10 research outputs found
A numerical study of the 3D random interchange and random loop models
We have studied numerically the random interchange model and related loop
models on the three-dimensional cubic lattice. We have determined the
transition time for the occurrence of long loops. The joint distribution of the
lengths of long loops is Poisson-Dirichlet with parameter 1 or 1/2.Comment: 11 page
A General Method for Calibrating Stochastic Radio Channel Models with Kernels
Publisher Copyright: CCBYCalibrating stochastic radio channel models to new measurement data is challenging when the likelihood function is intractable. The standard approach to this problem involves sophisticated algorithms for extraction and clustering of multipath components, following which, point estimates of the model parameters can be obtained using specialized estimators. We propose a likelihood-free calibration method using approximate Bayesian computation. The method is based on the maximum mean discrepancy, which is a notion of distance between probability distributions. Our method not only by-passes the need to implement any high-resolution or clustering algorithm, but is also automatic in that it does not require any additional input or manual pre-processing from the user. It also has the advantage of returning an entire posterior distribution on the value of the parameters, rather than a simple point estimate. We evaluate the performance of the proposed method by fitting two different stochastic channel models, namely the Saleh-Valenzuela model and the propagation graph model, to both simulated and measured data. The proposed method is able to estimate the parameters of both the models accurately in simulations, as well as when applied to 60 GHz indoor measurement data.Peer reviewe
Statistical Inference for Generative Models with Maximum Mean Discrepancy
While likelihood-based inference and its variants provide a statistically
efficient and widely applicable approach to parametric inference, their
application to models involving intractable likelihoods poses challenges. In
this work, we study a class of minimum distance estimators for intractable
generative models, that is, statistical models for which the likelihood is
intractable, but simulation is cheap. The distance considered, maximum mean
discrepancy (MMD), is defined through the embedding of probability measures
into a reproducing kernel Hilbert space. We study the theoretical properties of
these estimators, showing that they are consistent, asymptotically normal and
robust to model misspecification. A main advantage of these estimators is the
flexibility offered by the choice of kernel, which can be used to trade-off
statistical efficiency and robustness. On the algorithmic side, we study the
geometry induced by MMD on the parameter space and use this to introduce a
novel natural gradient descent-like algorithm for efficient implementation of
these estimators. We illustrate the relevance of our theoretical results on
several classes of models including a discrete-time latent Markov process and
two multivariate stochastic differential equation models
Optimally-weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.Peer reviewe