A Note on Prediction Markets

In a prediction market, individuals can sequentially place bets on the outcome of a future event. This leaves a trail of personal probabilities for the event, each being conditional on the current individual's private background knowledge and on the previously announced probabilities of other individuals, which give partial information about their private knowledge. By means of theory and examples, we revisit some results in this area. In particular, we consider the case of two individuals, who start with the same overall probability distribution but different private information, and then take turns in updating their probabilities. We note convergence of the announced probabilities to a limiting value, which may or may not be the same as that based on pooling their private information.Comment: 12 page

Sensitivity of inferences in forensic genetics to assumptions about founding genes

Many forensic genetics problems can be handled using structured systems of discrete variables, for which Bayesian networks offer an appealing practical modeling framework, and allow inferences to be computed by probability propagation methods. However, when standard assumptions are violated--for example, when allele frequencies are unknown, there is identity by descent or the population is heterogeneous--dependence is generated among founding genes, that makes exact calculation of conditional probabilities by propagation methods less straightforward. Here we illustrate different methodologies for assessing sensitivity to assumptions about founders in forensic genetics problems. These include constrained steepest descent, linear fractional programming and representing dependence by structure. We illustrate these methods on several forensic genetics examples involving criminal identification, simple and complex disputed paternity and DNA mixtures.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS235 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference about complex relationships using peak height data from DNA mixtures

In both criminal cases and civil cases there is an increasing demand for the analysis of DNA mixtures involving relationships. The goal might be, for example, to identify the contributors to a DNA mixture where the donors may be related, or to infer the relationship between individuals based on a mixture. This paper introduces an approach to modelling and computation for DNA mixtures involving contributors with arbitrarily complex relationships. It builds on an extension of Jacquard's condensed coefficients of identity, to specify and compute with joint relationships, not only pairwise ones, including the possibility of inbreeding. The methodology developed is applied to two casework examples involving a missing person, and simulation studies of performance, in which the ability of the methodology to recover complex relationship information from synthetic data with known `true' family structure is examined. The methods used to analyse the examples are implemented in the new KinMix R package, that extends the DNAmixtures package to allow for modelling DNA mixtures with related contributors. KinMix inherits from DNAmixtures the capacity to deal with mixtures with many contributors, in a time- and space-efficient way.Comment: 29 pages, 12 figures, 20 tables; V2 has different casework examples, and general minor edits; V3 has general edits following review, including lengthier exposition; V4 has further explanation, and a supplementary appendix on related softwar

Object-oriented Bayesian networks for a decision support system for antitrust enforcement

We study an economic decision problem where the actors are two firms and the Antitrust Authority whose main task is to monitor and prevent firms' potential anti-competitive behaviour and its effect on the market. The Antitrust Authority's decision process is modelled using a Bayesian network where both the relational structure and the parameters of the model are estimated from a data set provided by the Authority itself. A number of economic variables that influence this decision process are also included in the model. We analyse how monitoring by the Antitrust Authority affects firms' strategies about cooperation. Firms' strategies are modelled as a repeated prisoner's dilemma using object-oriented Bayesian networks. We show how the integration of firms' decision process and external market information can be modelled in this way. Various decision scenarios and strategies are illustrated

Object-Oriented Bayesian Networks for a Decision Support System

We study an economic decision problem where the actors are two rms and the Antitrust Authority whose main task is to monitor and prevent rms potential anti-competitive behaviour. The Antitrust Au- thority's decision process is modelled using a Bayesian network whose relational structure and parameters are estimated from data provided by the Authority itself. Several economic variables in uencing this de- cision process are included in the model. We analyse how monitoring by the Antitrust Authority aects rms cooperation strategies. These are modelled as a repeated prisoners dilemma using object-oriented Bayesian networks, thus enabling integration of rms decision process and external market information.Antitrust Authority, Bayesian networks, mergers, model integration, prisoners dilemma, repeated games.

Default Bayes Factors for one-sided hypothesis testing

Bayesian hypothesis testing for non-nested hypotheses various "default" Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing and expected intrinsic Bayes factors. The different default methods are first compared with each other and with the p-value in normal one-sides testing, to illustrate the basic issues. General results for one-sides testing in location and scale models are then presented. The default Bayes factors are also studied for specific models involving multiple hypotheses. In most of the examples presented we also derive the intrinsic prior; this is the prior distribution which, if used directly, would yield answers (asymtotically) equivalent to those for the given default Bayes factor.Bayes factor, fractional Bayes factor, intrinsic Bayes factor, model comparison, one-sided hypothesis testing, multiple hypothesistesting

Testing the CAPM: Evidences from Italian Equity Markets

The aim of the following work is to exploit principal econometric tecniques to test the Capital Asset Pricing Model theory in Italian equity markets. CAPM is a financial model which describes expected returns of any assets (or asset portfolio) as a function of the expected return on the market portfolio. In this paper I will first explain the meaning of the market risk and I will measure it via the estimation of beta coeffcients, which are seen as a measure of assets sensitivity to market portfolio fluctuations. The theoretical framework is based on the Sharpe (1964) and Lintner (1965) version of the CAPM and on the Pettengill's hypothesis (1995) over the relationship between betas and returns. Secondly, I will test the presence of specific effects which usually occur in financial markets; in particular, I will check the presence of the well-known January effect and detect the existence of structural breaks over the considered period of time