Jesse Frey

Spatial prediction on a river network

This article develops methods for spatially predicting daily change of dissolved oxygen (Dochange) at both sampled locations (134 freshwater sites in 2002 and 2003) and other locations of interest throughout a river network in South East Queensland, Australia. In order to deal with the relative sparseness of the monitoring locations in comparison to the number of locations where one might want to make predictions, we make a classification of the river and stream locations. We then implement optimal spatial prediction (ordinary and constrained kriging) from geostatistics. Because of their directed-tree structure, rivers and streams offer special challenges. A complete approach to spatial prediction on a river network is given, with special attention paid to environmental exceedances. The methodology is used to produce a map of Dochange predictions for 2003. Dochange is one of the variables measured as part of the Ecosystem Health Monitoring Program conducted within the Moreton Bay Waterways and Catchments Partnership.

Likelihood-Based Control of Engine Knock

Engine knock is an undesirable phenomenon, which requires feedback control in order to maximize engine efficiency and avoid damage to the engine. In this paper, an analysis of experimental data is used to provide further evidence that knock behaves as a cyclically uncorrelated random process. It is argued that all knock controllers are therefore ultimately stochastic in nature and that the knock control problem is best undertaken within a stochastic framework. The properties of knock events are discussed and, based on these properties, a new likelihood-based stochastic knock controller is presented. The new controller achieves a significantly improved regulatory response relative to conventional strategies, while also maintaining a rapid transient response. It is therefore possible to operate closer to the knock limit without increasing the risk of engine damage.

Nonparametric Tests for Perfect Judgment Rankings

The ranked-set sampling literature includes both inference procedures that rely on the assumption of perfect rankings and inference procedures that are robust to violations of this assumption. Procedures that assume perfect rankings tend to be more efficient when rankings are in fact perfect, but they may be invalid when perfect rankings fail. As a result, users of ranked-set sampling must decide between efficiency and robustness, and there is at present little to guide their decision. In this article we introduce three rank-based goodness-of-fit tests that may be consulted in making these decisions. Our strategy in producing these tests is to think of the judgment order statistic classes as separate samples, compute the ranks of the units from each sample within the combined sample, and use these ranks to test whether the judgment rankings are perfect. Consideration of both power and ease of use leads us to recommend use of a test that rejects when the concordance between the vector of mean ranks and its null expectation is small. Tables of critical values and appropriate asymptotic theory for applying this test are provided, and we illustrate the use of the tests by applying them to a biological dataset.

Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population

Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.

A cumulative-summation-based stochastic knock controller

Abstract In this paper, an analysis of knock signals suggests that the knock intensity is a cyclically uncorrelated random process, and that it is therefore not possible to control individual cycles to a specified knock intensity in a deterministic manner. A new knock control algorithm is therefore developed on the basis of a stochastic interpretation of the knock signal, and on the basis of a control objective specified as a certain percentage of knocking cycles. Unlike traditional controllers, the new algorithm does not respond to knock events provided that these are occurring within a specified tolerance of the target knock rate. The new controller uses the cumulative summation of knock events to make this determination, thereby avoiding the slow transient response times sometimes associated with ‘stochastic’ knock controllers. When a spark adjustment is deemed necessary, the magnitude of the control action is scaled according to the likelihood ratio of the observed events since the last spark adjustment was made. A theoretical analysis of the new controller is presented and a simulation tool which is closely based on experimental data is used to assess its performance. The results show that the new controller is able to achieve the same target knock rate as a traditional controller while operating at a more advanced mean spark angle. There is also less cyclic variance about this mean and the regulatory response is significantly improved. The transient response to overly advanced or retarded conditions is similar to the traditional controller. These results suggest that the new controller will deliver increased torque and engine efficiency under knock-limited conditions without increasing the risk of engine damage.

Characterization of knock intensity distributions: Part 1: statistical independence and scalar measures

The characterization of knock intensity distributions can provide useful insights into the process and help to improve knock control system designs. In this paper, an extensive statistical analysis is performed on knock intensity data recorded under a broad range of operating conditions. First, the critical issue of whether the data exhibit any cycle-to-cycle correlations is investigated, and it is shown that knock intensity closely approximates a cyclically independent random process. The study then focuses on the variation of knock intensity distributions with operating condition, and on the quantification of these distributions using simple scalar measures. The relationship between knock event distributions and knock intensity distributions is also investigated, and it is shown that knock event data are binomially distributed regardless of the underlying knock intensity distribution. This supports ongoing efforts to exploit binomial probability theory in knock event simulation and controller design.

An improved mean estimator for judgment post-stratification

We prove that the standard nonparametric mean estimator for judgment post-stratification is inadmissible under squared error loss within a certain class of linear estimators. We derive alternate estimators that are admissible in this class, and we show that one of them is always better than the standard estimator. The reduction in mean squared error from using this alternate estimator can be as large as 10% for small set sizes and small sample sizes.

A note on a probability involving independent order statistics

Suppose that we have a sample consisting of independent order statistics from the same continuous parent distribution. Kvam and Samaniego [Kvam, P.H. and Samaniego, F.J., 1993, On the inadmissibility of empirical averages as estimators in ranked set sampling. Journal of Statistical Planning and Inference, 36, 39–55.] developed a formula for the probability that these order statistics have a particular ordering, but their formula is computationally feasible only for small sample sizes. In this paper, an alternate, combinatorial proof of their result is presented. It is then shown how ideas from the new proof allow one to compute such probabilities even when the sample size is large. An example is given to illustrate how the method may be used to produce distribution-free confidence intervals for quantiles of the unknown parent distribution.

Characterization of knock intensity distributions: Part 2: parametric models

Knock intensity behaves as a random process which may be characterized using simple scalar metrics such as the mean and variance, or (more commonly) by the probability of knock events. However, such measures discard much of the information present in the signal. Several researchers have therefore sought to obtain a more complete characterization of the process by fitting parametric log-normal or gamma distribution models to knock intensity distributions. The present study extends this work both in terms of the range of engine operating conditions considered and in terms of the evaluation of the goodness of fit between two different models and the experimental data. In particular, new and arguably more application-appropriate measures of the goodness of fit provide a clearer assessment of the performance of the models, and a like-for-like comparison of log-normal and gamma distribution model forms demonstrates that the log-normal model better characterizes the experimental data used in this study.

Nonparametric mean estimation using partially ordered sets

In ranked-set sampling (RSS), the ranker must give a complete ranking of the units in each set. In this paper, we consider a modification of RSS that allows the ranker to declare ties. Our sampling method is simply to break the ties at random so that we obtain a standard ranked-set sample, but also to record the tie structure for use in estimation. We propose several different nonparametric mean estimators that incorporate the tie information, and we show that the best of these estimators is substantially more efficient than estimators that ignore the ties. As part of our comparison of estimators, we develop new results about models for ties in rankings. We also show that there are settings where, to achieve more efficient estimation, ties should be declared not just when the ranker is actually unsure about how units rank, but also when the ranker is sure about the ranking, but believes that the units are close.