Why bayesian “evidence for H1” in one condition and bayesian “evidence for H0” in another condition does not mean good-enough bayesian evidence for a difference between the conditions

Psychologists are often interested in whether an independent variable has a different effect in condition A than in condition B. To test such a question, one needs to directly compare the effect of that variable in the two conditions (i.e., test the interaction). Yet many researchers tend to stop when they find a significant test in one condition and a nonsignificant test in the other condition, deeming this as sufficient evidence for a difference between the two conditions. In this Tutorial, we aim to raise awareness of this inferential mistake when Bayes factors are used with conventional cutoffs to draw conclusions. For instance, some researchers might falsely conclude that there must be good-enough evidence for the interaction if they find good-enough Bayesian evidence for the alternative hypothesis, H1, in condition A and good-enough Bayesian evidence for the null hypothesis, H0, in condition B. The case study we introduce highlights that ignoring the test of the interaction can lead to unjustified conclusions and demonstrates that the principle that any assertion about the existence of an interaction necessitates the direct comparison of the conditions is as true for Bayesian as it is for frequentist statistics. We provide an R script of the analyses of the case study and a Shiny app that can be used with a 2 × 2 design to develop intuitions on this issue, and we introduce a rule of thumb with which one can estimate the sample size one might need to have a well-powered design

Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The "Statistical Curse of the Second Half Rank" is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior

How Do Households Discount Over Centuries? Evidence from Singapore's Private Housing Market

We examine Singapore's fairly homogeneous private-housing market and show that new apartments on historical multi-century leases trade at a non-zero discount relative to property owned in perpetuity. Descriptive regressions indicate that new apartments with 825 to 986 years of tenure remaining are priced 4 to 6% below new apartments under perpetual ownership contracts that are otherwise comparable. We consider an empirical model in which asset value is decomposed into the utility of housing services and a second factor that shifts with asset tenure and the discount rate schedule. Exploiting the supply of new property with tenure ranging from multiple decades to multiple centuries, we estimate the discount rate schedule, restricting it to vary smoothly over time through alternative parametric forms. Across different specifications and subsamples, we estimate discount rates that decline over time and, accounting for the observed price differences, are of the order of 0.5% p.a. by year 400-500. The finding that households making sizable transactions do not entirely discount benefits accruing many centuries from today is new to the empirical literature on discounting and, with the appropriate risk adjustment, of relevance to evaluating climate-change investments

Why physicians are lousy gatekeepers: Sicklisting decisions when patients have private information on symptoms

In social insurance systems that grant workers paid sick leave, physicians act as gatekeepers, supposedly granting sickness certificates to the sick and not to shirkers. Previous research has emphasized the physician's superior ability to judge patients' need of treatment and potential collusion with the patient vis‐á‐vis an insurer. What is less well understood is the role of patients' private information. We explore the case where patients have private information about the presence of nonverifiable symptoms. Anyone can then claim to experience such symptoms, reducing physicians' ability to distinguish between sick patients and shirkers. Doubting a patients' reported symptoms may prevent good medical treatment of the truly sick. We show that for all parameter values, the Bayesian Nash equilibrium is that some physicians trust all claims of nonverifiable symptoms, sicklisting shirkers as well as sick; for many values, every physician is trusting. In particular, if physician strategies are observable by patients, extremely strong gatekeeping preferences are required to make physicians mistrust. To limit unwarranted sicklisting, policies reducing the benefits of shirking for healthy workers may be better suited than attempts to convince physicians to be strict.publishedVersio

Adaptive Investment Strategies For Periodic Environments

In this paper, we present an adaptive investment strategy for environments with periodic returns on investment. In our approach, we consider an investment model where the agent decides at every time step the proportion of wealth to invest in a risky asset, keeping the rest of the budget in a risk-free asset. Every investment is evaluated in the market via a stylized return on investment function (RoI), which is modeled by a stochastic process with unknown periodicities and levels of noise. For comparison reasons, we present two reference strategies which represent the case of agents with zero-knowledge and complete-knowledge of the dynamics of the returns. We consider also an investment strategy based on technical analysis to forecast the next return by fitting a trend line to previous received returns. To account for the performance of the different strategies, we perform some computer experiments to calculate the average budget that can be obtained with them over a certain number of time steps. To assure for fair comparisons, we first tune the parameters of each strategy. Afterwards, we compare the performance of these strategies for RoIs with different periodicities and levels of noise.Comment: Paper submitted to Advances in Complex Systems (November, 2007) 22 pages, 9 figure

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Reservefonds gegen Naturkatastrophen auf nationaler und europäischer Ebene

Katastrophenfonds funktionieren nach dem Prinzip der Kapitalakkumulation. Sie werden teilweise auf nationaler und europäischer Ebene eingesetzt, um sich gegen die finanziellen Schäden, verursacht durch extreme Naturereignisse, zu schützen. Basierend auf Beispielen in Europa, wie dem österreichischen Katastrophenfonds sowie dem europäischen Solidaritätsfonds, werden die Vor- und Nachteile von Reservefonds aufgezeigt und mögliche Lösungsvorschläge für gegenwärtige Probleme präsentiert. Vor allem die nichtrisikobasierte Anwendung wird als Problem betrachtet. Es werden Methoden vorgestellt, wie ein wahrscheinlichkeitstheoretischer Ansatz aussehen könnte, um sowohl direkte als auch indirekte Schäden bei der Analyse mit einzubeziehen und daraus Strategien zu entwickeln, die sich langfristig als nachhaltig erweisen.Catastrophe reserve funds are used to cover the potential costs of a disaster by capital accumulation. Based on examples in Europe, especially the national disaster fund in Austria and the European Solidarity Fund, the advantages and disadvantages of such a risk management instrument are shown and possible solutions are proposed. The main criticism is the non-risk based approach of these instruments. Methodologies how one can incorporate direct as well as indirect losses within a probability based approach are presented

Profiling a decade of information systems frontiers’ research

This article analyses the first ten years of research published in the Information Systems Frontiers (ISF) from 1999 to 2008. The analysis of the published material includes examining variables such as most productive authors, citation analysis, universities associated with the most publications, geographic diversity, authors’ backgrounds and research methods. The keyword analysis suggests that ISF research has evolved from establishing concepts and domain of information systems (IS), technology and management to contemporary issues such as outsourcing, web services and security. The analysis presented in this paper has identified intellectually significant studies that have contributed to the development and accumulation of intellectual wealth of ISF. The analysis has also identified authors published in other journals whose work largely shaped and guided the researchers published in ISF. This research has implications for researchers, journal editors, and research institutions