Browsing by Subject "Bayes' theorem"

Now showing 1 - 4 of 4
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    Accident Prediction Models using Macro and Micro Scale Analysis: Dynamic Tree and Zero Inflated Negative Binomial Models with Empirical Bayes Accident History Adjustment
    (Center for Transportation Studies, 2019-02) Mathew, Jacob; Benekohal, Rahim F; Medina, Juan C
    This report presents two ways to analyze accidents at highway rail grade crossings: a microscopic approach that looks at individual accidents at a crossing or a group of crossings, and a macroscopic approach to identify correlations between accident counts at crossings and crossing characteristics. The outcome of the microscopic approach is a data-driven dynamic tree that helps to visualize accident trends at a single crossing or a group of crossings. The dynamic tree is also used to identify new variables (crossing angle and distance to nearby highway intersection). The outcome of the macroscopic approach were new accident prediction models for crossings with gates, flashing lights, and crossbucks. Zero Inflated Negative Binomial models were used to predict the accident counts and the Empirical Bayes approach was used to adjust the predicted based on accident history at the crossing. Data from the state of Illinois was used to develop the model and data from four other states were used to validate the model. The newly developed models resulted in cumulative predicted accident distributions that closely represent the field data. The EB adjusted ZINB accident predictions value were significantly closer to the actual accident counts for the crossings than the USDOT models. More accurate predictions from the EB-adjusted ZINB model were obtained for the top 10, 20, 30, 40 and 50 locations with highest accident frequency for all three warning devices.
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    Bayesian Methods for Estimating Average Vehicle Classification Volumes
    (Minnesota Department of Transportation, 1999-10) Davis, Gary A.; Yang, Shimin
    This report describes the development of a data-driven methodology for estimating the mean daily traffic (MDT) for different vehicle classes from short classification-count samples. Implementation of the methodology requires that an agency maintain a small number of permanent classification counters (PCC), whose output is used to estimate parameters describing their monthly and day-of-week variation patterns and covariance characteristics. The probability of a match between a short classification count sample and each of the PCCs is computed, as well as the estimates of the short-counts site's MDTs which would arise if the short-count site had variation patterns identical to each of the PCCs. The final MDT estimates are then simply the weighted averages of these component MDTs, with the matching probabilities providing the weights. Empirical evaluation of the methods using data collected at the Long Term Pavement Performance Project sites in Minnesota indicated that a reliable match of a short-count site could be made using a sample consisting of a one-day classification count from each month of the year. An evaluation of two-day classification count samples indicated that a two-day count is not sufficient to reliably match the site to a factor group, justifying estimation of MDT using weighted averages. For estimating combination vehicle MDT, these samples should be taken between May and October, and between Tuesday and Thursday. In this case the estimated MDT differed on average by about 10% - 12% compared to estimates based on full year's worth of counts, and differed by less than 26%, 95% of the time.
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    Estimation Theory Approach to Monitoring and Updating Average Daily Traffic: Final Report
    (Minnesota Department of Transportation, 1997-01) Davis, Gary A.
    This report describes the application of Bayesian statistical methods to several related problems arising in the estimation of mean daily traffic for roadway locations lacking permanent automatic traffic recorders. A lognormal regression model is fit to daily count data obtained from automatic traffic recorders, and this model is then used to develop (1) a heuristic algorithm for developing traffic sampling plans which minimize the likelihood of assigning a site to an incorrect factor group, (2) an empirical Bayes method for assigning a short-count site to a factor group using the information in a sample of traffic counts, and (3) an empirical Bayes estimator of mean daily traffic which allows for uncertainty concerning the appropriate factors to be used in adjusting a sample count. An evaluation of these methods confirmed results reported in other work, in which a sample consisting of two, 1-week counts was found to be adequate for overcoming prior uncertainty concerning the correct adjustments for a site. The empirical Bayes method produced sample-based estimates of mean daily traffic that on the average differed by 5%-6% from estimates based on daily counts for an entire year. The report concludes with suggestions for agencies wishing to implement these methods.
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    Statistical Methods for Materials Testing
    (Minnesota Department of Transportation, 2009-12) Gupta, Diwakar; Peterson, Amy
    Mn/DOT provides incentives to contractors who achieve high relative density via a pay factor applied to each unit of work. To determine the pay factor, Mn/DOT divides each day of a contractor’s work into a small number of lots. Then, core samples are taken from two locations within each lot and the relative densities of the cores are calculated by performing standardized tests in materials testing laboratories. The average of these two values is used as an estimate of the lot's relative density, which determines the pay factor. This research develops two Bayesian procedures (encapsulated in computer programs) for determining the required number of samples that should be tested based on user-specified reliability metrices. The first procedure works in an offline environment where the number of tests must be known before any samples are obtained. The second procedure works in the field where the decision to continue testing is made after knowing the result of each test. The report also provides guidelines for estimating key parameters needed to implement our protocol. A comparison of the current and proposed sampling procedures showed that the recommended procedure resulted in more accurate pay factor calculations. Specifically, in an example based on historical data, the accuracy increased from 47.0% to 70.6%, where accuracy is measured by the proportion of times that the correct pay factor is identified. In monetary terms, this amounted to a change from average over and under payment of $109.60 and $287.33 per lot, to $44.50 and $90.74 per lot, respectively.