Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

Stress intensity factor histories of a steadily propagating crack under 3-D combined mode traction

Elastodynamic stress intensity factor histories of an unbounded solid containing a semi-infinite plane crack that propagates at a constant velocity under 3-D time-independent combined mode loading are considered. The fundamental solution, which is the response of point loading, is obtained. Then, stress intensity factor histories of a general loading system are written out in terms of superposition integrals. The methods used here are the Laplace transform methods in conjunction with the Wiener-Hopf technique.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

球形粒子的热致迁移及各跳跃系数对适应系数的依赖关系

本文讨论有温度梯度场的稀薄气体(K_n(?)1时)中圆球所受的热泳力问题。在内区设分子在壁面作Maxwell类型反射求解B-K-W方程,与外区的Stokes方程和Laplace方程的解匹配。滑移系数C_m,热蠕动系数C_s和温度跳跃系数C_t,做为待定量在内区解的一阶近似中定出。所得的热泳力与实验相符,计算所得的C_m,C_s和C_t之值及对适应系数α的依赖关系与用变分等方法对平板问题所得结果相符。

分层流中的瞬变波

本文用Laplace-Fourier变换方法研究两层流体中的瞬变波,分析了近似色散关系,讨论了不同模式波的主次关系,导出了由初始位移、大气扰动、水下爆炸,地震等因素所激励的表面波和内波的波形及其远场的渐近表达式。

摄动法在研究弹-粘塑性波问题中的应用

采用控制金属材料宏观塑性流动的两个无量纲物理参数作为小参数,将一维弹/粘-塑性问题的解摄动展开,从而,求解非线性波动方程的问题可以转化成求解相应的齐次或非齐次电报方程的问题,用Laplace积分变换或级数展开技术首先得到零次精确解。然后,用Riemann函数方法可获得一次和高次摄动解。与非线性问题的数值解比较,在恒应力或恒速度边界条件下,一次摄动解给出了波动问题的良好近似。这就表明,摄动技术在研究一类广泛的弹/粘-塑波问题中是有效的。

轴向热传导对交流电弧性质的影响

本文研究了有限长度交流电弧的动力特性,采用二维电弧模型,考虑轴向热传导作用,得到一个非线性能量方程,用变量分离、非线性变换和Laplace变换求得电弧的热流势和电场强度的分析解。指出充满管道的有限长度的交流电弧动力特性仅由两个无量纲参数决定,并且指出热流势和电场强度存在轴向梯度,必须考虑轴向热传导的影响,当电弧的长度趋于无限大时,本解与R•L•Phillips的解一致。

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

A BIEM optimization method for fracture dynamics inverse problem

In the present paper, based on the theory of dynamic boundary integral equation, an optimization method for crack identification is set up in the Laplace frequency space, where the direct problem is solved by the author's new type boundary integral equations and a method for choosing the high sensitive frequency region is proposed. The results show that the method proposed is successful in using the information of boundary elastic wave and overcoming the ill-posed difficulties on solution, and helpful to improve the identification precision.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

How Does the New Keynesian Monetary Model Fit in the U.S. and the Eurozone? an Indirect Inference Approach

This paper estimates a standard version of the New Keynesian monetary (NKM) model under alternative specifications of the monetary policy rule using U.S. and Eurozone data. The estimation procedure implemented is a classical method based on the indirect inference principle. An unrestricted VAR is considered as the auxiliary model. On the one hand, the estimation method proposed overcomes some of the shortcomings of using a structural VAR as the auxiliary model in order to identify the impulse response that defines the minimum distance estimator implemented in the literature. On the other hand, by following a classical approach we can further assess the estimation results found in recent papers that follow a maximum-likelihood Bayesian approach. The estimation results show that some structural parameter estimates are quite sensitive to the specification of monetary policy. Moreover, the estimation results in the U.S. show that the fit of the NKM under an optimal monetary plan is much worse than the fit of the NKM model assuming a forward-looking Taylor rule. In contrast to the U.S. case, in the Eurozone the best fit is obtained assuming a backward-looking Taylor rule, but the improvement is rather small with respect to assuming either a forward-looking Taylor rule or an optimal plan.

An empirical comparison of the performance of alternative option pricing models

Published as an article in: Investigaciones Economicas, 2005, vol. 29, issue 3, pages 483-523.

颗粒增强复合材料相界面的动态应力分析

针对硬微粒填充高聚物复合材料因相界面脱粘开裂生成微孔洞的微损伤成核机制，取材料的代表体积单元进行动力分析，通过对粘弹性基体本构关系作Laplace变换建立了基本方程，并引入Hankel变换，得到了球对称动荷载作用下的相界面应力变化规律的解析解，据此分析了惯性效应和粘性效应对界面脱粘的影响。