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Modeling Economic Activities and Random Catastrophic Failures of Financial Networks via Gibbs Random Fields

COMPUTATIONAL ECONOMICS 2021年第2期58卷 203-232页

作者： Onural, Levent Pinar, Mustafa Celebi Firtina, Can Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey

The complicated economic behavior of entities in a population can be modeled as a Gibbs random field (GRF). Even with simple GRF models, which restrict direct statistical interactions with a small number of neighbors of an entity, real life economic and financial activities may be effectively described. A computer simulator is developed to run empirical experiments to assess different coupling structures and parameters of the presented model;it is possible to test many economic and financial models and policies in terms of their transient and steady-state consequences.

关键词： Economic networks Financial networks Gibbs random fields Markov random fields metropolis algorithm

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Stochastic matching pursuit for Bayesian variable selection

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STATISTICS AND COMPUTING 2011年第2期21卷 247-259页

作者： Chen, Ray-Bing Chu, Chi-Hsiang Lai, Te-You Wu, Ying Nian Natl Univ Kaohsiung Inst Stat Kaohsiung Taiwan Univ Calif Los Angeles Dept Stat Los Angeles CA USA

This article proposes a stochastic version of the matching pursuit algorithm for Bayesian variable selection in linear regression. In the Bayesian formulation, the prior distribution of each regression coefficient is assumed to be a mixture of a point mass at 0 and a normal distribution with zero mean and a large variance. The proposed stochastic matching pursuit algorithm is designed for sampling from the posterior distribution of the coefficients for the purpose of variable selection. The proposed algorithm can be considered a modification of the componentwise Gibbs sampler. In the componentwise Gibbs sampler, the variables are visited by a random or a systematic scan. In the stochastic matching pursuit algorithm, the variables that better align with the current residual vector are given higher probabilities of being visited. The proposed algorithm combines the efficiency of the matching pursuit algorithm and the Bayesian formulation with well defined prior distributions on coefficients. Several simulated examples of small n and large p are used to illustrate the algorithm. These examples show that the algorithm is efficient for screening and selecting variables.

关键词： Gibbs sampler metropolis algorithm Stochastic search variable selection

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Critical exponents for extended dynamical systems with simultaneous updating:: the case of the Ising model

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PHYSICA D-NONLINEAR PHENOMENA 2002年 168卷 318-324页

作者： Pérez, G Sastre, F Medina, R Inst Politecn Nacl Dept Fis Aplicada Ctr Invest & Estudios Avanzados Apartado Postal 73 Cordemex Merida 97310 Yucatan Mexico

The behavior of a simultaneously updated metropolis simulation of the two-dimensional (2D) Ising model is explored. The configurations generated by such a simulation are not constructed to be equilibrium configurations, and may therefore display a different critical behavior, assuming a phase transition is present. This is relevant to the recently posed question of how the updating scheme affects the critical exponents for chaotic extended systems that show continuous phase transitions. It is found that the simultaneously updated algorithm drives the lattice, for all non-zero temperatures, into blinking maximum energy configurations, making it of little use. A small modification, given by a reduction in the acceptance probabilities for spin flips, restores the ability of the algorithm to generate ordered and disordered states, with a well-defined phase transition between them. The critical temperature becomes a function of the acceptance probability for energy lowering spin flips. The critical exponents still fall into the 2D Ising universality class. This happens even though the simultaneously updated metropolis algorithm does not really simulate the Ising model in equilibrium. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： metropolis algorithm Ising model phase transition

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Speedup of the metropolis protocol via algorithmic optimization

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JOURNAL OF COMPUTATIONAL SCIENCE 2023年 66卷

作者： Macias-Medri, A. E. Viswanathan, G. M. Fiore, C. E. Koehler, M. da Luz, M. G. E. Univ Fed Parana Dept Fis CP 19044 BR-81531980 Curitiba Parana Brazil Univ Fed Rio Grande do Norte Dept Phys BR-59078900 Natal RN Brazil Univ Fed Rio Grande do Norte Natl Inst Sci & Technol Complex Syst BR-59078900 Natal RN Brazil Univ Sao Paulo Inst Fis BR-05315970 Sao Paulo SP Brazil

