6,218 research outputs found
Why bayesian âevidence for H1â in one condition and bayesian âevidence for H0â 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 Ă 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 Ï = (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(Ï) = { x | x is a mean of Ï } 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 Arrowâs theorem, all voting methods must be seriously flawed. Arrowâs 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 Arrowâs result.
Parallel to Arrowâs 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 Arrowâs theorem, but rather from restrictions imposed on votersâ expression of their preferences.
The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior
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
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 visâĂĄâvis 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
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
Profiling a decade of information systems frontiersâ 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, authorsâ 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
The Limits to Sustainability Science: Ecological Constraints or Endless Innovation?
Ecological principles must govern sustainability, yet sustainability science is largely concerned with social-environmental interactions and barely considers physical limits on resource use. Whether it is possible to overcome such limits can be contested, but the issues raised by a macroecological perspective should be a fundamental part of the United Nations Conference on Sustainable Development (Rio+20)
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