Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than nonfriends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.

Most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small. Motivated by the Naturalistic Teenage Driving Study (NTDS), which represents the exact opposite situation, we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences. We consider standard methods based on generalized estimating equations, under working independence or an appropriate correlation structure, and find them unsatisfactory for dealing with time-dependent covariates when the counts are low. For this situation, we explore a within-cluster resampling (WCR) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples. This leads to a novel WCR method which operates on separated blocks within subjects and which performs better than all of the previously considered methods. The methods are applied to the NTDS data and evaluated in simulation experiments mimicking the NTDS.

We show how a retailer can estimate the optimal price of a new product using observed transaction prices from online second-price auction experiments. For this purpose we propose a Bayesian Pólya tree approach which, given the limited nature of the data, requires a specially tailored implementation. Avoiding the need for a priori parametric assumptions, the Pólya tree approach allows for flexible inference of the valuation distribution, leading to more robust estimation of optimal price than competing parametric approaches. In collaboration with an online jewelry retailer, we illustrate how our methodology can be combined with managerial prior knowledge to estimate the profit maximizing price of a new jewelry product.

A sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of a naïve analysis that presumes all biases were removed by matching or by other analytic adjustments. The power of a sensitivity analysis and the design sensitivity anticipate the outcome of a sensitivity analysis under an assumed model for the generation of the data. It is known that the power of a sensitivity analysis is affected by the choice of test statistic, and, in particular, that a statistic with good Pitman efficiency in a randomized experiment, such as Wilcoxon’s signed rank statistic, may have low power in a sensitivity analysis and low design sensitivity when compared to other statistics. For instance, for an additive treatment effect and errors that are Normal or logistic or t-distributed with 3 degrees of freedom, Brown’s combined quantile average test has Pitman efficiency close to that of Wilcoxon’s test but has higher power in a sensitivity analysis, while a version of Noether’s test has poor Pitman efficiency in a randomized experiment but much higher design sensitivity so it is vastly more powerful than Wilcoxon’s statistic in a sensitivity analysis if the sample size is sufficiently large. A new exact distribution-free test is proposed that rejects if either Brown’s test or Noether’s test rejects after adjusting the two critical values so the overall level of the combined test remains at α, conventionally α = 0.05. In every sampling situation, the design sensitivity of the adaptive test equals the larger of the two design sensitivities of the component tests. The adaptive test exhibits good power in sensitivity analyses asymptotically and in simulations. In one sampling situation—Normal errors and an additive effect that is three-quarters of the standard deviation with 500 matched pairs—the power of Wilcoxon’s test in a sensitivity analysis was 2% and the power of the adaptive test was 87%. A study of treatments for ovarian cancer in the Medicare population is discussed in detail.

A predictive model of terrorist activity is developed by examining the daily number of terrorist attacks in Indonesia from 1994 through 2007. The dynamic model employs a shot noise process to explain the self-exciting nature of the terrorist activities. This estimates the probability of future attacks as a function of the times since the past attacks. In addition, the excess of nonattack days coupled with the presence of multiple coordinated attacks on the same day compelled the use of hurdle models to jointly model the probability of an attack day and corresponding number of attacks. A power law distribution with a shot noise driven parameter best modeled the number of attacks on an attack day. Interpretation of the model parameters is discussed and predictive performance of the models is evaluated.

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.

This paper examines historical patterns of ROA (return on assets) for a cohort of 53,038 publicly traded firms across 93 countries, measured over the past 45 years. Our goal is to screen for firms whose ROA trajectories suggest that they have systematically outperformed their peer groups over time. Such a project faces at least three statistical difficulties: adjustment for relevant covariates, massive multiplicity, and longitudinal dependence. We conclude that, once these difficulties are taken into account, demonstrably superior performance appears to be quite rare. We compare our findings with other recent management studies on the same subject, and with the popular literature on corporate success.

