Emma J. McCoy

AN IMPROVED METHOD OF MATCHING RESPONSE SPECTRA OF RECORDED EARTHQUAKE GROUND MOTION USING WAVELETS

Dynamic nonlinear analysis of structures requires the seismic input to be defined in the form of acceleration time-series, and these will generally be required to be compatible with the elastic response spectra representing the design seismic actions at the site. The advantages of using real accelerograms matched to the target response spectrum using wavelets for this purpose are discussed. The program RspMatch, which performs spectral matching using wavelets, is modified using new wavelets that obviate the need to subsequently apply a baseline correction. The new version of the program, RspMatch2005, enables the accelerograms to be matched to the pseudo-acceleration or displacement spectral ordinates as well as the spectrum of absolute acceleration, and additionally allows the matching to be performed simultaneously to a given spectrum at several damping ratios.

The variance of multitaper spectrum estimates for real Gaussian processes

Multitaper spectral estimation has proven very powerful as a spectral analysis method wherever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range. In his original paper D.J. Thomson (1982) gave a simple approximation for the variance of a multitaper spectral estimate which is generally adequate when the spectrum is slowly varying over the taper bandwidth. The authors show that near zero or Nyquist frequency this approximation is poor even for white noise and derive the exact expression of the variance in the general case of a stationary real-valued time series. This expression is illustrated on an autoregressive time series and a convenient computational approach outlined. It is shown that this multitaper variance expression for real-valued processes is not derivable as a special case of the multitaper variance for complex-valued, circularly symmetric processes, as previously suggested in the literature. >

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is , where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples.

Predicting patient arrivals to an accident and emergency department.

Objectives: To characterise and forecast daily patient arrivals into an accident and emergency (A&E) department based on previous arrivals data. Methods: Arrivals between 1 April 2002 and 31 March 2007 to a busy case study A&E department were allocated to one of two arrival streams (walk-in or ambulance) by mode of arrival and then aggregated by day. Using the first 4 years of patient arrival data as a “training” set, a structural time series (ST) model was fitted to characterise each arrival stream. These models were used to forecast walk-in and ambulance arrivals for 1–7 days ahead and then compared with the observed arrivals given by the remaining 1 year of “unseen” data. Results: Walk-in arrivals exhibited a strong 7-day (weekly) seasonality, with ambulance arrivals showing a distinct but much weaker 7-day seasonality. The model forecasts for walk-in arrivals showed reasonable predictive power (r = 0.6205). However, the ambulance arrivals were harder to characterise (r = 0.2951). Conclusions: The two separate arrival streams exhibit different statistical characteristics and so require separate time series models. It was only possible to accurately characterise and forecast walk-in arrivals; however, these model forecasts will still assist hospital managers at the case study hospital to best use the resources available and anticipate periods of high demand since walk-in arrivals account for the majority of arrivals into the A&E department.

Approximate Bayesian Inference for Doubly Robust Estimation

Doubly robust estimators are typically constructed by combining out- come regression and propensity score models to satisfy moment restrictions that ensure consistent estimation of causal quantities provided at least one of the com- ponent models is correctly specified. Standard Bayesian methods are difficult to apply because restricted moment models do not imply fully specified likelihood functions. This paper proposes a Bayesian bootstrap approach to derive approx- imate posterior predictive distributions that are doubly robust for estimation of causal quantities. Simulations show that the approach performs well under various sources of misspecification of the outcome regression or propensity score models. The estimator is applied in a case study of the effect of area deprivation on the incidence of child pedestrian casualties in British cities.

Quantifying Causal Effects of Road Network Capacity Expansions on Traffic Volume and Density via a Mixed Model Propensity Score Estimator

Road network capacity expansions are frequently proposed as solutions to urban traffic congestion but are controversial because it is thought that they can directly “induce” growth in traffic volumes. This article quantifies causal effects of road network capacity expansions on aggregate urban traffic volume and density in U.S. cities using a mixed model propensity score (PS) estimator. The motivation for this approach is that we seek to estimate a dose-response relationship between capacity and volume but suspect confounding from both observed and unobserved characteristics. Analytical results and simulations show that a longitudinal mixed model PS approach can be used to adjust effectively for time-invariant unobserved confounding via random effects (RE). Our empirical results indicate that network capacity expansions can cause substantial increases in aggregate urban traffic volumes such that even major capacity increases can actually lead to little or no reduction in network traffic densities. This result has important implications for optimal urban transportation strategies. Supplementary materials for this article are available online.

Correntropy: Implications of nonGaussianity for the moment expansion and deconvolution

The recently introduced correntropy function is an interesting and useful similarity measure between two random variables which has found myriad applications in signal processing. A series expansion for correntropy in terms of higher-order moments of the difference between the two random variables has been used to try to explain its statistical properties for uses such as deconvolution. We examine the existence and form of this expansion, showing that it may be divergent, e.g., when the difference has the Laplace distribution, and give sufficient conditions for its existence for differently characterized sub-Gaussian distributions. The contribution of the higher-order moments can be quite surprising, depending on the size of the Gaussian kernel in the definition of the correntropy. In the blind deconvolution setting we demonstrate that statistical exchangeability explains the existence of sub-optimal minima in the correntropy cost surface and show how the positions of these minima are controlled by the size of the Gaussian kernel.

Wavelet-Based Modelling of Persistent Periodicities

The k-factor Gegenbauer ARMA (Auto Regressive Moving Average) models of Woodward, Zhang and Gray (J. Time Ser. Anal. 19 (1998), 485-504) can model persistent periodic behaviour associated with each of k frequencies in [0, 0.5]. Current methods of parameter estimation of such processes is not automatic, and often involve many approximations, in addition to problems of model order identification. We propose a wavelet packet based analysis of such processes which utilizes a reversible jump Markov Chain Monte Carlo (MCMC) algorithm. This algorithm automatically accounts for model order determination of the number of AR and MA parameters as well as the number of persistent periodicities. From a Bayesian perspective, there is no fundamental difference between observables and parameters, and so missing values and forecasts could easily be incorporated into the algorithm. We demonstrate the method by applying the model to the Mauna Loa atmospheric CO2 data.