Maximum Likelihood Estimation for Combined Travel Choice Model Parameters

1998 ◽  
Vol 1645 (1) ◽  
pp. 160-169 ◽  
Author(s):  
James E. Hicks ◽  
Mounir M. Abdel-Aal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Minimization Problem ◽  
Urban Areas ◽  
Choice Model ◽  
Stable Solution ◽  
Bilevel Optimization ◽  
Estimation Problem ◽  
Parameter Estimates ◽  
Model Parameters

Equilibrium models of combined location and travel choices solve for the modal link flow pattern, which simultaneously solves a constrained minimization problem and satisfies a set of equilibrium conditions characterizing a rational behavior for traveler choices in an urban transportation system. The minimization problem typically is made to be representative of the particular urban area being studied by including coefficients of travel costs and travel choices that have been estimated from locally available observed data. For large urban areas, in practice, it is possible to derive interzonal travel times and costs only from the travel model, because suitable observed data are nonexistent. In this case, the estimation problem is a function of the travel model variables and, at the same time, the travel model is a function of the parameters determined by the estimation problem. Procedures to computationally search for a stable solution to this bilevel optimization problem have been addressed with limited success. The parameter estimation is solved in an iterative procedure in which first parameters are held fixed and the travel model is solved, then travel patterns are held fixed and the maximum likelihood parameters are solved by the Newton-Raphson method. Each successive parameter estimation resulting from these two steps results in a new set of parameter values for the next iteration until stable values for the parameters are achieved. The quality of the convergence of the parameter estimates is reported.

Genetic Algorithm-Based Maximum Likelihood Parameter Estimation for Transit Buses

2001 ◽  
Author(s):  
Jie Xiao ◽  
Bohdan T. Kulakowski
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Dynamic Models ◽  
Estimation Method ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Parameter Estimation Method ◽  
Transit Buses ◽  
Simulation And Control ◽  
And Control

Abstract Vehicle dynamic models include parameters that qualify the dependence of input forces and moments on state and control variables. The accuracy of the model parameter estimates is important for modeling, simulation, and control. In general, the most accurate method for determining values of model parameters is by direct measurement. However, some parameters of vehicle dynamics, such as suspension damping or moments of inertia, are difficult to measure accurately. This study aims at establishing an efficient and accurate parameter estimation method for developing dynamic models for transit buses, such that this method can be easily implemented for simulation and control design purposes. Based on the analysis of robustness, as well as accuracy and efficiency of optimization techniques, a parameter estimation method that integrates Genetic Algorithms and the Maximum Likelihood Estimation is proposed. Choices of output signals and estimation criterion are discussed involving an extensive sensitivity analysis of the predicted output with respect to model parameters. Other experiment-related aspects, such as imperfection of data acquisition, are also considered. Finally, asymptotic Cramer-Rao lower bounds for the covariance of estimated parameters are obtained. Computer simulation results show that the proposed method is superior to gradient-based methods in accuracy, as well as robustness to the initial guesses and measurement uncertainty.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

scholarly journals Conditional Maximum Likelihood Estimation in Probability-Branched Multistage Designs

2021 ◽  
Author(s):  
Jan Steinfeld ◽  
Alexander Robitzsch
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Parameter Estimate ◽  
Item Parameter ◽  
Parameter Estimates ◽  
Conditional Maximum Likelihood ◽  
Item Parameter Estimates ◽  
Item Parameter Estimation ◽  
Conditional Maximum

This article describes the conditional maximum likelihood-based item parameter estimation in probabilistic multistage designs. In probabilistic multistage designs, the routing is not solely based on a raw score j and a cut score c as well as a rule for routing into a module such as j < c or j ≤ c but is based on a probability p(j) for each raw score j. It can be shown that the use of a conventional conditional maximum likelihood parameter estimate in multistage designs leads to severely biased item parameter estimates. Zwitser and Maris (2013) were able to show that with deterministic routing, the integration of the design into the item parameter estimation leads to unbiased estimates. This article extends this approach to probabilistic routing and, at the same time, represents a generalization. In a simulation study, it is shown that the item parameter estimation in probabilistic designs leads to unbiased item parameter estimates.

