Same-decision probability: A confidence measure for threshold-based decisions

We consider in this paper the robustness of decisions based on probabilistic thresholds. To this effect, we propose the same-decision probability as a query that can be used as a confidence measure for threshold-based decisions. More specifically, the same-decision probability is the probability that we would have made the same threshold-based decision, had we known the state of some hidden variables pertaining to our decision.We study a number of properties about the same-decision probability. First, we analyze its computational complexity. We then derive a bound on its value, which we can compute using a variable elimination algorithm that we propose. Finally, we consider decisions based on noisy sensors in particular, showing through examples that the same-decision probability can be used to reason about threshold-based decisions in a more refined way.     

A note on studentized confidence intervals for the change-point

We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. It is known how to construct resampling confidence intervals using blocking techniques, but so far no studentizing has been considered. A simulation study shows that we obtain better intervals by studentizing. When studentizing dependent data, we need to use flat-top kernels for the estimation of the asymptotic variance. It turns out that this estimator taking possible changes into account behaves much better than the corresponding Bartlett estimator. Since the asymptotic distribution of change-point statistics for time-series depends on this value, having a good estimator under the null as well as alternatives is also essential for testing problems.     

A new car-following model with consideration of the prevision driving behavior

In the paper, a new car-following model is presented with the consideration of the prevision driving behavior on a single-lane road. The model’s linear stability condition is obtained by applying the linear stability theory. And through nonlinear analysis, a modified Korteweg–de Vries (mKdV) equation is derived to describe the propagating behavior of traffic density wave near the critical point. Numerical simulation shows that the new model can improve the stability of traffic flow by adjusting the driver’s prevision intensity parameter, which is consistent with the theoretical analysis.     

Exact confidence coefficients of simultaneous confidence intervals for multinomial proportions

Simultaneous confidence intervals for multinomial proportions are useful in many areas of science. Since 1964, approximate simultaneous 1-α confidence intervals have been proposed for multinomial proportions. Although at each point in the parameter space, these confidence sets have asymptotic 1-α coverage probability, the exact confidence coefficients of these simultaneous confidence intervals for a fixed sample size are unknown before.In this paper, we propose a procedure for calculating exact confidence coefficients for simultaneous confidence intervals of multinomial proportions for any fixed sample size. With this methodology, exact confidence coefficients can be clearly derived, and the point at which the infimum of the coverage probability occurs can be clearly identified.     

Full velocity difference and acceleration model for a car-following theory

In order to describe the car-following behavior more actually in real traffic, a full velocity difference and acceleration model (for short, FVDAM) is proposed by synthetically taking into account headway, velocity difference and acceleration of the leading car on the basis of full velocity difference model. The analytical method and numerical simulation results show that the proposed model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, that incorporating the acceleration of the leading car into car-following model can stabilize traffic flow, suppress the traffic jam and increase capacity, and that the following car in FVDAM can accelerate more quickly than in FVDM.     

Safe solution of a car-following problem

A system of nonlinear car-following equations with random delay times is considered. Conditions which ensure a safe response (according to a natural safety criterion) are given.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.     

A conceptual pathway to confidence intervals

Finding ways for the majority of students to better understand conventional normal theory-based statistical inference seems to be an intractable problem area for researchers. In this paper we propose a conceptual pathway for developing confidence interval ideas for the one-sample situation only from an intuitive sense to bootstrapping for students from about age 14 to first-year university. We make the case that conceptual development should start early; that probability and statistical instruction should change so that both orientate students towards interconnected stochastic conceptions; and that the use of visual imagery has the potential to stimulate students towards such a perspective. We analyse our conceptual pathway based on a theoretical framework for a stochastic conception of statistical inference based on imagery and some research evidence. Our analysis suggests that the pathway has the potential for students to become conversant with the concepts underpinning inference, to view statistics probabilistically and to integrate concepts into a coherent comprehension of inference.     

Improved confidence intervals for quantiles

We derive the Edgeworth expansion for the studentized version of the kernel quantile estimator. Inverting the expansion allows us to get very accurate confidence intervals for the pth quantile under general conditions. The results are applicable in practice to improve inference for quantiles when sample sizes are moderate.     

