Calibration of microscopic traffic-flow models using multiple data sources

2010 ◽  
Vol 368 (1928) ◽  
pp. 4497-4517 ◽  
Author(s):  
Serge Hoogendoorn ◽  
Raymond Hoogendoorn
Keyword(s):  
Driving Simulator ◽  
Likelihood Estimation ◽  
Joint Estimation ◽  
Data Sources ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Ratio Test ◽  
Estimation Of Parameters ◽  
Flow Models ◽  
Car Following

Parameter identification of microscopic driving models is a difficult task. This is caused by the fact that parameters—such as reaction time, sensitivity to stimuli, etc.—are generally not directly observable from common traffic data, but also due to the lack of reliable statistical estimation techniques. This contribution puts forward a new approach to identifying parameters of car-following models. One of the main contributions of this article is that the proposed approach allows for joint estimation of parameters using different data sources, including prior information on parameter values (or the valid range of values). This is achieved by generalizing the maximum-likelihood estimation approach proposed by the authors in previous work. The approach allows for statistical analysis of the parameter estimates, including the standard error of the parameter estimates and the correlation of the estimates. Using the likelihood-ratio test, models of different complexity (defined by the number of model parameters) can be cross-compared. A nice property of this test is that it takes into account the number of parameters of a model as well as the performance. To illustrate the workings, the approach is applied to two car-following models using vehicle trajectories of a Dutch freeway collected from a helicopter, in combination with data collected with a driving simulator.

Driver Reactions to Uphill Grades: Inference from a Stochastic Car-Following Model

2020 ◽  
Vol 2674 (11) ◽  
pp. 343-351 ◽  
Author(s):  
Tu Xu ◽  
Jorge Laval
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Truck Drivers ◽  
Model Parameters ◽  
Gravitational Effects ◽  
Car Following ◽  
Car Following Model ◽  
Operational Impacts ◽  
The Impact ◽  
Engine Power

This paper analyzes the impact of uphill grades on the acceleration drivers choose to impose on their vehicles. Statistical inference is made based on the maximum likelihood estimation of a two-regime stochastic car-following model using Next Generation SIMulation (NGSIM) data. Previous models assume that the loss in acceleration on uphill grades is given by the effects of gravity. We find evidence that this is not the case for car drivers, who tend to overcome half of the gravitational effects by using more engine power. Truck drivers only compensate for 5% of the loss, possibly because of limited engine power. This indicates not only that current models are severely overestimating the operational impacts that uphill grades have on regular vehicles, but also underestimating their environmental impacts. We also find that car-following model parameters are significantly different among shoulder, median and middle lanes but more data is needed to understand clearly why this happens.

Likelihood and Its Applications

2021 ◽  
pp. 125-148
Author(s):  
Timothy E. Essington
Keyword(s):  
Maximum Likelihood ◽  
Dynamic Model ◽  
Likelihood Estimation ◽  
Worked Examples ◽  
Multiple Models ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Multiple Parameters ◽  
Weight Support ◽  
Estimation Of Model Parameters

The chapter “Likelihood and Its Applications” introduces the likelihood concept and the concept of maximum likelihood estimation of model parameters. Likelihood is the link between data and models. It is used to estimate model parameters, judge the degree of precision of parameter estimates, and weight support for alternative models. Likelihood is therefore a crucial concept that underlies the ability to test multiple models. The chapter contains several worked examples that progress the reader through increasingly complex problems, ending at likelihood profiles for models with multiple parameters. Importantly, it illustrates how one can take any dynamic model and data and use likelihood to link the data (random variables) to a probability function that depends on the dynamic model.

scholarly journals EXPLICIT FORMULAE FOR PARAMETERS OF STOCHASTIC MODELS OF A DISCOUNTED EQUITY INDEX USING MAXIMUM LIKELIHOOD ESTIMATION WITH APPLICATIONS

2017 ◽  
Vol 12 (02) ◽  
pp. 1750010 ◽  
Author(s):  
K. FERGUSSON
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Market Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
No Arbitrage ◽  
Explicit Formulae ◽  
Equity Index

A discounted equity index is computed as the ratio of an equity index to the accumulated savings account denominated in the same currency. In this way, discounting provides a natural way of separating the modeling of the short rate from the market price of risk component of the equity index. In this vein, we investigate the applicability of maximum likelihood estimation to stochastic models of a discounted equity index, providing explicit formulae for parameter estimates. We restrict our consideration to two important index models, namely the Black–Scholes model and the minimal market model of Platen, each having an explicit formula for the transition density function. Explicit formulae for estimates of the model parameters and their standard errors are derived and are used in fitting the two models to US data. Further, we demonstrate the effect of the model choice on the no-arbitrage assumption employed in risk neutral pricing.

