Robust Bayesian analysis of loss reserving data using scale mixtures distributions

It is vital for insurance companies to have appropriate levels of loss reserving to pay outstanding claims and related settlement costs. With many uncertainties and time lags inherently involved in the claims settlement process, loss reserving therefore must be based on estimates. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserving. This paper extends the conventional normal error distribution in loss reserving modeling to a range of heavy-tailed distributions which are expressed by certain scale mixtures forms. This extension enables robust analysis and, in addition, allows an efficient implementation of Bayesian analysis via Markov chain Monte Carlo simulations. Various models for the mean of the sampling distributions, including the log-Analysis of Variance (ANOVA), log-Analysis of Covariance (ANCOVA) and state space models, are considered and the straightforward implementation of scale mixtures distributions is demonstrated using OpenBUGS.     

Un cas élémentaire d'oscillations

The probability laws describing the numbers of oscillations of the continuous symmetric random walk express themselves through the numbers of Stirling of first kind. The asymptotic behavior can easily be derived using characteristic functions.     

Victims of the Genocidal Mind: Societal Indicators and Individual Case Treatment Considerations

This paper uses the theoretical lens of object relations and takes the position that the paranoid-schizoid position and the related mechanism of projective identification—cornerstone pathology found in the phenomenon of fascism and totalitarianism—are not atypical, but rather live within the seemingly normal individual. Using Rwanda as a case example, the author illustrates the continuum of beliefs and actions that can result in genocide, and then describes some of the treatment considerations facing the clinician dealing with victims of genocide.

Brexit and the Future of the Left

The referendum on British membership in the European Union divided not only the society in the UK but also the left both in Britain and all over the continent. This division however is produced not so much by this specific debate but by a deeper problem of the left capitulating ideologically and accepting neoliberalism as something objectively inevitable (even without publically recognizing it), replacing class struggle by ‘progressive’ cultural values that themselves form an essential part of the new capitalist hegemony. Leftist intelligentsia with its cultural critique of capitalism is no alternative to the current system, rather it is one of its pillars. While class division was very visible in the Brexit vote, with the working class and poor massively voting for ‘Leave’, most of the left either sided with the establishment or was wavering. Thus the success of the ‘Leave’ vote can be claimed by nationalists. Even after this political disaster instead criticizing itself leftist intelligentsia is blaming the people for being provincial and not accepting their progressive European values. However it was exactly the mass of common people in England who by voting for ‘Leave’ contributed to the formation of the new European agenda. Overcoming and unmaking bureaucratic, authoritarian, and neoliberal EU institutions is the only way to progress towards the making of a new democratic Europe.     

Loss-based optimal control statistics for control charts

This work proposes a means for interconnecting optimal sample statistics with parameters of the process output distribution irrespective of the specific way in which these parameters change during transition to the out-of-control state (jumps, trends, cycles, etc). The approach, based on minimization of the loss incurred by the two types of decision errors, leads to a unique sample statistic and, therefore, to a single control chart. The optimal sample statistics are obtained as a solution of the developed optional boundary equation. The paper demonstrates that, for particular conditions, this equation leads to the same statistics as are obtained through the Neyman-Pearson fundamental lemma. Application examples of the approach when the process output distribution is Gamma and Weibull are given. A special loss function representing out-of-control state detection as a pattern recognition problem is presented.     

Empirical Bayes models of Poisson clinical trials and sample size determination

Bayesian methods are often used to reduce the sample sizes and/or increase the power of clinical trials. The right choice of the prior distribution is a critical step in Bayesian modeling. If the prior not completely specified, historical data may be used to estimate it. In the empirical Bayesian analysis, the resulting prior can be used to produce the posterior distribution. In this paper, we describe a Bayesian Poisson model with a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework under two estimation schemes. The straightforward numerical search for the maximum likelihood (ML) solution using the marginal negative binomial distribution is unfeasible occasionally. We propose a simplification to the maximization procedure. The Markov Chain Monte Carlo method is used to create a set of Poisson parameters from the historical count data. These Poisson parameters are used to uniquely define the Gamma likelihood function. Easily computable approximation formulae may be used to find the ML estimations for the parameters of gamma distribution. For the sample size calculations, the ML solution is replaced by its upper confidence limit to reflect an incomplete exchangeability of historical trials as opposed to current studies. The exchangeability is measured by the confidence interval for the historical rate of the events. With this prior, the formula for the sample size calculation is completely defined. Published in 2009 by John Wiley & Sons, Ltd.     

Employment‐Housing Paradigm of Internal Migration: Evidence from Norway

In a previous article (Portnov, 1999), the employment‐housing paradigm of interregional migration was introduced. According to this paradigm, different patterns of employment‐housing change in various geographic areas are likely to result in three different migration events – predominant in migration, out‐migration or “migration neutrality”. The latter is considered as a state of equilibrium in which a region or community neither gains nor loses its population in migration exchanges with other areas. Using preconditions for such migration neutrality as a “reference line”, planners and decision‐makers can determine regional policies aimed at a more balanced distribution of a country's population through generating a “migration push” in overpopulated regions and encouraging inward migration to development areas in which population growth is desirable. In the present article, the validity of this concept is tested using 1970‐89 statistical data for 430 municipalities in Norway. It appeared feasible to separate the band of migration neutrality from other migration cases and establish the quantitative thresholds of employment‐housing change that are conducive to the occurrence of different migration events – migration neutrality, in‐migration and out‐migration.     

Return to Education and the Changing Role of Credentials in the Croatian Labor Market

The countries of Central and Eastern Europe experienced a rapid increase of return to education with the advent of the transition. We look at the dynamics of wage premiums in Croatia and estimate how much the return to education has changed between 1996 and 2004 on the basis of labor force survey data. We also extend the paper in order to address additional features of the wage structure, such as non-linearities in the return to education associated with attainment of credentials. We find that contrary to most transition countries, premiums for education in Croatia began to grow only after the mid 1990s. However, by 2004, they reached the levels of premiums found in other transition countries and advanced market economies, thus creating market incentives for investment in education. We also find that major part of this higher rate of return came through higher return to credentials.

Authors’ response

In this rejoinder, we address all or almost all comments that have been provided by the discussants. In particular, we include additional references to literature related to change-point detection as well as to intrusion detection; analyze distributions of stopping times of the CUSUM and Shiryaev–Roberts detection procedures under the no change hypothesis in more detail; and provide an overview of the detection-isolation problem.