170,772 research outputs found
Asymptotic behaviour of a BIPF algorithm with an improper target
No full textsummary:The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical log-linear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even when these marginals do not come from a joint table. In this case the target distribution of the algorithm is necessarily improper. In this paper we investigate the simplest non trivial case, i. e. the hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law
Functionally Compatible Local Characteristics for the Local Specification of Priors in Graphical Models
No full textThe local specification of priors in non-decomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma distribution (conjugate prior for Poisson counts) and the Wishart distribution (conjugate prior for Gaussian models). These results link the existence of a locally specified joint prior to the solvability of a related marginal problem over the cliques of the graph. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..
A note on the IPF algorithm when the marginal problem is unsolvable
No full textsummary:In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold
Asymptotic behavior of an affine random recursion in (Z_p)^k defined by a matrix with an eigenvalue of size 1
No full textIn this paper we study the rate of convergence of the Markov chain XnC1 D AXn C Bn.mod p/, where A is an integer invertible matrix, and fBngn is a sequence of independent and identically distributed integer vectors. If A has an eigenvalue of size 1, then n D O.p2/ steps are necessary and sufficient to have Xn sampling from a nearly uniform distribution
Beta-hypergeometric distributions and random continued fractions
No full textIn this paper an enlargement of the beta family of distributions on (0, 1) is presented. Distributions in this class are characterized as being the laws of certain random continued fractions associated with products of independent random matrices of order 2 whose entries are either constant or beta distributed. The result can be proved by a famous 1879 Thomae formula on generalized hypergeometric functions 3F2
The hyper-Dirichlet process and its discrete approximations: The butterfly model
No full textThe aim of this paper is the study of some random probability distributions, called hyper-Dirichlet processes. In the simplest situation considered in the paper these distributions charge the product of three sample spaces, with the property that the first and the last component are independent conditional to the middle one. The law of the marginals on the first two and on the last two components are specified to be Dirichlet processes with the same marginal parameter measure on the common second component. The joint law is then obtained as the hyper-Markov combination, introduced in [A.P. Dawid, S.L. Lauritzen, Hyper-Markov laws in the statistical analysis of decomposable graphical models, Ann. Statist. 21 (3) (1993) 1272–1317], of these two Dirichlet processes. The processes constructed in this way are in fact generalizations of the hyper-Dirichlet laws on contingency tables considered in the above paper
LLNL Site-Specific ASCI Software Quality Engineering Recommended Practices
No full textThe LLNL Site-Specific Advanced Simulation and Computing (ASCI) Software Quality Engineering Recommended Practices VI.I\u27\u27 document describes a set of recommended software quality engineering (SQE) practices for ASCI code projects at Lawrence Livermore National Laboratory (LLNL). In this context, SQE is defined as the process of building quality into software products by applying the appropriate guiding principles and management practices. Continual code improvement and ongoing process improvement are expected benefits. Certain practices are recommended, although projects may select the specific activities they wish to improve, and the appropriate time lines for such actions. Additionally, projects can rely on the guidance of this document when generating ASCI Verification and Validation (VSrV) deliverables. ASCI program managers will gather information about their software engineering practices and improvement. This information can be shared to leverage the best SQE practices among development organizations. It will further be used to ensure the currency and vitality of the recommended practices. This Overview is intended to provide basic information to the LLNL ASCI software management and development staff from the \u27\u27LLNL Site-Specific ASCI Software Quality Engineering Recommended Practices VI.I\u27\u27 document. Additionally the Overview provides steps to using the \u27\u27LLNL Site-Specific ASCI Software Quality Engineering Recommended Practices VI.I\u27\u27 document. For definitions of terminology and acronyms, refer to the Glossary and Acronyms sections in the \u27\u27LLNL Site-Specific ASCI Software Quality Engineering Recommended Practices VI.I\u2
Global validity of the Master kinetic equation for hard-sphere systems
No full textFollowing the recent establishment of an exact kinetic theory realized by the Master kinetic equation
which describes the statistical behavior of the Boltzmann-Sinai Classical Dynamical System (CDS), in
this paper the problem is posed of the construction of the related global existence and regularity theorems.
For this purpose, based on the global prescription of the same CDS for arbitrary single- and multiplecollision
events, first global existence is extablished for the N-body Liouville equation which is written
in Lagrangian differential and integral forms. This permits to reach the proof of global existence both
of generic N-body probability density functions (PDF) as well as of particular solutions which maximize
the statistical Boltzmann-Shannon entropy and are factorized in terms of the corresponding 1-body PDF.
The latter PDF is shown to be uniquely defined and to satisfy the Master kinetic equation globally in the
extended 1-body phase space. Implications concerning the global validity of the asymptotic Boltzmann
equation and Boltzmann H-theorem are discussed
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2002 SNL ASCI Applications Software Engineering Assessment Report
No full textThis document describes the 2002 SNL Accelerated Strategic Computing Initiative (ASCI) Applications Software Quality Engineering (SQE) Assessment and the assessment results. The primary purpose of the assessment was to establish the current state of software engineering practices within the SNL ASCI Applications Program
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