High resolution estimation for sub-gaussian stable signals in a linear array model

The authors describe a high resolution subspace fitting (HRE) algorithm for robust estimation of direction of arrival (DOA) in the uniform linear array model with heavy-tailed signals and noise. Electromagnetic disturbances on telephone lines, atmospheric noise and underwater acoustic noise often exhibit heavy-tailed behaviour with differing characteristics. Although statistical models under Gaussian assumptions of signals and noise have been extensively investigated in the literature, there is limited research on robust methods in the non-Gaussian setting. A general model with sub-Gaussian alpha-stable signals is described, which includes the isotropic alpha-stable, and independent and dependent Gaussian models as special cases. It is shown that the HRE algorithm provides strongly consistent estimates of the DOAs. In addition, Monte Carlo simulation studies show that the proposed algorithm works extremely well for closely spaced targets, and outperforms the multiple signal classification-type algorithms for strongly dependent signals, both in the stable and the Gaussian cases     

Selecting exposure measures in crash rate prediction for two-lane highway segments

A critical part of any risk assessment is identifying how to represent exposure to the risk involved. Recent research shows that the relationship between crash count and traffic volume is non-linear; consequently, a simple crash rate computed as the ratio of crash count to volume is not proper for comparing the safety of sites with different traffic volumes. To solve this problem, we describe a new approach for relating traffic volume and crash incidence. Specifically, we disaggregate crashes into four types: (1) single-vehicle, (2) multi-vehicle same direction, (3) multi-vehicle opposite direction, and (4) multi-vehicle intersecting, and define candidate exposure measures for each that we hypothesize will be linear with respect to each crash type. This paper describes initial investigation using crash and physical characteristics data for highway segments in Michigan from the Highway Safety Information System (HSIS). We use zero-inflated-Poisson (ZIP) modeling to estimate models for predicting counts for each of the above crash types as a function of the daily volume, segment length, speed limit and roadway width. We found that the relationship between crashes and the daily volume (AADT) is non-linear and varies by crash type, and is significantly different from the relationship between crashes and segment length for all crash types. Our research will provide information to improve accuracy of crash predictions and, thus, facilitate more meaningful comparison of the safety record of seemingly similar highway locations.     

Analysis of driver and passenger crash injury severity using partial proportional odds models

The question of whether crash injury severity should be modeled using an ordinal response model or a non-ordered (multinomial) response model is persistent in traffic safety engineering. This paper proposes the use of the partial proportional odds (PPO) model as a statistical modeling technique that both bridges the gap between ordered and non-ordered response modeling, and avoids violating the key assumptions in the behavior of crash severity inherent in these two alternatives. The partial proportional odds model is a type of logistic regression that allows certain individual predictor variables to ignore the proportional odds assumption which normally forces predictor variables to affect each level of the response variable with the same magnitude, while other predictor variables retain this proportional odds assumption. This research looks at the effectiveness of this PPO technique in predicting vehicular crash severities on Connecticut state roads using data from 1995 to 2009. The PPO model is compared to ordinal and multinomial response models on the basis of adequacy of model fit, significance of covariates, and out-of-sample prediction accuracy. The results of this study show that the PPO model has adequate fit and performs best overall in terms of covariate significance and holdout prediction accuracy. Combined with the ability to accurately represent the theoretical process of crash injury severity prediction, this makes the PPO technique a favorable approach for crash injury severity modeling by adequately modeling and predicting the ordinal nature of the crash severity process and addressing the non-proportional contributions of some covariates.     

Monte Carlo Studies of the Aqueous Hydration of cis- and trans- N- Methyl-Acetamide: Sensitivity of Results to Convergence and to Choice of Intermolecular Potential Functions

A series of liquid state Monte Carlo computer simulations on the N-methyl acetamide in water (NMA molecule) are described, considering both the cis and trans isomeric forms of NMA. Two independent sets of calculations were performed, one set based on the potential functions developed by Clementi and co-workers (CPF) used in conjunction with the Matsuoka et al. (MCY) water-water potential, and the other set using the OPLS potential of Jorgensen and coworkers for solute-water interactions and the TIP4P potential for the water-water interactions. The relative hydration energies of the cis and trans isomers of NMA and the transfer energies of NMA from free space to water are discussed with respect to the convergence level of the simulations and the sensitivity of results to the choice of the intermolecular potential functions. The structural chemistry of the aqueous hydration for NMA is developed from the simulation result based on Proximity Analysis. The sensitivity of the structural and energetic indices of analysis to choice of potential is described. Preliminary results of the calculation of the hydration contribution to the free energy are also presented.     

