On finite sample performance of confidence intervals methods for willingness to pay measures

This paper systematically compares finite sample performances of methods to build confidence intervals for willingness to pay measures in a choice modeling context. It contributes to the field by also considering methods developed in other research fields. Various scenarios are evaluated under an extensive Monte Carlo study. Results show that the commonly used Delta method, producing symmetric intervals around the point estimate, often fails to account for skewness in the estimated willingness to pay distribution. Both the Fieller method and the likelihood ratio test inversion method produce more realistic confidence intervals for small samples. Some bootstrap methods also perform reasonably well, in terms of effective coverage. Finally, empirical data are used to illustrate an application of the methods considered.     

动车组产品可靠性评估与验证

针对动车组整车和零部件等产品的不同特点,按照不同车型、不同产品、不同运用条件、不同故障后果和不同置信度要求等分类评估的原则,研究动车组产品的可靠度评估方法,包括可靠度置信下限评估方法和故障率置信上限评估方法;以提高验证效率、效益为目标,从最少验证样本、最短验证时间、最低验证成本的原则出发,研究无故障状况下动车组可靠度和故障率的验证方法;示例进行动车组整车故障率和轴箱轴承可靠度评估与验证。结果表明:采用评估与验证方法,可得到动车组产品置信度分别为50%,90%,95%,99%,产品可靠度下限分别为0.9~0.99,0.991~0.999时所需试验验证样本数量,以及百万km故障率上限分别为0.1~1.0时所需累计试验验证里程,实现基于可靠性目标要求的定量评估和验证考核。     

Confidence intervals of willingness-to-pay for random coefficient logit models

Random coefficient logit (RCL) models containing random parameters are increasingly used for modelling travel choices. Willingness-to-pay (WTP) measures, such as the value of travel time savings (VTTS) are, in the case of RCL models estimated in preference space, ratios of random parameters. In this paper we apply the Delta method to compute the confidence intervals of such WTP measures, taking into account the variance–covariance matrix of the estimates of the distributional parameters. The same Delta method can be applied when the model is estimated in WTP space. Compared to simulation methods such as proposed by Krinsky and Robb, the Delta method is able to avoid most of the simulations by deriving partly analytical expressions for the standard errors. Examples of such computations are shown for different combinations of random distributions.     

Bayesian committee of neural networks to predict travel times with confidence intervals

Short-term prediction of travel time is one of the central topics in current transportation research and practice. Among the more successful travel time prediction approaches are neural networks and combined prediction models (a ‘committee’). However, both approaches have disadvantages. Usually many candidate neural networks are trained and the best performing one is selected. However, it is difficult and arbitrary to select the optimal network. In committee approaches a principled and mathematically sound framework to combine travel time predictions is lacking. This paper overcomes the drawbacks of both approaches by combining neural networks in a committee using Bayesian inference theory. An ‘evidence’ factor can be calculated for each model, which can be used as a stopping criterion during training, and as a tool to select and combine different neural networks. Along with higher prediction accuracy, this approach allows for accurate estimation of confidence intervals for the predictions. When comparing the committee predictions to single neural network predictions on the A12 motorway in the Netherlands it is concluded that the approach indeed leads to improved travel time prediction accuracy.     

Interval Analysis of the Finite Element Method for Stochastic Structures

A random parameter can be transformed into an interval number in the structural analysis with the concept of the confidence interval．Hence，analyses of uncertain structural systems Can be used in the traditional FEM software．In some cases，the amount of solutions in stochastic structures is nearly as many as that in the traditional structural problems．In addition，a new method to evaluate the failure probability of structures is presented for the needs of the modern engineering design．     

Uncertainty in traffic forecasts: literature review and new results for The Netherlands

This paper provides a review of transport model applications that not only provide a central traffic forecast (or forecasts for a few scenarios), but also quantify the uncertainty in the traffic forecasts in the form of a confidence interval or related measures. Both uncertainty that results from using uncertain inputs (e.g. on income) and uncertainty in the model itself are treated. The paper goes on to describe the methods used and the results obtained for a case study in quantifying uncertainty in traffic forecasts in The Netherlands.

The inherent precision of regression estimated route probabilities

From basic assumptions about independent and consistent driver behaviour, and with data from traffic counts, we derive statistical properties of regression or correlation estimates of route selection probabilities, turning probabilities and travelling times. Our modelling is conditional in a way that avoids most traffic generation problems and permits an asymptotic analysis of the precision under mild assumptions allowing non-stationarity. This allows us to put together non-stationary data from the corresponding time intervals during several days when we aim at high precision estimates.     

Confidence interval estimation for path flow estimator

The uncertainty of an origin-destination (O-D) trip table estimate is affected by two factors: (i) the multiplicity of solutions due to the underspecified nature of the problem, and (ii) the errors of traffic counts. In this paper, a confidence interval estimation procedure for path flow estimator (PFE) is developed for assessing the quality of O-D trip tables estimated from traffic counts. The confidence interval estimation consists of two parts: (i) a generalized demand scale (GDS) measure for quantifying the intrinsic underspecified nature of the O-D estimation problem at various spatial levels, and (ii) an error bound to quantify the contribution of input errors (traffic counts) to the estimation results. Numerical results using PFE as the O-D estimator show that the proposed confidence interval estimation procedure is able to separate the two sources of uncertainty in constructing the confidence intervals at various spatial levels. Simulation results also confirm that the proposed quality measure indeed contain the true estimates within the defined confidence intervals.