Accelerating delayed-acceptance Markov chain Monte Carlo algorithms

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster, albeit approximate, DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. When the evaluation of the likelihood function is computationally intensive, our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC. However, the acceleration is highly problem dependent. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our algorithm can return reliable Bayesian inference. As a computationally intensive case study, we introduce a novel stochastic differential equation model for protein folding data.Comment: 40 pages, 21 figures, 10 table

Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful

Expectations and the Forward Exchange Rate

This paper provides an empirical examination of the hypothesis that the forward exchange rate provides an "optimal" forecast of the future spot ex-change rate, for five currencies relative to the dollar. This hypothesis provides a convenient norm for examining the erratic behavior of exchange rates; this erratic behavior represents an efficient market that is quickly incorporating new information into the current exchange rate. This hypothesis is analyzed using two distinct, but related, approaches. The first approach is based on a regression of spot rates on lagged forward rates. When using weekly data and a one month forward exchange rate, ordinary least squares regression analysis of market efficiency is incorrect. Econometric methods are proposed which allow for consistent (though not fully efficient) estimation of the parameters and their standard errors. This paper also presents a new approach for testing exchange market efficiency. This approach is based on a general time series process generating the spot and forward exchange rate. The hypothesis of efficiency implies a set of cross-equation restrictions imposed on the parameters of the time series model. This paper derives these restrictions, proposes a maximum likelihood method of estimating the constrained likelihood function, estimates the model and tests the validity of the restrictions with a likelihood ration statistic.

Fisher Lecture: Dimension Reduction in Regression

Beginning with a discussion of R. A. Fisher's early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with descriptions of general approaches to model-based and model-free dimension reduction in regression. It is argued that the role for principal components and related methodology may be broader than previously seen and that the common practice of conditioning on observed values of the predictors may unnecessarily limit the choice of regression methodology.Comment: This paper commented in: [arXiv:0708.3776], [arXiv:0708.3777], [arXiv:0708.3779]. Rejoinder in [arXiv:0708.3781]. Published at http://dx.doi.org/10.1214/088342306000000682 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org