APPROXIMATE SIMULTANEOUS SIGNIFICANCE INTERVALS FOR RESIDUAL AUTOCORRELATIONS OF AUTOREGRESSIVE MOVING-AVERAGE TIME SERIES MODELS

Abstract. Bonferroni-type inequalities are used to approximate probabilities of the joint distribution of residual autocorrelation coefficients from an autoregressive moving-average time series model. The approximations are useful for testing the goodness of fit of the model:they can be used to find critical values of a test of whether the largest residual autocorrelation is significantly different from zero. The approximation based on the first-order Bonferroni inequality is simple to use and adequate in practice.     

Bayesian estimation of hourly exposure functions by crash type and time of day

The study describes an investigation of the relationship between crash occurrence and hourly volume counts for small samples of highway segments from two states: Michigan and Connecticut. We used a hierarchical Bayesian framework to fit binary regression models for predicting crash occurrence for each of four crash types: (1) single-vehicle, (2) multi-vehicle same direction, (3) multi-vehicle opposite direction, and (4) multi-vehicle intersecting direction, as a function of the hourly volume, segment length, speed limit and pavement width. The results reveal how the relationship between crashes and hourly volume varies by time of day, thus improving the accuracy of crash occurrence predictions. The results show that even accounting for time of day, the disaggregate exposure measure – hourly volume – is indeed non-linear for each of the four crash types. This implies that at any time of day, the crash occurrence is not proportional to the hourly volume. These findings help us to further understand the relationship between crash occurrence and hourly volume, segment length and other risk factors, and facilitate more meaningful comparisons of the safety record of seemingly similar highway locations.     

Bayesian analysis of autoregressive fractionally integrated moving-average processes

For the autoregressive fractionally integrated moving-average (ARFIMA) processes which characterize both long-memory and short-memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of the parameters that is computationally feasible for repetitive evaluation within a modified Gibbs sampling algorithm that we employ. We illustrate our approach through two examples.     

Dynamic compositional modeling of pedestrian crash counts on urban roads in Connecticut

Uncovering the temporal trend in crash counts provides a good understanding of the context for pedestrian safety. With a rareness of pedestrian crashes it is impossible to investigate monthly temporal effects with an individual segment/intersection level data, thus the time dependence should be derived from the aggregated level data. Most previous studies have used annual data to investigate the differences in pedestrian crashes between different regions or countries in a given year, and/or to look at time trends of fatal pedestrian injuries annually. Use of annual data unfortunately does not provide sufficient information on patterns in time trends or seasonal effects. This paper describes statistical methods uncovering patterns in monthly pedestrian crashes aggregated on urban roads in Connecticut from January 1995 to December 2009. We investigate the temporal behavior of injury severity levels, including fatal (K), severe injury (A), evident minor injury (B), and non-evident possible injury and property damage only (C and O), as proportions of all pedestrian crashes in each month, taking into consideration effects of time trend, seasonal variations and VMT (vehicle miles traveled). This type of dependent multivariate data is characterized by positive components which sum to one, and occurs in several applications in science and engineering. We describe a dynamic framework with vector autoregressions (VAR) for modeling and predicting compositional time series. Combining these predictions with predictions from a univariate statistical model for total crash counts will then enable us to predict pedestrian crash counts with the different injury severity levels. We compare these predictions with those obtained from fitting separate univariate models to time series of crash counts at each injury severity level. We also show that the dynamic models perform better than the corresponding static models. We implement the Integrated Nested Laplace Approximation (INLA) approach to enable fast Bayesian posterior computation.     

DIFFERENTIAL GEOMETRY OF ARMA MODELS

Abstract. A general approach for the development of a statistical inference on autoregressive moving-average (ARMA) models is presented based on geometric arguments. ARMA models are characterized as members of the curved exponential family. Geometric properties of ARMA models are computed and used to suggest parameter transformations that satisfy predetermined properties. In particular, the effect on the asymptotic bias of the maximum likelihood estimator of model parameters is illustrated. Hypothesis testing of parameters is discussed through the application of a modified form of the likelihood ratio test statistic.     

Optimization of PVC– PAN‐based polymer electrolytes

The hybrid plasticized polymer electrolyte composed of the blend of poly(vinyl chloride) (PVC) and poly(acrylonitrile) (PAN) as host polymer, propylene carbonate as plasticizer, and LiClO₄ as a salt was studied. An attempt was made to optimize the polymer blend ratio. XRD, Fourier transform infrared, and DSC studies confirm the formation of polymer–salt complex and miscibility of the PVC and PAN. The electrical conductivity and temperature dependence of ionic conductivity of polymer films are also studied and reported here. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009