The workings of human visual perception play a strong role in the interpretation of graphs. Consideration of the mechanisms of perception should therefore play a more prominent role in their design than is often the case in current practice.

This talk will explore the impact on graphics of a number of perceptual features and suggest more effective alternatives to some common graphical techniques. In each case, examples of different options for plotting the same data will be examined and compared.

Globally robust inference takes into account the asymptotic bias of the point estimates (Adrover, Salibian-Barrera and Zamar, 2002). To construct robust confidence intervals for the simple linear regression slope, the authors selected the generalized median of slopes (GMS) as their point estimate, considering its good bias behavior and asymptotic normality. However, GMS has a breakdown point of only 0.25, its asymptotic normality is established under very restrictive conditions, and its bias bound is known only for symmetric carrier distributions. In this study, we propose the repeated median slope (RMS) estimate as an alternative choice. RMS has a breakdown point of 0.50, its asymptotic normality holds under mild assumptions, and the bias bound for RMS is known for general carrier distributions. The proposed method achieves, more or less, the same observed coverage levels while it constructs intervals of smaller lengths, as compared to the GMS approach.

We consider novel class of non-linear models based on mixtures of local time series. In these models, at any given time point t, we have a number J of regression models, denoted experts, and a latent indicator variable, whose distribution may depend on the same covariates as the experts, that determines which regression model is observed. These models are referred to as mixtures-of-experts of time series, and they bear some similarity to many other non-linear models in the literature, such as the threshold autoregressive (TAR) models and the Bayesian treed models. For the experts, we considered normal, Poisson, binomial, gamma and generalized-t (heavy tail) regressions. For a fixed number J of components, we present the asymptotic properties of the maximum likelihood estimator for mixtures-of-experts of time series, under the assumptions of correctly and incorrectly specified models. We also provide sufficient conditions to guarantee stochastic stability (uniform ergodicity). Assuming the model is correctly specified, Monte Carlo simulations suggested that the BIC provides a consistent estimator for the true number of experts J. One of the advantages of mixtures-of-experts is their ability of modeling general conditional densities by increasing the number of mixed components J. Finally we illustrate the performance of mixture-of-experts in density forecast for simulated and real financial data.

The McDonald Research Laboratories (MRL) / iCAPTUR4E Centre is a UBC research laboratory located at the St. Paul's Hospital campus. It is a publicly funded research organization that uses advanced methods and technology to formulate, design, execute, analyze, synthesize, and report experimental findings regarding the causes, mechanisms, outcomes and implications of circulatory and respiratory diseases. Similarly, IBM Life Sciences is dedicated to rapidly bringing leading-edge technology out of the laboratory and into the marketplace for customers and Business Partners in the fields of pharmaceutical research, biotechnology, genomics, proteomics, health care, and academic research. It is these parallel missions that have led to the IQ Engine research collaboration between IBM Life Sciences and the MRL/iCAPTUR4E Centre aimed at producing a powerful query engine for data mining and innovation discovery. This IQ Engine enables the Centre to explore and understand the interrelationships between genomic and phenotypic data in relation to heart, lung and blood vessel disease.

The Pilot Project will use a narrow subsection of data with a view to expanding it to query MRL/iCAPTUR4E's complete data framework. The Pilot Project is focused on control or rheumatic human heart valve datasets including patient information (clinical and demographic), echocardiography and gross pathology. Datasets on the valve tissue include immunohistochemical quantitation of valve structural components, microarray profiles, and proteome profiles. Datasets on cultured myofibroblasts from the valve tissue include microarray profiles, proteome profiles, immunohistochemical quantitation, calcium imaging and kinase signalling data. With these datasets, the Pilot Project attempts to answer two specific research questions:

(1) Is there any correlation between the expression of a certain gene/pathway and Ca2+ regulation in valve myofibroblast cells?

(2) What are the phenotypic, transcriptomic and proteomic differences between control heart valves and diseased heart valves?

The implementation of the Pilot Project will combine existing IBM program products, third party products, IBM Research code, and custom written code to create a search tool to uncover relationships in the selected input data. Statistical analysis is performed by SAS. Display of textual data and visualization of data trends is performed using Spotfire's DecisionSite as a means of visually displaying and exploring the query results.

The IQ Engine is an integration infrastructure for various data sources coupled with a flexible and general purpose set of query, display, analysis, and visualization capabilities. This solution will enable the MRL/iCAPTUR4E Centre to search for new pathogenesis mechanisms within diverse datasets and allows for new research synergies across our organization.

