ترغب بنشر مسار تعليمي؟ اضغط هنا

Asymptotic Analysis of the Random-Walk Metropolis Algorithm on Ridged Densities

431   0   0.0 ( 0 )
 نشر من قبل Alexandre Thiery
 تاريخ النشر 2015
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales, where most of the probability mass is distributed along certain key directions with the `orthogonal directions containing relatively less mass. Such class of probability measures arise in various applied contexts including Bayesian inverse problems where the posterior measure concentrates on a sub-manifold when the noise variance goes to zero. When the target measure concentrates on a linear sub-manifold, we derive analytically a diffusion limit for the Random-Walk Metropolis Markov chain as the scale parameter goes to zero. In contrast to the existing works on scaling limits, our limiting Stochastic Differential Equation does not in general have a constant diffusion coefficient. Our results show that in some cases, the usual practice of adapting the step-size to control the acceptance probability might be sub-optimal as the optimal acceptance probability is zero (in the limit).



قيم البحث

اقرأ أيضاً

215 - Somak Dutta 2010
In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov chain Monte Ca rlo literature. The associated kernel is shown to have standard properties like irreducibility, aperiodicity and Harris recurrence under some mild assumptions. These ensure basic convergence (ergodicity) of the kernel. Further the kernel is shown to be geometric ergodic for a large class of target densities on $mathbb{R}$. This class even contains realistic target densities for which random walk or Langevin MH are not geometrically ergodic. Three simulation studies are given to demonstrate the mixing property and superiority of RDMH to standard MH algorithms on real line. A share-price return data is also analyzed and the results are compared with those available in the literature.
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Su rprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or non-lazy random walks, which is related to a notion of permeability of the system. We also provide a strong law of large numbers, a functional central limit theorem and large deviation bounds under an ellipticity condition.
80 - Laurent Michel 2021
We study the Metropolis algorithm on a bounded connected domain $Omega$ of the euclidean space with proposal kernel localized at a small scale $h > 0$. We consider the case of a domain $Omega$ that may have cusp singularities. For small values of the parameter $h$ we prove the existence of a spectral gap $g(h)$ and study the behavior of $g(h)$ when $h$ goes to zero. As a consequence, we obtain exponentially fast return to equilibrium in total variation distance.
We present a detailed circuit implementation of Szegedys quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly arithmetic oper ations and thus reformulate the quantum walk in a way that circumvents the implementation of that specific oracle and which closely follows the classical Metropolis-Hastings walk. We also present heuristic quantum algorithms that use the quantum walk in the context of discrete optimization problems and numerically study their performances. Our numerical results indicate polynomial quantum speedups in heuristic settings.
179 - U. Haboeck 2008
We show that the twisted planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process is alpha-mi xing and of finite second moment, then the twisted random walk is recurrent for every angle fixed choice of the angle out of a set of full Lebesgue measure, no matter how slow the mixing coefficients decay.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا