Rates of Convergence for Sequential Monte Carlo Optimization Methods

1978 ◽  
Vol 16 (1) ◽  
pp. 150-168 ◽  
Author(s):  
Harold J. Kushner
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Rates Of Convergence ◽  
Optimization Methods ◽  
Monte Carlo Optimization

scholarly journals Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting

2012 ◽  
Vol 9 (73) ◽  
pp. 1925-1933 ◽  
Author(s):  
Mariano Beguerisse-Díaz ◽  
Baojun Wang ◽  
Radhika Desikan ◽  
Mauricio Barahona
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
A Priori ◽  
Monte Carlo Optimization ◽  
Parameter Fitting ◽  
Search Optimization ◽  
Order Of Magnitude ◽  
Complex Optimization ◽  
Real Experimental Data ◽  
Modelling Process

Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy datasets. Over the years, a variety of heuristics have been proposed to solve this complex optimization problem, with good results in some cases yet with limitations in the biological setting. In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimization. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimization combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.

Estimation of the derivative of a stationary measure with respect to a control parameter

1992 ◽  
Vol 29 (2) ◽  
pp. 343-352 ◽  
Author(s):  
Felisa J. Vázquez-Abad ◽  
Harold J. Kushner
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Transition Probability ◽  
Transition Function ◽  
Stationary Measure ◽  
Time Interval ◽  
Monte Carlo Optimization ◽  
Statistical Estimates ◽  
Approximating Sequence ◽  
Step Transition

The paper deals with a problem which arises in the Monte Carlo optimization of steady state or ergodic systems which can be modelled by Markov chains. The transition probability depends on a parameter, and one wishes to find the parameter value at which some performance function is minimum. The only available data are obtained from either simulation or actual operating information. For such a problem one needs good statistical estimates of the derivatives. Conditions are given for the existence of the derivative of the stationary measure with respect to the parameter, in the sense that the derivative is a signed measure, and is the limit of the natural approximating sequence. Some properties and a useful characterization of the derivative are obtained. It is also shown that, under appropriate conditions, the derivative of the n-step transition function converges to the derivative of the stationary measure as n tends to ∞. This latter result is of particular importance whether one is simply estimating or is actually optimizing via some sequential Monte Carlo procedure, since the basic observations are always taken over a finite time interval.

Sequential Monte Carlo Optimization Using Artificial State-Space Models

2009 ◽  
Author(s):  
Joaquin Miguez ◽  
Cristina S. Maiz ◽  
Petar M. Djuric ◽  
Dan Crisan
Keyword(s):  
Monte Carlo ◽  
State Space ◽  
Sequential Monte Carlo ◽  
State Space Models ◽  
Monte Carlo Optimization

Estimation of the derivative of a stationary measure with respect to a control parameter

1992 ◽  
Vol 29 (02) ◽  
pp. 343-352 ◽  
Author(s):  
Felisa J. Vázquez-Abad ◽  
Harold J. Kushner
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Transition Probability ◽  
Transition Function ◽  
Stationary Measure ◽  
Time Interval ◽  
Monte Carlo Optimization ◽  
Statistical Estimates ◽  
Approximating Sequence ◽  
Step Transition

The paper deals with a problem which arises in the Monte Carlo optimization of steady state or ergodic systems which can be modelled by Markov chains. The transition probability depends on a parameter, and one wishes to find the parameter value at which some performance function is minimum. The only available data are obtained from either simulation or actual operating information. For such a problem one needs good statistical estimates of the derivatives. Conditions are given for the existence of the derivative of the stationary measure with respect to the parameter, in the sense that the derivative is a signed measure, and is the limit of the natural approximating sequence. Some properties and a useful characterization of the derivative are obtained. It is also shown that, under appropriate conditions, the derivative of the n-step transition function converges to the derivative of the stationary measure as n tends to ∞. This latter result is of particular importance whether one is simply estimating or is actually optimizing via some sequential Monte Carlo procedure, since the basic observations are always taken over a finite time interval.

Bayesian Estimation of DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Academic Research ◽  
Dynamic Stochastic General Equilibrium ◽  
Computational Techniques ◽  
Dsge Models ◽  
Monte Carlo Techniques ◽  
Dynamic Stochastic ◽  
Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

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