A method commonly used for estimating the onset of change involves fitting a sharply kinked line, sometimes called a broken stick, to a graph of the response and explanatory variables. For example, consider the relationship of abundance versus time for a declining fish population. A fisheries manager would commonly use the estimated date of onset based on a broken-stick fit as a clue to the actual cause of the decline. However, researchers in this and other fields are often tempted to conclude abruptness even when there is seldom solid theory to justify such claims. To address this issue, we use what we call the bent-cable model whose quadratic bend of non-negative width generalizes the kink of a broken stick.

Part 1 of this talk features worked examples of bent-cable regression for assessing abruptness of change. They demonstrate that data for typical biological phenomena are far too imprecise to support the abruptness notion associated with the broken-stick model. Part 2 briefly discusses the irregularity intrinsic to bent-cable regression, and the practical design conditions that yield regular asymptotics for the estimation problem.

Calibration typically relates a standard unit x to an instrumental measurement Y by using data x_i and Y_i collected from a calibration experiment to estimate the calibration curve. After the calibration curve is estimated, new measurements Y^* are taken and the calibration curve is then used with the Y^* to estimate the associated standard values, by point and interval estimates. The standard or classical formula was derived by Eisenhardt (1939). While his formula is useful in many instances, there are other cases where either it is not applicable or it gives too wide of an interval.

In this talk, a different approach is suggested. It is based on reparametrizing the linear model so that the unknown value of the standard becomes a parameter in the nonlinear regression model. Then, standard packages for nonlinear regression can easily provide a point estimator, as well as its standard error, which can then be modified and used as the basis for the confidence interval. The intervals are centered at the point estimator (as opposed to Eisenhardt's intervals), and it can be shown that they are shorter, for a reasonable coverage rate. We show, via simulation, that the major advantage of the proposed method is when the measurement errors are moderately big.

Gini Mean Difference (GMD) is an alternative measure of variability, which is more robust to extreme values, and is used in the area of income distributions. There are more than a dozen ways to write Gini. One of them is as the covariance between the variable and its cumulative distribution. This presentation of the Gini index opens a wide area of research, leading to definitions of Gini covariance, Gini correlation, Gini regression, etc. In this brief talk I'll introduce some of the indices and define a new family of (extended) Gini correlations

This talk will overview statistical methods and issues arising in drug discovery, specifically the collection and analysis of high throughput screening (HTS) data.

Statistical analysis of HTS data is aimed at predicting activity of chemical compounds (potential drugs) against a given biological target. The explanatory variables used are chemical descriptors of compound structure. Data sets tend to have large numbers of observations, and there are many potential explanatory variables.

Some work comparing statistical analysis methods on several HTS data sets shows that local methods, namely K-nearest neighbours (KNN) and classification and regression trees (CART), perform well. Methods like CART have to be used with the objectives of HTS in mind, however. For example, tree pruning to avoid over-fitting seems unnecessary and may even be harmful to identifying activecompounds. I shall also describe some adaptations to KNN and CART that are based on model averaging.

This is joint work with Hugh Chipman and Marcia Wang at the University of Waterloo and with Raymond Lam and Stan Young of GlaxoSmithKline.

In recent years more effort has been directed to the development of statistical methods for the detection, estimation and prediction of environmental changes. The aim is to generate efficient information for use in environmental management. In this talk an overview will be presented and areas where further research is needed will be emphasized. Environmental data are routinely collected from a fixed set of locations within an ecosystem and comprise of time series of discrete and continuous measurements. The interest is to model trend and seasonality at each location and to combine the location specific models into an overall model for making inferences about the entire ecosystem. The results of using kernel smoothing, regression models with dependent error processes and quasi-likelihood methods to investigate the spatial and temporal structure of several water and air quality data will be discussed.