The metropolis algorithm is widely used in Monte Carlo (MC) simulations in diverse areas of science and technology, especially for problems formulated in terms of lattice models. A common situation is the necessity to perform long sequential processing, e.g., when looking for equilibrium states of distinct physical systems. Hence, even marginal increases in efficiency of the algorithm individual steps can lead to significant reductions in absolute execution runtimes. Usual speedup procedures include hardware updates, parallelization (when possible) and sampling methods. Here we follow a different direction in trying to decrease the full execution times of MC approaches: algorithmic optimization. We show that the algorithms can be improved by implementing relatively few and simple changes in their organization and structure. First, we discuss some refinements for the pseudo-random number generator, addressing the broadly employed Mersenne-Twister algorithm (MT19937-64). Second, we develop a protocol to precalculate the Boltzmann factor, thereby avoiding the high cost of repeatedly calls to this exponential function (indeed, a very recurring step in the standard metropolis method). To benchmark our proposals we choose the Ising model since it is one of the best known and more extensively studied problems in statistical physics. We consider the mentioned optimizations and different computational elements, like compilers and Hamiltonian variables ranges, testing the efficiency to obtain the system solutions. Our results suggest that the present set of improvement schemes-namely;decreasing the processing time for both, to generate a random number and to implement the one-flip metropolis step;systematically enforcing optimization for the maximum quantity of algorithm structures accessing random numbers in a code;and considerably reducing the amount of required computations of the MC probabilistic actualization term-might constitute a relevant addition to the existing coll

关键词： metropolis algorithm Monte Carlo optimization Pseudo-random number generators Precalculated Boltzmann factor Ising model

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Quantum computation of thermal averages for a non-Abelian D4 lattice gauge theory via quantum metropolis sampling

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Physical Review D 2024年第3期109卷 034510-034510页

作者： Edoardo Ballini Giuseppe Clemente Massimo D’Elia Lorenzo Maio Kevin Zambello Pitaevskii BEC Center and Department of Physics University of Trento Via Sommarive 14 I-38123 Trento Italy INFN-TIFPA Trento Institute for Fundamental Physics and Applications Via Sommarive 14 38123 Povo Trento Italy Deutsches Elektronen-Synchrotron (DESY) Platanenallee 6 15738 Zeuthen Germany Dipartimento di Fisica dell’Università di Pisa and INFN—Sezione di Pisa Largo Pontecorvo 3 I-56127 Pisa Italy Aix Marseille Université Université de Toulon CNRS CPT UMR 7332 13288 Marseille France

In this paper, we show the application of the quantum metropolis sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group D4 in (2+1)-dimensions, discussing in general how some components of hybrid quantum-classical algorithms should be adapted in the case of gauge theories. In particular, we discuss the construction of random unitary operators which preserve gauge invariance and act transitively on the physical Hilbert space, constituting an ergodic set of quantum metropolis moves between gauge invariant eigenspaces, and introduce a protocol for gauge invariant measurements. Furthermore, we show how a finite resolution in the energy measurements distorts the energy and plaquette distribution measured via QMS, and propose a heuristic model that takes into account part of the deviations between numerical results and exact analytical results, whose discrepancy tends to vanish by increasing the number of qubits used for the energy measurements.

关键词： Finite temperature field theory Gauge theories Quantum algorithms & computation metropolis algorithm

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CONSTRAINED MONTE-CARLO MAXIMUM-LIKELIHOOD FOR DEPENDENT DATA

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 1992年第3期54卷 657-699页

作者： GEYER, CJ THOMPSON, EA UNIV WASHINGTON SEATTLE WA 98195 USA

Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this function approximates the MLE. When no parameter point in the model maximizes the likelihood, the MLE in the closure of the exponential family may exist and can be calculated by a two-phase algorithm, first finding the support of the MLE by linear programming and then finding the distribution within the family conditioned on the support by maximizing the likelihood for that family. These methods are illustrated by a constrained autologistic model for DNA fingerprint data. MLEs are compared with maximum pseudolikelihood estimates (MPLEs) and with maximum conditional likelihood estimates (MCLEs), neither of which produce acceptable estimates, the MPLE because it overestimates dependence, and the MCLE because conditioning removes the constraints.

关键词： AUTOLOGISTIC MODEL CONDITIONAL LIKELIHOOD DEOXYRIBONUCLEIC ACID FINGERPRINT GIBBS SAMPLER MAXIMUM ENTROPY metropolis algorithm PSEUDOLIKELIHOOD

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Asynchronous parallel Potts model for simulation of grain growth

Asynchronous parallel Potts model for simulation of grain gr...