Our methodological contribution is to propose a new class of priors for use in large-scale simultaneous testing. These priors are based on the hypergeometric inverted-beta family, and have two main attractive features: heavy tails and computational tractability. The family is a four-parameter generalization of the normal/inverted-beta prior, and is the natural conjugate prior for shrinkage coefficients in a hierarchical normal model. Our results emphasize the usefulness of these heavy-tailed priors in large multiple-testing problems, as they have a mild rate of tail decay in the marginal likelihood m(y)—a property long recognized to be important in testing.

The starting point of this article is the question “How to retrieve fingerprints of rhythm in written texts?” We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres–Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.

The estimation of the total of an attribute defined over a continuous planar domain is required in many applied settings, such as the estimation of canopy coverage in the Monterano Nature Reserve in Italy. If the design-based approach is considered, the scheme for the placement of the sample sites over the domain is fundamental in order to implement the survey. In real situations, a commonly adopted scheme is based on partitioning the domain into suitable strata, in such a way that a single sample site is uniformly placed (i.e., selected with uniform probability density) in each stratum and sample sites are independently located. Under mild conditions on the function representing the target attribute, it is shown that this scheme gives rise to an unbiased spatial total estimator which is “superefficient” with respect to the estimator based on the uniform placement of independent sample sites over the domain. In addition, the large-sample normality of the estimator is proven and variance estimation issues are discussed.

When releasing data to the public, data stewards are ethically and often legally obligated to protect the confidentiality of data subjects’ identities and sensitive attributes. They also strive to release data that are informative for a wide range of secondary analyses. Achieving both objectives is particularly challenging when data stewards seek to release highly resolved geographical information. We present an approach for protecting the confidentiality of data with geographic identifiers based on multiple imputation. The basic idea is to convert geography to latitude and longitude, estimate a bivariate response model conditional on attributes, and simulate new latitude and longitude values from these models. We illustrate the proposed methods using data describing causes of death in Durham, North Carolina. In the context of the application, we present a straightforward tool for generating simulated geographies and attributes based on regression trees, and we present methods for assessing disclosure risks with such simulated data.

Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting issues in higher dimensions. To address both concerns, we present an algorithm, which we term Isotonic Recursive Partitioning (IRP), for isotonic regression based on recursively partitioning the covariate space through solution of progressively smaller “best cut” subproblems. This creates a regularized sequence of isotonic models of increasing model complexity that converges to the global isotonic regression solution. The models along the sequence are often more accurate than the unregularized isotonic regression model because of the complexity control they offer. We quantify this complexity control through estimation of degrees of freedom along the path. Success of the regularized models in prediction and IRPs favorable computational properties are demonstrated through a series of simulated and real data experiments. We discuss application of IRP to the problem of searching for gene–gene interactions and epistasis, and demonstrate it on data from genome-wide association studies of three common diseases.

We propose a model-based vulnerability index of the population from Uruguay to vector-borne diseases. We have available measurements of a set of variables in the census tract level of the 19 Departmental capitals of Uruguay. In particular, we propose an index that combines different sources of information via a set of micro-environmental indicators and geographical location in the country. Our index is based on a new class of spatially hierarchical factor models that explicitly account for the different levels of hierarchy in the country, such as census tracts within the city level, and cities in the country level. We compare our approach with that obtained when data are aggregated in the city level. We show that our proposal outperforms current and standard approaches, which fail to properly account for discrepancies in the region sizes, for example, number of census tracts. We also show that data aggregation can seriously affect the estimation of the cities vulnerability rankings under benchmark models.