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

Car-Following Model Calibration Based on Driving Simulator Data to Study Driver Characteristics and to Investigate Model Validity in Extreme Traffic Situations

2021 ◽  
pp. 036119812110326
Author(s):  
Moritz Berghaus ◽  
Eszter Kallo ◽  
Markus Oeser
Keyword(s):  
Driving Simulator ◽  
Driver Behavior ◽  
Field Studies ◽  
Driving Behavior ◽  
Model Parameters ◽  
Prediction Errors ◽  
Trajectory Data ◽  
Car Following ◽  
Model Validity ◽  
Simulator Study

In this paper we use traffic data from a driving simulator study to calibrate four different car-following models. We also present two applications for which the calibration results can be used. The first application relied on the advantage that driving simulator data also contain information on driver characteristics, for example, age, gender, or the self-assessment of driver behavior. By calibrating the models for each driver individually, the resulting model parameters could be used to analyze the influence of driver characteristics on driver behavior. The analysis revealed that certain characteristics, for example, self-identification as an aggressive driver, were reflected in the model parameters. The second application was based on the capability to simulate dangerous situations that require extreme driving behavior, which is often not included in datasets from real traffic and cannot be provoked in field studies. The model validity in these situations was analyzed by comparing the prediction errors of normal and extreme driving behavior. The results showed that all four car-following models underestimated the deceleration in an emergency braking scenario in which the drivers were momentarily shocked. The driving simulator study was validated by comparing the calibration results with those obtained from real trajectory data. We concluded that driving simulator data were suitable for the two proposed applications, although the validity of driving simulator studies must always be regarded.

scholarly journals An Analytical EM Algorithm for Sub-Gaussian Vectors

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 945
Author(s):  
Audrius Kabašinskas ◽  
Leonidas Sakalauskas ◽  
Ingrida Vaičiulytė
Keyword(s):  
Em Algorithm ◽  
Likelihood Ratio ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Normal Vector ◽  
Ratio Test ◽  
Estimation Of Parameters ◽  
Goodness Of Fit Test

The area in which a multivariate α-stable distribution could be applied is vast; however, a lack of parameter estimation methods and theoretical limitations diminish its potential. Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α-stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate α-stable random variables. Our numerical results show that the convergence of the proposed algorithm is much faster than that of existing algorithms. Moreover, the likelihood ratio (goodness-of-fit) test for a multivariate α-stable distribution was implemented. Empirical examples with simulated and real world (stocks, AIS and cryptocurrencies) data showed that the likelihood ratio test can be useful for assessing goodness-of-fit.

scholarly journals Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Gamma regression model

2021 ◽  
Vol 880 (1) ◽  
pp. 012044
Author(s):  
Desy Wasani ◽  
Purhadi ◽  
Sutikno
Keyword(s):  
Maximum Likelihood ◽  
Panel Data ◽  
Gamma Distribution ◽  
Likelihood Estimation ◽  
Complete Information ◽  
Model Parameters ◽  
Large Sample Size ◽  
Ratio Test ◽  
Spatial Effects ◽  
Test Statistic

Abstract Geographically Weighted Regression (GWR) study potential relationships in regression models that distinguish geographic spaces using non-stationary parameters to overcome spatial effects. The use of gamma regression, namely regression with the dependent variable with a gamma distribution, can be an alternative if the data do not follow a normal distribution. Gamma distribution is a continuous set of non-negative values, generally skewed to the right or positive skewness. Gamma regression is developed to be Bivariate Gamma Regression (BGR) when there are two dependent variables with gamma distribution. If the observation units are location points, spatial effects may occur. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model can be a solution for spatial heterogeneity. However, during its development, many cases require information from panel data. Using panel data can provide complete information because it covers several periods, but it allows for temporal effects. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to handle spatial and temporal heterogeneity simultaneously. The estimation of the GTWBGR model parameters uses the Maximum Likelihood Estimation (MLE) method that followed by the numerical iteration of Berndt Hall Hall Hausman (BHHH). The simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT) method to get a test statistic. With a large sample size, the distribution of the test statistic approaches chi-square. Meanwhile, partial testing uses the Z test statistic.

scholarly journals Parameter Estimation of the Macroscopic Fundamental Diagram: A Maximum Likelihood Approach

