Gareth Roberts

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In this paper we consider Foster-Lyapunov type drift conditions for Markov chains which imply polynomial rate convergence to stationarity in appropriate V-norms. We also show how these results can be used to prove Central Limit Theorems for functions of the Markov chain. Examples are considered to random walks on the half line and the independence sampler.
We present and study a Langevin MCMC approach for sampling nonlinear diffusion bridges. The method is based on recent theory concerning stochastic partial differential equations (SPDEs) reversible with respect to the target bridge, derived by applying the Langevin idea on the bridge pathspace. In the process, a Random-Walk Metropolis algorithm and an(More)
Africa is the single largest continental source of biomass burning emissions and one where emission source strengths are characterized by strong diurnal and seasonal cycles. This paper describes the development of a fire detection and characterization algorithm for generating high temporal resolution African pyrogenic emission data sets using data from the(More)
Continuous-time stochastic volatility models are becoming an increasingly popular way to describe moderate and high-frequency financial data. Recently, Barndorff-Nielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an Ornstein-Uhlenbeck process, driven by a positive Lévy process without Gaussian component. These(More)
Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Criteria for scaling based on empirical acceptance rates of algorithms have been found to work consistently well across a broad range of problems. Essentially, proposal jump sizes are increased when acceptance rates are high and decreased when rates are(More)
We investigate local MCMC algorithms, namely the random-walk Metropolis and the Langevin algorithms, and identify the optimal choice of the local step-size as a function of the dimension n of the state space, asymptotically as n→∞. We consider target distributions defined as a change of measure from a product law. Such structures arise, for instance, in(More)
In this paper we consider both the dynamical and parameter planes for the complex exponential family Eλ(z) = λez where the parameter λ is complex. We show that there are infinitely many curves or “hairs” in the dynamical plane that contain points whose orbits underEλ tend to infinity and hence are in the Julia set. We also show that there are similar hairs(More)
Satellite-based remote sensing of active fires is the only practical way to consistently and continuously monitor diurnal fluctuations in biomass burning from regional, to continental, to global scales. Failure to understand, quantify, and communicate the performance of an active fire detection algorithm, however, can lead to improper interpretations of the(More)