29,441 research outputs found
Approximate Bayesian Computation by Subset Simulation
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating
of model parameters is proposed in this paper, which combines the ABC
principles with the technique of Subset Simulation for efficient rare-event
simulation, first developed in S.K. Au and J.L. Beck [1]. It has been named
ABC- SubSim. The idea is to choose the nested decreasing sequence of regions in
Subset Simulation as the regions that correspond to increasingly closer
approximations of the actual data vector in observation space. The efficiency
of the algorithm is demonstrated in two examples that illustrate some of the
challenges faced in real-world applications of ABC. We show that the proposed
algorithm outperforms other recent sequential ABC algorithms in terms of
computational efficiency while achieving the same, or better, measure of ac-
curacy in the posterior distribution. We also show that ABC-SubSim readily
provides an estimate of the evidence (marginal likelihood) for posterior model
class assessment, as a by-product
Simulation in Statistics
Simulation has become a standard tool in statistics because it may be the
only tool available for analysing some classes of probabilistic models. We
review in this paper simulation tools that have been specifically derived to
address statistical challenges and, in particular, recent advances in the areas
of adaptive Markov chain Monte Carlo (MCMC) algorithms, and approximate
Bayesian calculation (ABC) algorithms.Comment: Draft of an advanced tutorial paper for the Proceedings of the 2011
Winter Simulation Conferenc
Tandem: A Context-Aware Method for Spontaneous Clustering of Dynamic Wireless Sensor Nodes
Wireless sensor nodes attached to everyday objects and worn by people are able to collaborate and actively assist users in their activities. We propose a method through which wireless sensor nodes organize spontaneously into clusters based on a common context. Provided that the confidence of sharing a common context varies in time, the algorithm takes into account a window-based history of believes. We approximate the behaviour of the algorithm using a Markov chain model and we analyse theoretically the cluster stability. We compare the theoretical approximation with simulations, by making use of experimental results reported from field tests. We show the tradeoff between the time history necessary to achieve a certain stability and the responsiveness of the clustering algorithm
Study of new rare event simulation schemes and their application to extreme scenario generation
This is a companion paper based on our previous work on rare event simulation
methods. In this paper, we provide an alternative proof for the ergodicity
of shaking transformation in the Gaussian case and propose two variants of
the existing methods with comparisons of numerical performance. In numerical
tests, we also illustrate the idea of extreme scenario generation based on
the convergence of marginal distributions of the underlying Markov chains
and show the impact of the discretization of continuous time models on rare
event probability estimation
- …