2021 ◽  
Author(s):  
Rafegh Aghamohammadi ◽  
Jorge Laval
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Fundamental Diagram ◽  
Urban Networks ◽  
Loop Detectors ◽  
Unsignalized Intersections ◽  
Macroscopic Fundamental Diagram ◽  
Parameter Values

This paper extends the Stochastic Method of Cuts (SMoC) to approximate of the Macroscopic Fundamental Diagram (MFD) of urban networks and uses Maximum Likelihood Estimation (MLE) method to estimate the model parameters based on empirical data from a corridor and 30 cities around the world. For the corridor case, the estimated values are in good agreement with the measured values of the parameters. For the network datasets, the results indicate that the method yields satisfactory parameter estimates and graphical fits for roughly 50\% of the studied networks, where estimations fall within the expected range of the parameter values. The satisfactory estimates are mostly for the datasets which (i) cover a relatively wider range of densities and (ii) the average flow values at different densities are approximately normally distributed similar to the probability density function of the SMoC. The estimated parameter values are compared to the real or expected values and any discrepancies and their potential causes are discussed in depth to identify the challenges in the MFD estimation both analytically and empirically. In particular, we find that the most important issues needing further investigation are: (i) the distribution of loop detectors within the links, (ii) the distribution of loop detectors across the network, and (iii) the treatment of unsignalized intersections and their impact on the block length.

scholarly journals Sequential Parameter Estimation for Mammalian Cell Model Based on In Silico Design of Experiments

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 100 ◽  
Author(s):  
Zhenyu Wang ◽  
Hana Sheikh ◽  
Kyongbum Lee ◽  
Christos Georgakis
Keyword(s):  
Parameter Estimation ◽  
Mammalian Cells ◽  
Cell Model ◽  
Cell Metabolism ◽  
Model Performance ◽  
Sequential Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Estimation Of Parameters

Due to the complicated metabolism of mammalian cells, the corresponding dynamic mathematical models usually consist of large sets of differential and algebraic equations with a large number of parameters to be estimated. On the other hand, the measured data for estimating the model parameters are limited. Consequently, the parameter estimates may converge to a local minimum far from the optimal ones, especially when the initial guesses of the parameter values are poor. The methodology presented in this paper provides a systematic way for estimating parameters sequentially that generates better initial guesses for parameter estimation and improves the accuracy of the obtained metabolic model. The model parameters are first classified into four subsets of decreasing importance, based on the sensitivity of the model’s predictions on the parameters’ assumed values. The parameters in the most sensitive subset, typically a small fraction of the total, are estimated first. When estimating the remaining parameters with next most sensitive subset, the subsets of parameters with higher sensitivities are estimated again using their previously obtained optimal values as the initial guesses. The power of this sequential estimation approach is illustrated through a case study on the estimation of parameters in a dynamic model of CHO cell metabolism in fed-batch culture. We show that the sequential parameter estimation approach improves model accuracy and that using limited data to estimate low-sensitivity parameters can worsen model performance.

A maximum likelihood approach for identifying dive bouts improves accuracy, precision and objectivity

Behaviour ◽  
2007 ◽  
Vol 144 (11) ◽  
pp. 1315-1332 ◽  
Author(s):  
Sebastián Luque ◽  
Christophe Guinet
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Systematic Effect ◽  
Fur Seals ◽  
Accuracy And Precision

AbstractForaging behaviour frequently occurs in bouts, and considerable efforts to properly define those bouts have been made because they partly reflect different scales of environmental variation. Methods traditionally used to identify such bouts are diverse, include some level of subjectivity, and their accuracy and precision is rarely compared. Therefore, the applicability of a maximum likelihood estimation method (MLM) for identifying dive bouts was investigated and compared with a recently proposed sequential differences analysis (SDA). Using real data on interdive durations from Antarctic fur seals (Arctocephalus gazella Peters, 1875), the MLM-based model produced briefer bout ending criterion (BEC) and more precise parameter estimates than the SDA approach. The MLM-based model was also in better agreement with real data, as it predicted the cumulative frequency of differences in interdive duration more accurately. Using both methods on simulated data showed that the MLM-based approach produced less biased estimates of the given model parameters than the SDA approach. Different choices of histogram bin widths involved in SDA had a systematic effect on the estimated BEC, such that larger bin widths resulted in longer BECs. These results suggest that using the MLM-based procedure with the sequential differences in interdive durations, and possibly other dive characteristics, may be an accurate, precise, and objective tool for identifying dive bouts.

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