In 1980, a burial tomb was unearthed in Jerusalem containing ossuaries (limestone coffins) bearing such inscriptions as Yeshua son of Yehosef, Marya, Yoseh—names which match those of New Testament (NT) figures, but were otherwise in common use. This paper discusses certain statistical aspects of authenticating or repudiating links between this find and the NT family. The available data are laid out, and we examine the distribution of names (onomasticon) of the era. An approach is proposed for measuring the “surprisingness” of the observed outcome relative to a “hypothesis” that the tombsite belonged to the NT family. On the basis of a particular—but far from uncontested—set of assumptions, our measure of “surprisingness” is significantly high.

We critique the analysis by A. Feuerverger of an archaeological find that has been alleged by some to be the tomb of Jesus of Nazareth. We show that his analysis rests on six faulty assumptions that have been severely criticized by historians, archaeologists, and scholars in related disciplines. We summarize the results of an alternative computation using Bayes’ theorem that estimates a probability of less than 2% that the Talpiot tomb belongs to Jesus of Nazareth.

Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called “at-bats”), an observed number of successes (“hits”) distributed according to the binomial distribution, and with a true (but unknown) value of p_i that represents the player’s latent ability. This is a common data structure in many statistical applications; and so the methodological study here has implications for such a range of applications.

We look at batting records for each Major League player over the course of a single season (2005). The primary focus is on using only the batting records from an earlier part of the season (e.g., the first 3 months) in order to estimate the batter’s latent ability, p_i, and consequently, also to predict their batting-average performance for the remainder of the season. Since we are using a season that has already concluded, we can then validate our estimation performance by comparing the estimated values to the actual values for the remainder of the season.

The prediction methods to be investigated are motivated from empirical Bayes and hierarchical Bayes interpretations. A newly proposed nonparametric empirical Bayes procedure performs particularly well in the basic analysis of the full data set, though less well with analyses involving more homogeneous subsets of the data. In those more homogeneous situations better performance is obtained from appropriate versions of more familiar methods. In all situations the poorest performing choice is the naïve predictor which directly uses the current average to predict the future average.

One feature of all the statistical methodologies here is the preliminary use of a new form of variance stabilizing transformation in order to transform the binomial data problem into a somewhat more familiar structure involving (approximately) Normal random variables with known variances. This transformation technique is also used in the construction of a new empirical validation test of the binomial model assumption that is the conceptual basis for all our analyses.

Diffusion tensor imaging (DTI) is a novel modality of magnetic resonance imaging that allows noninvasive mapping of the brain’s white matter. A particular map derived from DTI measurements is a map of water principal diffusion directions, which are proxies for neural fiber directions. We consider a study in which diffusion direction maps were acquired for two groups of subjects. The objective of the analysis is to find regions of the brain in which the corresponding diffusion directions differ between the groups. This is attained by first computing a test statistic for the difference in direction at every brain location using a Watson model for directional data. Interesting locations are subsequently selected with control of the false discovery rate. More accurate modeling of the null distribution is obtained using an empirical null density based on the empirical distribution of the test statistics across the brain. Further, substantial improvements in power are achieved by local spatial averaging of the test statistic map. Although the focus is on one particular study and imaging technology, the proposed inference methods can be applied to other large scale simultaneous hypothesis testing problems with a continuous underlying spatial structure.

Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman’s nonparametric model. Previous results are generalized, and more intuitive proofs are given. A bias term is isolated, and conditions are given for unbiased estimation in finite samples.

Modern statisticians are often presented with hundreds or thousands of hypothesis testing problems to evaluate at the same time, generated from new scientific technologies such as microarrays, medical and satellite imaging devices, or flow cytometry counters. The relevant statistical literature tends to begin with the tacit assumption that a single combined analysis, for instance, a False Discovery Rate assessment, should be applied to the entire set of problems at hand. This can be a dangerous assumption, as the examples in the paper show, leading to overly conservative or overly liberal conclusions within any particular subclass of the cases. A simple Bayesian theory yields a succinct description of the effects of separation or combination on false discovery rate analyses. The theory allows efficient testing within small subclasses, and has applications to “enrichment,” the detection of multi-case effects.

Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the number of cases. This paper tests two exceptionally fast algorithms for estimating regression coefficients with a lasso penalty. The previously known ℓ₂ algorithm is based on cyclic coordinate descent. Our new ℓ₁ algorithm is based on greedy coordinate descent and Edgeworth’s algorithm for ordinary ℓ₁ regression. Each algorithm relies on a tuning constant that can be chosen by cross-validation. In some regression problems it is natural to group parameters and penalize parameters group by group rather than separately. If the group penalty is proportional to the Euclidean norm of the parameters of the group, then it is possible to majorize the norm and reduce parameter estimation to ℓ₂ regression with a lasso penalty. Thus, the existing algorithm can be extended to novel settings. Each of the algorithms discussed is tested via either simulated or real data or both. The Appendix proves that a greedy form of the ℓ₂ algorithm converges to the minimum value of the objective function.

The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, but, unlike regular Lasso applied to the entries of the Cholesky factor, results in a sparse estimator for the inverse of the covariance matrix. An iterative algorithm for solving the optimization problem is developed. The estimator is compared to a number of other covariance estimators and is shown to do best, both in simulations and on a real data example. Simulations show that the margin by which the estimator outperforms its competitors tends to increase with dimension.