Evidence-based medicine is recognized widely as a major contribution to medicine. However, the interpretation of evidence in EBM has been narrow in many aspects. The evidence in EBM is derived primarily from randomized controlled trials (RCTs), an emphasis that has drawn criticism because the conditions under which RCTs are conducted differ dramatically from everyday clinical care, raising doubts as to the relevance of RCT-based evidence to routine practice. The production and utilization of evidence under EBM follows a top-down approach, with experts conducting trials, synthesizing the literature, and developing guidelines, for the practitioners to adopt. Ironically, EBM has largely ignored the evidence that is available in practitioners' own data (e.g., patient records). We propose "evidence farming" as a paradigm to incorporate practice data systematically as a source of evidence, as an articulated form of clinical experience. With the spread of electronic medical record systems, it is feasible for practitioners to retrieve local endogenous evidence (or "home grown evidence") from their own data. Compared to externally (or exogenously) generated evidence emphasized in EBM, such local endogenous evidence is potentially more relevant and more palatable to practitioners. Furthermore, with the development of networked medical record systems such as the proposed National Health Information System, it is conceivable that practitioners can also "borrow from strength" and utilize data from other practices to derive global endogenous evidence. Local and global evidence can be combined using empirical Bayes methods. Evidence farming suggests several statistical research questions, e.g., the extension of the play-the-winner design to accommodate the multi-level structure, and the consideration of bandwidth selection in bin-smoothing of patient records data at different levels. Evidence farming might exert an important impact on the medical profession, especially on medical education: as clinicians take a proactive role as investigators and participants in the production and utilization of endogenous evidence, the emphasis in medical education will likely shift from rote memorization and literature-based learning to more comprehensive training in research methods, including statistical methods.

* Joint work with Junius Gonzales, Joel Braslow, David Chambers, and Richard Kravitz.

Routinely in statistical applications, hierarchical models arise in which unobserved random effects contribute to heterogeneity amongst sampling units. An easily computable, smooth nonparametric estimate of the underlying mixing distribution can be derived as an approximate nonparametric Bayes estimate under a Dirichlet process prior. I will discuss the recursive estimation algorithm, its consistency properties, and its application in several examples, including its use in the analysis of microarray gene expression data.

The Canadian and US governments have advisories in place to limit the consumption of the Great Lakes fish. Most advisories use fish length or age as a surrogate variable for the concentration of the contaminants in fish. The approach commonly employed is to divide the range of the surrogate variable into a set of successive intervals such that some intervals are identified as no consumption categories (high risk); others as restricted consumption (limited risk) and the remaining intervals as risk free. It is important then to model the relationship between the surrogate variable and the contaminants concentrations. The model allows the estimation of the: 1) concentration of the contaminants for a specified value of the surrogate variable and its precision, and 2) probability that the concentration of the contaminants falling in a certain interval as a function of the surrogate variable.

The aim of this paper is to present a model for the concentration of polychlorinated biphenyl (PCB) in lake trout from Lakes Superior and Ontario waters using age as a surrogate variable. The model highlights the contrasts and similarities between the evolving patterns of the PCB accumulation in whole fish tissue from the two lakes. Classical and bootstrapping techniques are implemented to make inferences about various quantities of interest.

We have established a multi-disciplinary approach to the large-scale high-throughput identification of genes involved in early stage cancers, under the auspices of Genome Canada. As part of this study we will be analyzing 166 Serial Analysis of Gene Expression (SAGE) libraries to profile mRNA expression in approximately 20 different tissue types. One particular focus has been the development of gene expression profiles for early stage lung cancer. By utilizing novel bronchoscopy techniques we have been able to obtain tissue samples from lung carcinoma in-situ. Although only small amounts of tissue are obtained, these are sufficient for the preparation of SAGE and micro-SAGE libraries. By sequencing the SAGE libraries we have been able to generate comprehensive and deep expression profiles for lung cancer. Ten libraries have been analyzed to date, five each for both cancerous and normal samples. We have identified, 14,624 different transcripts in these data. Eighty-four of these genes are consistently up-regulated within the lung cancer samples (58 of which are lung cancer specific and not observed in normal lung) and 122 genes have been identified as being consistently down-regulated in these early-stage lung tumors.

To facilitate analysis of our SAGE data we have developed an expression visualization tool, SageSpace and an analysis database, SageDB. Using these tools, we have been able to assess the heterogeneity between lung cancer samples. Through orthogonal comparison to other publicly available SAGE and EST data we have also been able to assess the representation of these lung cancer associated genes in other adult tissues. Our analysis indicates that four of the transcripts found to be lung cancer specific show expression in only one normal adult tissue. This approach has also allowed us to compare lung cancer expression with expression data from other cancers and other diseases. This information will be useful in determining the potential of existing drug therapies for application in lung cancer treatment. The SageDB system links expression data with a number of biological databases, including PFAM, SwissProt, OMIM, dbEST, BIND and KEGG. This functionality allows us to recreate expression profiles for specific biological pathways, e.g. apoptosis, allowing heterogeneity to be assessed in a pathway specific manner, the results being graphically visualized using the SageSpace viewer.

