scholarly journals Graphical Model Market Maker for Combinatorial Prediction Markets

2018 ◽  
Vol 63 ◽  
pp. 421-460
Author(s):  
Kathryn Blackmond Laskey ◽  
Wei Sun ◽  
Robin Hanson ◽  
Charles Twardy ◽  
Shou Matsumoto ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Prediction Markets ◽  
Probability Models ◽  
Prediction Market ◽  
Market Mechanisms ◽  
Inference Algorithms

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

Learning Bayesian Networks

2011 ◽  
pp. 315-321
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

scholarly journals On the distribution of an arbitrary subset of the eigenvalues for some finite dimensional random matrices

2019 ◽  
Vol 09 (01) ◽  
pp. 2040004
Author(s):  
Marco Chiani ◽  
Alberto Zanella
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Random Matrices ◽  
Probability Distribution Function ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Arbitrary Subset ◽  
Finite Dimensional ◽  
Joint Probability Distribution Function

We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.

Learning Bayesian Networks

2011 ◽  
pp. 674-677
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

JOINT DISTRIBUTIONS OF PORTFOLIO LOSSES AND EXOTIC PORTFOLIO PRODUCTS

2007 ◽  
Vol 10 (04) ◽  
pp. 733-748 ◽  
Author(s):  
FRIEDEL EPPLE ◽  
SAM MORGAN ◽  
LUTZ SCHLOEGL
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Market Prices ◽  
Joint Distributions ◽  
Time Horizons ◽  
Path Dependent

The pricing of exotic portfolio products, e.g. path-dependent CDO tranches, relies on the joint probability distribution of portfolio losses at different time horizons. We discuss a range of methods to construct the joint distribution in a way that is consistent with market prices of vanilla CDO tranches. As an example, we show how our loss-linking methods provide estimates for the breakeven spreads of forward-starting tranches. .

Learning Bayesian Networks

2011 ◽  
pp. 1124-1128
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.

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