To analyze and project age-specific mortality or morbidity rates age-period-cohort (APC) models are very popular. Bayesian approaches facilitate estimation and improve predictions by assigning smoothing priors to age, period and cohort effects. Adjustments for overdispersion are straightforward using additional random effects. When rates are further stratified, for example, by countries, multivariate APC models can be used, where differences of stratum-specific effects are interpretable as log relative risks. Here, we incorporate correlated stratum-specific smoothing priors and correlated overdispersion parameters into the multivariate APC model, and use Markov chain Monte Carlo and integrated nested Laplace approximations for inference. Compared to a model without correlation, the new approach may lead to more precise relative risk estimates, as shown in an application to chronic obstructive pulmonary disease mortality in three regions of England and Wales. Furthermore, the imputation of missing data for one particular stratum may be improved, since the new approach takes advantage of the remaining strata if the corresponding observations are available there. This is shown in an application to female mortality in Denmark, Sweden and Norway from the 20th century, where we treat for each country in turn either the first or second half of the observations as missing and then impute the omitted data. The projections are compared to those obtained from a univariate APC model and an extended Lee–Carter demographic forecasting approach using the proper Dawid–Sebastiani scoring rule.

We consider integrative modeling of multiple gene networks and diverse genomic data, including protein-DNA binding, gene expression and DNA sequence data, to accurately identify the regulatory target genes of a transcription factor (TF). Rather than treating all the genes equally and independently a priori in existing joint modeling approaches, we incorporate the biological prior knowledge that neighboring genes on a gene network tend to be (or not to be) regulated together by a TF. A key contribution of our work is that, to maximize the use of all existing biological knowledge, we allow incorporation of multiple gene networks into joint modeling of genomic data by introducing a mixture model based on the use of multiple Markov random fields (MRFs). Another important contribution of our work is to allow different genomic data to be correlated and to examine the validity and effect of the independence assumption as adopted in existing methods. Due to a fully Bayesian approach, inference about model parameters can be carried out based on MCMC samples. Application to an E. coli data set, together with simulation studies, demonstrates the utility and statistical efficiency gains with the proposed joint model.

RNA interference (RNAi) is an endogenous cellular process in which small double-stranded RNAs lead to the destruction of mRNAs with complementary nucleoside sequence. With the production of RNAi libraries, large-scale RNAi screening in human cells can be conducted to identify unknown genes involved in a biological pathway. One challenge researchers face is how to deal with the multiple testing issue and the related false positive rate (FDR) and false negative rate (FNR). This paper proposes a Bayesian hierarchical measurement error model for the analysis of data from a two-channel RNAi high-throughput experiment with replicates, in which both the activity of a particular biological pathway and cell viability are monitored and the goal is to identify short hair-pin RNAs (shRNAs) that affect the pathway activity without affecting cell activity. Simulation studies demonstrate the flexibility and robustness of the Bayesian method and the benefits of having replicates in the experiment. This method is illustrated through analyzing the data from a RNAi high-throughput screening that searches for cellular factors affecting HCV replication without affecting cell viability; comparisons of the results from this HCV study and some of those reported in the literature are included.

Parameter estimation in astrophysics often requires the use of complex physical models. In this paper we study the problem of estimating the parameters that describe star formation history (SFH) in galaxies. Here, high-dimensional spectral data from galaxies are appropriately modeled as linear combinations of physical components, called simple stellar populations (SSPs), plus some nonlinear distortions. Theoretical data for each SSP is produced for a fixed parameter vector via computer modeling. Though the parameters that define each SSP are continuous, optimizing the signal model over a large set of SSPs on a fine parameter grid is computationally infeasible and inefficient. The goal of this study is to estimate the set of parameters that describes the SFH of each galaxy. These target parameters, such as the average ages and chemical compositions of the galaxy’s stellar populations, are derived from the SSP parameters and the component weights in the signal model. Here, we introduce a principled approach of choosing a small basis of SSP prototypes for SFH parameter estimation. The basic idea is to quantize the vector space and effective support of the model components. In addition to greater computational efficiency, we achieve better estimates of the SFH target parameters. In simulations, our proposed quantization method obtains a substantial improvement in estimating the target parameters over the common method of employing a parameter grid. Sparse coding techniques are not appropriate for this problem without proper constraints, while constrained sparse coding methods perform poorly for parameter estimation because their objective is signal reconstruction, not estimation of the target parameters.

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric L-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.