Subsample distribution distance and McMC convergence

A new measure based on comparison of empirical distributions for sub sequences or parallel runs and the full sequence of Markov chain Monte Carlo simulations, is proposed as a criterion of stability or convergence. The measure is also put forward as a loss function when the design of a Markov chain is optimized. The comparison is based on a Kullback-Leibler (KL) type distance over value sets defined by the output data. The leading term in a series expansion gives an interpretation in terms of the relative uncertainty of cell frequencies. The validity of this term is studied by simulation in two analytically tractable cases with Markov dependency. The agreement between the leading term and the KL-measure is close, in particular when the simulations are extensive enough for stable results. Comparisons with established criteria turn out favourably in examples studied

Subsample distribution distance and McMC convergence

A new measure based on comparison of empirical distributions for sub sequences or parallel runs and the full sequence of Markov chain Monte Carlo simulations, is proposed as a criterion of stability or convergence. The measure is also put forward as a loss function when the design of a Markov chain is optimized. The comparison is based on a Kullback-Leibler (KL) type distance over value sets defined by the output data. The leading term in a series expansion gives an interpretation in terms of the relative uncertainty of cell frequencies. The validity of this term is studied by simulation in two analytically tractable cases with Markov dependency. The agreement between the leading term and the KL-measure is close, in particular when the simulations are extensive enough for stable results. Comparisons with established criteria turn out favourably in examples studied

Sleepiness and prediction of driver impairment in simulator studies using a Cox proportional hazard approach

Cox proportional hazard models were used to study relationships between the event that a driver is leaving the lane caused by sleepiness and different indicators of sleepiness. In order to elucidate different indicators\u27 performance, five different models developed by Cox proportional hazard on a data set from a simulator study were used. The models consisted of physiological indicators and indicators from driving data both as stand alone and in combination. The different models were compared on two different data sets by means of sensitivity and specificity and the models\u27 ability to predict lane departure was studied. In conclusion, a combination of blink indicators based on the ratio between blink amplitude and peak closing velocity of eyelid (A/PCV) (or blink amplitude and peak opening velocity of eyelid (A/POV)), standard deviation of lateral position and standard deviation of lateral acceleration relative road (ddy) was the most sensitive approach with sensitivity 0.80. This is also supported by the fact that driving data only shows the impairment of driving performance while blink data have a closer relation to sleepiness. Thus, an effective sleepiness warning system may be based on a combination of lane variability measures and variables related to eye movements (particularly slow eye closure) in order to have both high sensitivity (many correct warnings) and acceptable specificity (few false alarms). \ua9 2009 Elsevier Ltd. All rights reserved