This paper studies questionnaire design as a formal decision problem, focusing on one element of the design process: skip sequencing. We propose that a survey planner use an explicit loss function to quantify the trade-off between cost and informativeness of the survey and aim to make a design choice that minimizes loss. We pose a choice between three options: ask all respondents about an item of interest, use skip sequencing, thereby asking the item only of respondents who give a certain answer to an opening question, or do not ask the item at all. The first option is most informative but also most costly. The use of skip sequencing reduces respondent burden and the cost of interviewing, but may spread data quality problems across survey items, thereby reducing informativeness. The last option has no cost but is completely uninformative about the item of interest. We show how the planner may choose among these three options in the presence of two inferential problems, item nonresponse and response error.

Ready access to emerging databases of gene annotation and functional pathways has shifted assessments of differential expression in DNA microarray studies from single genes to groups of genes with shared biological function. This paper takes a critical look at existing methods for assessing the differential expression of a group of genes (functional category), and provides some suggestions for improved performance. We begin by presenting a general framework, in which the set of genes in a functional category is compared to the complementary set of genes on the array. The framework includes tests for overrepresentation of a category within a list of significant genes, and methods that consider continuous measures of differential expression. Existing tests are divided into two classes. Class 1 tests assume gene-specific measures of differential expression are independent, despite overwhelming evidence of positive correlation. Analytic and simulated results are presented that demonstrate Class 1 tests are strongly anti-conservative in practice. Class 2 tests account for gene correlation, typically through array permutation that by construction has proper Type I error control for the induced null. However, both Class 1 and Class 2 tests use a null hypothesis that all genes have the same degree of differential expression. We introduce a more sensible and general (Class 3) null under which the profile of differential expression is the same within the category and complement. Under this broader null, Class 2 tests are shown to be conservative. We propose standard bootstrap methods for testing against the Class 3 null and demonstrate they provide valid Type I error control and more power than array permutation in simulated datasets and real microarray experiments.

In 2004 the Dutch Department of Social Affairs conducted a survey to assess the extent of noncompliance with social security regulations. The survey was conducted among 870 recipients of social security benefits and included a series of sensitive questions about regulatory noncompliance. Due to the sensitive nature of the questions the randomized response design was used. Although randomized response protects the privacy of the respondent, it is unlikely that all respondents followed the design. In this paper we introduce a model that allows for respondents displaying self-protective response behavior by consistently giving the nonincriminating response, irrespective of the outcome of the randomizing device. The dependent variable denoting the total number of incriminating responses is assumed to be generated by the application of randomized response to a latent Poisson variable denoting the true number of rule violations. Since self-protective responses result in an excess of observed zeros in relation to the Poisson randomized response distribution, these are modeled as observed zero-inflation. The model includes predictors of the Poisson parameters, as well as predictors of the probability of self-protective response behavior.

Multi-sample microarray experiments have become a standard experimental method for studying biological systems. A frequent goal in such studies is to unravel the regulatory relationships between genes. During the last few years, regression models have been proposed for the de novo discovery of cis-acting regulatory sequences using gene expression data. However, when applied to multi-sample experiments, existing regression based methods model each individual sample separately. To better capture the dynamic relationships in multi-sample microarray experiments, we propose a flexible method for the joint modeling of promoter sequence and multivariate expression data.

In higher order eukaryotic genomes expression regulation usually involves combinatorial interaction between several transcription factors. Experiments have shown that spacing between transcription factor binding sites can significantly affect their strength in activating gene expression. We propose an adaptive model building procedure to capture such spacing dependent cis-acting regulatory modules.

We apply our methods to the analysis of microarray time-course experiments in yeast and in Arabidopsis. These experiments exhibit very different dynamic temporal relationships. For both data sets, we have found all of the well-known cis-acting regulatory elements in the related context, as well as being able to predict novel elements.

We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the more common orthogonal parametrization. First, analytical results are given for the 2×2 factorial. Since practical applications often involve a more complex factorial structure, we next explore general factorials and obtain a collection of optimal designs in the saturated, that is, most economic, case. This, in turn, is seen to yield an approach for finding optimal or efficient designs in the practically more important nearly saturated cases. Thereafter, the findings are extended to the more intricate situation where the underlying model incorporates dye-coloring effects, and the role of dye-swapping is critically examined.

Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21–29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.

Microarray time course (MTC) gene expression data are commonly collected to study the dynamic nature of biological processes. One important problem is to identify genes that show different expression profiles over time and pathways that are perturbed during a given biological process. While methods are available to identify the genes with differential expression levels over time, there is a lack of methods that can incorporate the pathway information in identifying the pathways being modified/activated during a biological process. In this paper we develop a hidden spatial-temporal Markov random field (hstMRF)-based method for identifying genes and subnetworks that are related to biological processes, where the dependency of the differential expression patterns of genes on the networks are modeled over time and over the network of pathways. Simulation studies indicated that the method is quite effective in identifying genes and modified subnetworks and has higher sensitivity than the commonly used procedures that do not use the pathway structure or time dependency information, with similar false discovery rates. Application to a microarray gene expression study of systemic inflammation in humans identified a core set of genes on the KEGG pathways that show clear differential expression patterns over time. In addition, the method confirmed that the TOLL-like signaling pathway plays an important role in immune response to endotoxins.