A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Lo\`eve expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings

Discontinuous information in the worst case and randomized settings

We believe that discontinuous linear information is never more powerful than continuous linear information for approximating continuous operators. We prove such a result in the worst case setting. In the randomized setting we consider compact linear operators defined between Hilbert spaces. In this case, the use of discontinuous linear information in the randomized setting cannot be much more powerful than continuous linear information in the worst case setting. These results can be applied when function evaluations are used even if function values are defined only almost everywhere

Adaptive Cross-Layer Distributed Energy-Efficient Resource Allocation Algorithms for Wireless Data Networks

The issue of adaptive and distributed cross-layer resource allocation for energy efficiency in uplink code-division multiple-access (CDMA) wireless data networks is addressed. The resource allocation problems are formulated as noncooperative games wherein each terminal seeks to maximize its own energy efficiency, namely, the number of reliably transmitted information symbols per unit of energy used for transmission. The focus of this paper is on the issue of adaptive and distributed implementation of policies arising from this approach, that is, it is assumed that only readily available measurements, such as the received data, are available at the receiver in order to play the considered games. Both single-cell and multicell networks are considered. Stochastic implementations of noncooperative games for power allocation, spreading code allocation, and choice of the uplink (linear) receiver are thus proposed, and analytical results describing the convergence properties of selected stochastic algorithms are also given. Extensive simulation results show that, in many instances of practical interest, the proposed stochastic algorithms approach with satisfactory accuracy the performance of nonadaptive games, whose implementation requires much more prior information

Investigations in adaptive processing of multispectral data

Adaptive data processing procedures are applied to the problem of classifying objects in a scene scanned by multispectral sensor. These procedures show a performance improvement over standard nonadaptive techniques. Some sources of error in classification are identified and those correctable by adaptive processing are discussed. Experiments in adaptation of signature means by decision-directed methods are described. Some of these methods assume correlation between the trajectories of different signature means; for others this assumption is not made

Adaptive Gibbs samplers and related MCMC methods

We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.Comment: Published in at http://dx.doi.org/10.1214/11-AAP806 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: substantial text overlap with arXiv:1001.279