Pi Wen Tsai

A General Criterion for Factorial Designs Under Model Uncertainty

Motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design, we show that the QB criterion, which aims to improve the estimation in as many models as possible by incorporating experimenters’ prior knowledge along with an approximation to the As criterion, is more general and has a better statistical interpretation than many standard criteria. The generalization and application of the criterion to different types of designs are presented. The relationships between QB and other criteria for different situations are explored. It is shown that the E(s2) criterion is a special case of QB and several aberration-type criteria are limiting cases of our criterion, so that QB provides a bridge between alphabetic optimality and aberration. The two case studies illustrate the potential benefits of the QB criterion. R programs for calculating QB are available online as supplemental materials.

ENSEMBLE EMPIRICAL MODE DECOMPOSITION WITH SUPERVISED CLUSTER ANALYSIS

Ensemble empirical mode decomposition (EEMD) is a noise-assisted data analysis method which decomposes a signal into a collection of intrinsic mode functions (IMFs). There nevertheless appears a multi-mode problem where signals with a similar timescale are decomposed into different IMF components. A possible solution to this problem is to recombine the multi-mode IMF components into a proper single mode but as of yet, no general rules have been proposed in the literature. This paper presents the incorporation of a statistical cluster analysis to assist in the diagnosis of multi-mode IMFs and to recombine them based on the classified clusters. As a result, signals are reorganized into a condensed set of clustered intrinsic mode functions (CIMFs). The method is applied to two sets of artificially synthesized signals and two sets of practical signals: wind turbine noise and earthquake motion. These applications demonstrate that, with the additional cluster analysis, the multi-mode problem can be largely eliminated in a statistically reliable manner, and in situ applications can be improved.

Empirical Modal Decomposition of Near Field Seismic Signals of Tsaoling Landslide

Giant landslides can achieve high-speed sliding and long run out distances and estimating the kinematic is crucial for the next generation of the hazard mitigation system. Direct measurement data when landslides are in motion are valuable for the purpose. However, because of their scarce occurrences and short flow durations, such measurements are rarely recorded with instruments. In 1999, the Chi–Chi earthquake triggered a major landslide in this area, with a source volume 125×106 m3. Near the scar area, there is a strong ground motion station, CHY080, recorded the seismic signals during the earthquake and the recorded data exhibit some distinctive signatures. We analyze the polarizations of the seismic waves and use Ensemble Empirical Mode Decomposition (EEMD) with an additional clustering analysis to decompose the seismic signals. Series of peculiar wave packets associated with the landslide are identified. Based on these results, a complementary rigid sliding model is deployed to verify the sliding process. The results reveal that with the sliding distance 1,990 m, the maximum velocity reaches 78 m/s, and the mass generates a large collision impact against the riverbed and the steep slope on the other side of the river. The friction angle of the sliding surface could be as low as 6.9o. These results are agreeable with the numerical simulation of the landslide. These findings provide the evidence that the earthquake and the landslide induced ground motion coexist in the seismogram records.

Split-Plot Microarray Experiments

This article focuses on microarray experiments with two or more factors in which treatment combinations of the factors corresponding to the samples paired together onto arrays are not completely random. A main effect of one (or more) factor(s) is confounded with arrays (the experimental blocks). This is called a split-plot microarray experiment. We utilise an analysis of variance (ANOVA) model to assess differentially expressed genes for between-array and within-array comparisons that are generic under a split-plot microarray experiment. Instead of standard t- or F-test statistics that rely on mean square errors of the ANOVA model, we use a robust method, referred to as ‘a pooled percentile estimator’, to identify genes that are differentially expressed across different treatment conditions. We illustrate the design and analysis of split-plot microarray experiments based on a case application described by Jin et al. A brief discussion of power and sample size for split-plot microarray experiments is also presented.

A Study of Two Types of Split-Plot Designs

This paper discusses two types of split-plot designs, split-plot designs with few whole-plot factors and blocked split-plot designs. We provide a list of efficient designs and compare them with the designs available in the literature with respect to a surrogate for the information capacity criterion derived in Cheng and Tsai (2011). In many cases, either better designs are found or additional designs are identified as possible alternatives. In the remaining cases, the optimality of the designs tabulated in design literature is confirmed.