Safe solutions of a nonlinear car-following equation

A leader-follower pair of cars whose motion is subject to a non-linear delay differential equation are travelling with the same constant velocity u_I when the leader begins to change his velocity in a smooth way to the non-negative velocity u_F < u_I. Conditions are found for the response of the follower to be a safe one according to certain natural safety criteria.     

A comparison of testing and confidence interval methods for the median

There are only relatively few confidence coefficients and levels available for distribution-free confidence intervals and test for the median based on the sign statistic. This problem can be overcome by interpolating confidence intervals or by studentizing the median by an estimate of its standard error. Such methods are discussed and then compared via simulation.     

A car-following collision prevention control device based on the cascaded fuzzy inference system

A car-following collision prevention control device based on the cascaded fuzzy inference system (CFIS), consisting of a velocity fuzzy controller and an acceleration fuzzy controller, to nonlinearly control car acceleration or deceleration rate is proposed. The distance and speed relative to the car in front are measured using spread spectrum radar and applied to the collision prevention control device. The output acceleration or deceleration rate obtained from the CFIS car-following collision prevention system is based on the characteristics of the vehicle. The simulation results demonstrate that the presented CFIS control device can solve the oscillation problems for final relative distance between the lead vehicle (LV) and following vehicle (FV) and relative speed. When the LV applies the brake suddenly or a stationary obstacle appears in front of vehicle moving at high speed on the roadway, the CFIS control device can safely avoid a collision. The CFIS car-following collision prevention control device proposed in this paper can provide a safe, reasonable and comfortable drive.     

Sequential confidence intervals for time series

Sequential estimation of parameters for time series observations is considered. The Chow-Robbins procedure is extended and Wald’s identity is proven for such data. Various confidence bands are defined. These give simultaneous confidence intervals for a sequence of sample sizes.     

A new confidence interval for all characteristic roots of a covariance matrix

Confidence intervals for all of the characteristic roots of a sample covariance matrix are derived. Using a perturbation expansion, we obtain a new confidence interval for these roots. Then, we propose another confidence interval based on the results of Monte Carlo simulations. Since it is based on simulations, this new confidence interval is both narrower and more accurate than others when the difference between the largest and smallest characteristic roots of the population covariance matrix is large.     

Generalized fiducial confidence intervals for extremes

The generalized Pareto distribution is relevant to many situations when modeling extremes of random variables. In particular, peaks over threshold data approximately follow the generalized Pareto distribution. We use a fiducial framework to perform inference on the parameters and the extreme quantiles of the generalized Pareto. This inference technique is demonstrated both when the threshold is a known and unknown parameter. Assuming the threshold is a known parameter resulted in fiducial intervals with good empirical properties and asymptotically correct coverage. Likewise, our simulation results suggest that the fiducial intervals and point estimates compare favorably to the competing methods seen in the literature. The proposed intervals for the extreme quantiles when the threshold is unknown also have good empirical properties regardless of the underlying distribution of the data. Comparisons to a similar Bayesian method suggest that the fiducial intervals have better coverage and are similar in length with fewer assumptions. In addition to simulation results, the proposed method is applied to a data set from the NASDAQ 100. The data set is analyzed using the fiducial approach and its competitors for both cases when the threshold is known and unknown. R code for our procedure can be downloaded at .     

Lower confidence limits for structure reliability

For a class of data often arising in engineering, we have developed an approach to compute the lower confidence limit for structure reliability with a given confidence level. Especially, in a case with no failure and a case with only one failure, the concrete computational methods are presented. Selected from Acta Scientiarum Naturalium Universitatis Pekinensis, 2004, 40(5): 702–711     

Asymptotic confidence intervals for Poisson regression

Let (X,Y) be a R^d×N₀-valued random vector where the conditional distribution of Y given X=x is a Poisson distribution with mean m(x). We estimate m by a local polynomial kernel estimate defined by maximizing a localized log-likelihood function. We use this estimate of m(x) to estimate the conditional distribution of Y given X=x by a corresponding Poisson distribution and to construct confidence intervals of level α of Y given X=x. Under mild regularity conditions on m(x) and on the distribution of X we show strong convergence of the integrated L₁ distance between Poisson distribution and its estimate. We also demonstrate that the corresponding confidence interval has asymptotically (i.e., for sample size tending to infinity) level α, and that the probability that the length of this confidence interval deviates from the optimal length by more than one converges to zero with the number of samples tending to infinity.