The use of empirical likelihood in survival analysis was initiated by Thomas and Grunkemeier (1975) who derived pointwise confidence intervals for the survival function. Since the breakthrough work of Owen (1988, 1990) the method has been applied to a variety of statistical problems. The goal of our research is to develop the approach for the comparison of survival functions for k-sample problems in survival analysis. We derive an empirical likelihood simultaneous confidence band for the ratio of two survival functions based on independent right-censored data. Earlier authors have studied such bands for the difference of two survival functions, but the ratio provides a more appropriate comparison in some applications, e.g., in comparing two treatments in biomedical settings. Our approach also works for the difference of two cumulative hazard functions. A test for equality of corresponding hazard functions is also constructed, and consistency against any fixed alternative is established. We develop a Monte Carlo simulation method to approximate the null distribution of the test statistic. Cumulative hazard ratios appear to be more tractable than ratios of survival functions or differences of cumulative hazard functions in the k-sample setting. However, the band for the ratio of survival functions is more stable and narrower than the band for the ratio of cumulative hazard functions. A goodness-of-fit test is developed for checking proportional hazards in k-sample problems. For the comparison of two distributions in the random censorship model (independent competing risks model without censoring), we construct empirical likelihood confidence bands for the ratio of the two cumulative hazards and the ratio of two survival functions. Goodness-of-fit tests for the Koziol--Green model and the equality of the corresponding hazard functions are also developed.

We extend our approach to adjust for covariate effects. All the corresponding results are established under quite general conditions. The proposed methods are illustrated with a real data from a Mayo Clinic trial involving a treatment for primary biliary cirrhosis (PBC) of the liver.

Runs and scans are two common patterns that are used for constructing stopping and switching rules in various fields (e.g., quality control, DNA sequencing, radar detection). Such rules are usually very intuitive and simple to apply, and are usually designed according to empirical rather than theoretical considerations. In contrast to the simplicity of understanding and using runs and scans rules, their probabilistic nature is quite complicated.

In this talk we present a new method that leads to expressions for runs- and scans-related probability and generating functions. The talk will focus both on the mathematical derivations and on the application of the resulting formulas to various industrial statistical procedures. Our method generalizes and modernizes Feller's method (1968). It is based on constructing recurrence relations and solving linear equations, leading to an expression for the probability generating function of the runs- or scans-related variables. We then use the special form of the generating function to derive the probability function with the aid of efficient numerical methods.

Finally we introduce the SQC Online website (http://www.stat.cmu.edu/~galit/SQCOnline). We created this interactive site in order to make our method useful for practitioners in the industry. According to the user's input, the site yields probabilities and plots for a variety of industrial applications (including sampling inspection, system reliability, control charts, and continuous sampling), allowing them to study and plan their process.

It is well known that classical multiple regression is extremely sensitive to outliers in a data set. The same problem holds in the case of multivariate regression. Therefore, we propose more robust methods for multivariate regression and investigate their properties such as influence function and breakdown point.

For a given data set of size n, the multivariate least trimmed squares estimator (MLTS) looks for the subset of size h (0

Using a C-step theorem similarly to Rousseeuw and Van Driessen (1999), we construct an efficient algorithm to compute the MLTS estimator. It is shown that the MLTS has a positive breakdown point that depends on the subset size h to be chosen by the user. In the case of elliptical error distributions we derive its influence function which is unbounded. Good leverage points can have a high effect on the estimator. We investigate the efficiency of the estimator and show that the choice of h is a trade-off between efficiency and breakdown. The use of reweighted versions of the estimator will also be investigated.

Another approach is based on robust estimation of the location and scatter of the joint explanatory and response variables. We show that the robustness properties of the resulting multivariate regression estimator are inherited from the robust location and scatter estimator. We concentrate on the minimum covariance determinant estimator (MCD) to robustly estimate the location and scatter. We show that the influence function of the corresponding 0A regression estimator is bounded. We also investigate efficiency and propose reweighted versions of the estimator to increase efficiency.

References:

Rousseeuw, P.J. (1984). "Least median of squares regression," Journal of the American Statistical Association, 79, 871-880.

Rousseeuw, P.J. and Van Driessen, K. (1999). "A fast algorithm for the minimum covariance determinant estimator," Technometrics, 41, 212-223.