Subjective Performance Evaluation and Inequality Aversion

Many firms use subjective performance appraisal systems due to lack of objective performance measures. In these cases, supervisors usually have to rate the performance of their subordinates. Using such systems, it is a well established fact that many supervisors tend to assess the employees too good (leniency bias) and that the appraisals hardly vary across employees of a certain supervisor (centrality bias). We explain these two biases in a model with a supervisor, who has preferences for the utility of her inequality averse subordinates, and discuss determinants of the size of the biases. Extensions of the basic model include the role of supervisor’s favoritism of one particular agent and the endogenous effort choice of agents. Whether inequality averse agents exert higher efforts then purely self-oriented ones, depends on the size of effort costs and inequality aversion.appraisals, inequality aversion, performance evaluation, centrality bias, leniency bias

Rejoinder: Harold Jeffreys's Theory of Probability Revisited

We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of Theory of Probability is alive and lasting. [arXiv:0804.3173]Comment: Published in at http://dx.doi.org/10.1214/09-STS284REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing hypotheses via a mixture estimation model

We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a specific model is to consider the models under comparison as components of a mixture model. We therefore replace the original testing problem with an estimation one that focus on the probability weight of a given model within a mixture model. We analyze the sensitivity on the resulting posterior distribution on the weights of various prior modeling on the weights. We stress that a major appeal in using this novel perspective is that generic improper priors are acceptable, while not putting convergence in jeopardy. Among other features, this allows for a resolution of the Lindley-Jeffreys paradox. When using a reference Beta B(a,a) prior on the mixture weights, we note that the sensitivity of the posterior estimations of the weights to the choice of a vanishes with the sample size increasing and avocate the default choice a=0.5, derived from Rousseau and Mengersen (2011). Another feature of this easily implemented alternative to the classical Bayesian solution is that the speeds of convergence of the posterior mean of the weight and of the corresponding posterior probability are quite similar.Comment: 25 pages, 6 figures, 2 table

Asymptotic Properties of Approximate Bayesian Computation

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, its limiting shape, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including supplementary materia