136 research outputs found
Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach
This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game
An overview of the essential differences and similarities of system identification techniques
Information is given in the form of outlines, graphs, tables and charts. Topics include system identification, Bayesian statistical decision theory, Maximum Likelihood Estimation, identification methods, structural mode identification using a stochastic realization algorithm, and identification results regarding membrane simulations and X-29 flutter flight test data
Classes of decision analysis
The ultimate task of an engineer consists of developing a consistent decision procedure for the
planning, design, construction and use and management of a project. Moreover, the utility over the
entire lifetime of the project should be maximized, considering requirements with respect to safety
of individuals and the environment as specified in regulations. Due to the fact that the information
with respect to design parameters is usually incomplete or uncertain, decisions are made under
uncertainty. In order to cope with this, Bayesian statistical decision theory can be used to incorporate
objective as well as subjective information (e.g. engineering judgement). In this factsheet, the
decision tree is presented and answers are given for questions on how new data can be combined
with prior probabilities that have been assigned, and whether it is beneficial or not to collect more
information before the final decision is made. Decision making based on prior analysis and posterior
analysis is briefly explained. Pre-posterior analysis is considered in more detail and the Value of
Information (VoI) is defined
Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach
This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game
Probabilistic Sensitivity Analysis in Health Economics
Health economic evaluations have recently built upon more advanced statistical decision-theoretic foundations and nowadays it is officially required that uncertainty about both parameters and observable variables be taken into account thoroughly, increasingly often by means of Bayesian methods. Among these, Probabilistic Sensitivity Analysis (PSA) has assumed a predominant role and Cost Effectiveness Acceptability Curves (CEACs) are established as the most important tool. The objective of
this paper is to review the problem of health economic assessment from the standpoint of Bayesian statistical decision theory with particular attention to the philosophy underlying the procedures for sensitivity analysis. We advocate here the use of an integrated vision that is based on the value of information analysis, a procedure that is well grounded in the theory of decision under uncertainty, and criticise the indiscriminate use of other approaches to sensitivity analysis
Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions
Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. The main difference between the Bayesian theory of games and the current games theory are: I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory. II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria. III. It differentiates between simultaneous move and imperfect information. The Bayesian theory of games treats sequential move with imperfect information as a special case of sequential move with observational noise term. When the variance of the noise term approaches its maximum such that the observation contains no informational value, there is imperfect information (with sequential move). IV. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games.Games Theory, Bayesian Statistical Decision Theory, Prior Distribution Function, Conjectures, Subjective Probabilities
Bayesian Analysis of ODE's: solver optimal accuracy and Bayes factors
In most relevant cases in the Bayesian analysis of ODE inverse problems, a
numerical solver needs to be used. Therefore, we cannot work with the exact
theoretical posterior distribution but only with an approximate posterior
deriving from the error in the numerical solver. To compare a numerical and the
theoretical posterior distributions we propose to use Bayes Factors (BF),
considering both of them as models for the data at hand. We prove that the
theoretical vs a numerical posterior BF tends to 1, in the same order (of the
step size used) as the numerical forward map solver does. For higher order
solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes
that would take far less computational effort. Considerable CPU time may be
saved by using coarser solvers that nevertheless produce practically error free
posteriors. Two examples are presented where nearly 90% CPU time is saved while
all inference results are identical to using a solver with a much finer time
step.Comment: 28 pages, 6 figure
Multiple integral representation for functionals of Dirichlet processes
We point out that a proper use of the Hoeffding--ANOVA decomposition for
symmetric statistics of finite urn sequences, previously introduced by the
author, yields a decomposition of the space of square-integrable functionals of
a Dirichlet--Ferguson process, written , into orthogonal subspaces of
multiple integrals of increasing order. This gives an isomorphism between
and an appropriate Fock space over a class of deterministic functions.
By means of a well-known result due to Blackwell and MacQueen, we show that
each element of the th orthogonal space of multiple integrals can be
represented as the limit of -statistics with degenerate kernel of
degree . General formulae for the decomposition of a given functional are
provided in terms of linear combinations of conditioned expectations whose
coefficients are explicitly computed. We show that, in simple cases, multiple
integrals have a natural representation in terms of Jacobi polynomials. Several
connections are established, in particular with Bayesian decision problems, and
with some classic formulae concerning the transition densities of multiallele
diffusion models, due to Littler and Fackerell, and Griffiths. Our results may
also be used to calculate the best approximation of elements of by
means of -statistics of finite vectors of exchangeable observations.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ5169 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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