scholarly journals A Policy-Sensitive Model of Parking Choice for Commercial Vehicles in Urban Areas

2020 ◽  
Vol 54 (3) ◽  
pp. 606-630 ◽  
Author(s):  
Giacomo Dalla Chiara ◽  
Lynette Cheah ◽  
Carlos Lima Azevedo ◽  
Moshe E. Ben-Akiva
Keyword(s):  
Traffic Congestion ◽  
Urban Areas ◽  
Commercial Vehicle ◽  
Choice Model ◽  
Discrete Event ◽  
Real Data ◽  
Behavior Modeling ◽  
Model Parameters ◽  
Commercial Vehicles ◽  
Real World Data

Understanding factors that drive the parking choice of commercial vehicles at delivery stops in cities can enhance logistics operations and the management of freight parking infrastructure, mitigate illegal parking, and ultimately reduce traffic congestion. In this paper, we focus on this decision-making process at large urban freight traffic generators, such as retail malls and transit terminals, that attract a large share of urban commercial vehicle traffic. Existing literature on parking behavior modeling has focused on passenger vehicles. This paper presents a discrete choice model for commercial vehicle parking choice in urban areas. The model parameters were estimated by using detailed, real-world data on commercial vehicle parking choices collected in two commercial urban areas in Singapore. The model analyzes the effect of several variables on the parking behavior of commercial vehicle drivers, including the presence of congestion and queueing, attitudes toward illegal parking, and pricing (parking fees). The model was validated against real data and applied within a discrete-event simulation to test the economic and environmental impacts of several parking measures, including pricing strategies and parking enforcement.

scholarly journals Estimating ARMA Model Parameters of an Industrial Process Using Meta-Heuristic Search Algorithms

2018 ◽  
Vol 7 (3.10) ◽  
pp. 187 ◽  
Author(s):  
Alaa F. Sheta ◽  
Hossam Faris ◽  
Ibrahim Aljarah
Keyword(s):  
Parameter Estimation ◽  
Heuristic Algorithms ◽  
Arma Model ◽  
Search Space ◽  
Estimation Problem ◽  
Production Costs ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Parameter Estimation Problem ◽  
Krill Herd

This paper addresses the parameter estimation problem for a manufacturing process based on the Auto-Regressive Moving Average (ARMA) model. The accurate estimation of the ARMA model’s parameter helps to reduce the production costs, provide better product quality, increase productivity and profit. Meta-heuristic algorithms are among these approximate techniques which have been successfully used to search for an optimal solution in complex search space. Meta-heuristic algorithms can converge to an optimal global solution despite traditional parameter estimation techniques which stuck by local optimal. A comparison between Meta-heuristic algorithms: Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and the Accelerated PSO, Cuckoo Search, Krill Herd and Firefly algorithm is provided to handle the parameter estimation problem for a Winding process in the industry. The developed ARMA-meta-heuristics models for a winding machine are evaluated based on different evaluation metrics. The results reveal that meta-heuristics can provide an outstanding modeling performance.

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.

Interpretation of Simulation Studies for Efficient Estimation of Population Pharmacokinetic Parameters

1993 ◽  
Vol 27 (9) ◽  
pp. 1034-1039 ◽  
Author(s):  
Ene I. Ette ◽  
Andrew W. Kelman ◽  
Catherine A. Howie ◽  
Brian Whiting
Keyword(s):  
Parameter Estimation ◽  
Efficient Estimation ◽  
Experimental Unit ◽  
Pharmacokinetic Parameters ◽  
Population Pharmacokinetic ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Good Precision ◽  
Simulation Studies ◽  
Individual Parameter

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (Φ) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The Φ approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the Φ for individual parameter estimation and the overall Φ for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.

scholarly journals Fault Detection in Wastewater Treatment Systems Using Multiparametric Programming

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 231 ◽  
Author(s):  
Ernie Che Mid ◽  
Vivek Dua
Keyword(s):  
Wastewater Treatment ◽  
Parameter Estimation ◽  
Fault Detection ◽  
Normal Operation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Multiparametric Programming ◽  
Nonlinear Algebraic Equations ◽  
Wastewater Treatment Systems

In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, ; concentration of organic matter, ; concentration of dissolved oxygen, ; and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

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.

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