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Symposium on Modeling, Control and Optimizatin in Ferrous and Nonferrous Industry held at the Materials Science and Technology Conference

作者： Manohar, PA Rollett, AD Carnegie Mellon Univ Dept Mat Sci & Engn Pittsburgh PA 15213 USA

ISBN: (纸本)0873395611

This paper describes an implementation of the Potts model for simulation of grain growth in 2D on a distributed-memory parallel architecture. The simulation scheme utilizes a continuous-time, asynchronous parallel version of the n-fold way algorithm. Each Processing Element (PE) carries a piece of the global simulation domain while the virtual topology of the PEs is in the form of a square grid in 2D and Torus in 3D. Different PEs have different local simulated times. Inter-processor communication is carried by the Message Passing Interface (MPI) routines. Sample results for grain growth simulation in 2D are presented for a 840 x 840 global domain size distributed over 16 PEs. The grain growth kinetics obtained in the simulation of pure, isotropic systems is in good agreement with the theory. Grain size distributions obtained in the parallel simulation are well described by the lognormal distribution, thus validating the simulation procedure.

关键词： metropolis algorithm n-fold way algorithm asynchronous parallelization grain growth

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Monte Carlo Renormalization Group Studies of the Baxter-Wu Model in the Presence of an External Magnetic Field

Monte Carlo Renormalization Group Studies of the Baxter-Wu M...

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International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)

作者： Velonakis, Ioannis N. Univ Athens Dept Phys GR-15784 Athens Greece

ISBN: (纸本)9780735412873

In the present work we use the well known Monte Carlo Renormalization Group method to study the phase transition of the Baxter-Wu model in the presence of a negative external magnetic field. We find that the critical exponent v is equal to 0.80 +/- 0.02, while the ratio gamma/v is 0.40 +/- 0.05. Our results are consistent to all scaling equalities, including the hyperscaling relation, within statistical errors. The validity of two usual order-parameters is also checked.

关键词： Baxter-Wu model Monte Carlo Renormalization Group critical exponents metropolis algorithm

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Bayesian Analysis of Extended Auto Regressive Model with Stochastic Volatility

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JOURNAL OF THE INDIAN SOCIETY FOR PROBABILITY AND STATISTICS 2019年第1期20卷 1-29页

作者： Tripathi, Praveen Kumar Upadhyay, Satyanshu Kumar DIT Univ Dept Math Dehra Dun 248009 Uttarakhand India Banaras Hindu Univ Inst Sci Dept Stat Varanasi 221005 UP India Banaras Hindu Univ Inst Sci DST Ctr Interdisciplinary Sci Varanasi 221005 UP India

This paper proposes an extension of the autoregressive model with stochastic volatility error. The Bayes analysis of the proposed model using vague priors for the parameters of the conditional mean equation and informative prior for the parameters of conditional volatility equation is done. The Gibbs sampler with intermediate metropolis steps is used to find out posterior inferences for the parameters of autoregressive model and independent metropolis-Hastings algorithm is used to simulate the volatility of the mean equation. The two data sets in the form of gross domestic product growth rate of India at constant prices and exchange rate of Indian rupees relative to US dollar are considered for numerical illustration. These data are used after assuring the stationarity by differencing the data once. The retrospective as well as prospective short term predictions of the data are provided based on the two simple components of the general autoregressive process. The findings based on the real data are expected to assist the policy makers and managers to make economic and business strategies more precisely.

关键词： Autoregressive model Stochastic volatility GDP growth rate Exchange rate Gibbs sampler metropolis algorithm Retrospective and prospective predictions 37M10 60J22 62C10 62M20 62F15 65C05

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Multinomial Logit Processes and Preference Discovery: Inside and Outside the Black Box

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REVIEW OF ECONOMIC STUDIES 2023年第3期90卷 1155-1194页

作者： Cerreia-Vioglio, Simone Maccheroni, Fabio Marinacci, Massimo Rustichini, Aldo Univ Bocconi Milan Italy IGIER Paris France Univ Minnesota Minneapolis MN 55455 USA

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation p(t) (a, A)= e(u(a)/lambda(t) +) (alpha(alpha))/Sigma(b is an element of A)e (u(b)/lambda(t) + alpha(b)), where p(t) (a, A) is the probability that alternative a is selected from the set A of feasible alternatives if t is the time available to decide, lambda is a time-dependent noise parameter measuring the unit cost of information, u is a time-independent utility function, and alpha is an alternative-specific bias that determines the initial choice probabilities (reflecting prior information and memory anchoring). Our axiomatic analysis provides a behavioural foundation of softmax (also known as Multinomial Logit Model when alpha is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behaviour. Jointly, the two approaches provide a thorough understanding of softmaximization in terms of internal causes (neuro-physiological mechanisms) and external effects (testable implications).

关键词： Discrete choice analysis Drift Diffusion Model Heteroscedastic extreme value models Luce model metropolis algorithm Multinomial Logit Model Quantal response equilibrium Rational inattention

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