex: Working memory modulates brainwaves in the endbrain of crows

We derive analytical estimators of non-life insurance risk in multi-year view for the multivariate additive loss reserving model. Thereby we jointly assess reserve and premium risks of multiple years for portfolios of possibly dependent lines of business in one integrated approach. By extending existing formulae for the univariate additive model to the multivariate case, risk estimators for the aggregated portfolio now include the inherent dependencies among all lines of business. The resulting risk evaluation over one-year and general multi-year horizons is fundamental to regulatory reporting (e.g. the ORSA process in Solvency II) and risk-based business planning of non-life insurers with multiple lines of business. A case study illustrates the fruitful application of our formulae and reproduces previous findings for the special case of ultimo view.

Multi-year non-life insurance risk of dependent lines of business in the multivariate additive loss reserving model

This is the first study to derive closed-form analytical expressions for multi-year non-life insurance risk in the chain ladder model. Extending on previous research on the additive reserving model, we define multi-year risk via prediction errors of multi-year claims development results including both observed and future accident years. A resampling argument and a first-order Taylor approximation address the quantification of estimation errors and multiplicative dependencies in the chain ladder framework, respectively. From our generalized multi-year approach, we deduce estimators for reserve and premium risks in multi-year view and their implicit correlation. We reproduce well-known results from literature for the special cases of one-year and ultimo view. Further, we comment on how to obtain estimators for generalized versions of the chain ladder method. A case study demonstrates the applicability of our analytical formulae. Highlights • Closed-form analytical expressions for multi-year non-life insurance risk. • Approach based on the chain ladder method using a first-order Taylor approximation. • Previous accident years and new accident years in one integrated analytical model. • Deduction of well-known results for one-year and ultimate reserve risk from our model. • Case study demonstrating the applicability and usefulness of our results. 1University of Ulm, 89081 Ulm, Germany, e-mail: dorothea.diers@provinzial.de 2BELTIOS P&C GmbH, 50688 Köln, Germany, e-mail: marc.linde@beltios.com 3University of Ulm, 89081 Ulm, Germany & Institute for Finance and Actuarial Sciences (ifa), 89081 Ulm, Germany, e-mail: l.hahn@ifa-ulm.de

Quantitative assessment of multi-year non-life insurance risk

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