No Arabic abstract
Modeling correlated or highly stratified multiple-response data becomes a common data analysis task due to modern data monitoring facilities and methods. Generalized estimating equations (GEE) is one of the popular statistical methods for analyzing this kind of data. In this paper, we present a sequential estimation procedure for obtaining GEE-based estimates. In addition to the conventional random sampling, the proposed method features adaptive subject recruiting and variable selection. Moreover, we equip our method with an adaptive shrinkage property so that it can decide the effective variables during the estimation procedure and build a confidence set with a pre-specified precision for the corresponding parameters. In addition to the statistical properties of the proposed procedure, we assess our method using both simulated data and real data sets.
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant models. Based on formal Bayesian decision-theoretic reasoning, we develop a time-adaptive approach to exploring, weighting, combining and selecting models that differ in terms of predictive variables included. The adaptivity allows for changes in the sets of favored models over time, and is guided by the specific forecasting goals. A synthetic example illustrates how decision-guided variable selection differs from traditional Bayesian model uncertainty analysis and standard model averaging. An applied study in one motivating application of long-term macroeconomic forecasting highlights the utility of the new approach in terms of improving predictions as well as its ability to identify and interpret different sets of relevant models over time with respect to specific, defined forecasting goals.
In this paper, we aim at solving a class of multiple testing problems under the Bayesian sequential decision framework. Our motivating application comes from binary labeling tasks in crowdsourcing, where the requestor needs to simultaneously decide which worker to choose to provide the label and when to stop collecting labels under a certain budget constraint. We start with the binary hypothesis testing problem to determine the true label of a single object, and provide an optimal solution by casting it under the adaptive sequential probability ratio test (Ada-SPRT) framework. We characterize the structure of the optimal solution, i.e., optimal adaptive sequential design, which minimizes the Bayes risk through log-likelihood ratio statistic. We also develop a dynamic programming algorithm that can efficiently approximate the optimal solution. For the multiple testing problem, we further propose to adopt an empirical Bayes approach for estimating class priors and show that our method has an averaged loss that converges to the minimal Bayes risk under the true model. The experiments on both simulated and real data show the robustness of our method and its superiority in labeling accuracy as compared to several other recently proposed approaches.
Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. The first example we undertook was for the purpose of accelerating imaging speed in a high resolution material imaging; the second was use of sequential design for the purpose of mapping a chemical phase diagram. In both examples, the underlying regression functions have discontinuities, so many of the existing design optimization approaches cannot be applied because they mostly assume a continuous regression function. Although some existing adaptive design strategies developed from treed regression models can handle the discontinuities, the Bayesian approaches come with computationally expensive Markov Chain Monte Carlo techniques for posterior inferences and subsequent design point selections, which is not appropriate for the first motivating example that requires computation at least faster than the original imaging speed. In addition, the treed models are based on the domain partitioning that are inefficient when the discontinuities occurs over complex sub-domain boundaries. We propose a simple and effective adaptive design strategy for a regression analysis with discontinuities: some statistical properties with a fixed design will be presented first, and then these properties will be used to propose a new criterion of selecting the design points for the regression analysis. Sequential design with the new criterion will be presented with comprehensive simulated examples, and its application to the two motivating examples will be presented.
The article considers the problem of estimating a high-dimensional sparse parameter in the presence of side information that encodes the sparsity structure. We develop a general framework that involves first using an auxiliary sequence to capture the side information, and then incorporating the auxiliary sequence in inference to reduce the estimation risk. The proposed method, which carries out adaptive SURE-thresholding using side information (ASUS), is shown to have robust performance and enjoy optimality properties. We develop new theories to characterize regimes in which ASUS far outperforms competitive shrinkage estimators, and establish precise conditions under which ASUS is asymptotically optimal. Simulation studies are conducted to show that ASUS substantially improves the performance of existing methods in many settings. The methodology is applied for analysis of data from single cell virology studies and microarray time course experiments.
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean and covariance structure informs the proposed mechanism and is also used in a delayed-acceptance algorithm. Information on the resulting state of the system is given by a Gaussian mixture. In on-line mode, the algorithm is adaptive and uses a sliding window approach to accelerate sampling speed and to maintain appropriate acceptance rates. We apply the algorithm to joined state and parameter estimation in the case of irregularly sampled GPS time series data.