Novel methods and the maximum likelihood estimation technique for estimating traffic critical gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers’ sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Critical gap estimation by numerical and statistical highest likelihood search

Many traffic situations require drivers to cross or merge into a stream having higher priority. Gap acceptance theory enables us to model such processes to analyse traffic operation. This discussion demonstrated that numerical search fine tuned by statistical analysis can be used to determine the most likely critical gap for a sample of drivers, based on their largest rejected gap and accepted gap. This method shares some common features with the Maximum Likelihood Estimation technique (Troutbeck 1992) but lends itself well to contemporary analysis tools such as spreadsheet and is particularly analytically transparent. This method is considered not to bias estimation of critical gap due to very small rejected gaps or very large rejected gaps. However, it requires a sufficiently large sample that there is reasonable representation of largest rejected gap/accepted gap pairs within a fairly narrow highest likelihood search band.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

Extraction of road lanes from high-resolution stereo aerial imagery based on maximum likelihood segmentation and texture enhancement

Accurate road lane information is crucial for advanced vehicle navigation and safety applications. With the increasing of very high resolution (VHR) imagery of astonishing quality provided by digital airborne sources, it will greatly facilitate the data acquisition and also significantly reduce the cost of data collection and updates if the road details can be automatically extracted from the aerial images. In this paper, we proposed an effective approach to detect road lanes from aerial images with employment of the image analysis procedures. This algorithm starts with constructing the (Digital Surface Model) DSM and true orthophotos from the stereo images. Next, a maximum likelihood clustering algorithm is used to separate road from other ground objects. After the detection of road surface, the road traffic and lane lines are further detected using texture enhancement and morphological operations. Finally, the generated road network is evaluated to test the performance of the proposed approach, in which the datasets provided by Queensland department of Main Roads are used. The experiment result proves the effectiveness of our approach.

Econometric Modelling with Time Series : Specification, Estimation and Testing

This book provides a general framework for specifying, estimating, and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalized method of moments estimation, nonparametric estimation, and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.