Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Sequential anomaly detection in the presence of noise and limited feedback

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: 1) filtering, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2) hedging, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset. © 1963-2012 IEEE.

Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition.

In this paper, we propose generalized sampling approaches for measuring a multi-dimensional object using a compact compound-eye imaging system called thin observation module by bound optics (TOMBO). This paper shows the proposed system model, physical examples, and simulations to verify TOMBO imaging using generalized sampling. In the system, an object is modulated and multiplied by a weight distribution with physical coding, and the coded optical signal is integrated on to a detector array. A numerical estimation algorithm employing a sparsity constraint is used for object reconstruction.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Chemical and biological applications of digital-microfluidic devices

The advent of digital microfluidic lab-on-a-chip (LoC) technology offers a platform for developing diagnostic applications with the advantages of portability, reduction of the volumes of the sample and reagents, faster analysis times, increased automation, low power consumption, compatibility with mass manufacturing, and high throughput. Moreover, digital microfluidics is being applied in other areas such as airborne chemical detection, DNA sequencing by synthesis, and tissue engineering. In most diagnostic and chemical-detection applications, a key challenge is the preparation of the analyte for presentation to the on-chip detection system. Thus, in diagnostics, raw physiological samples must be introduced onto the chip and then further processed by lysing blood cells and extracting DNA. For massively parallel DNA sequencing, sample preparation can be performed off chip, but the synthesis steps must be performed in a sequential on-chip format by automated control of buffers and nucleotides to extend the read lengths of DNA fragments. In airborne particulate-sampling applications, the sample collection from an air stream must be integrated into the LoC analytical component, which requires a collection droplet to scan an exposed impacted surface after its introduction into a closed analytical section. Finally, in tissue-engineering applications, the challenge for LoC technology is to build high-resolution (less than 10 microns) 3D tissue constructs with embedded cells and growth factors by manipulating and maintaining live cells in the chip platform. This article discusses these applications and their implementation in digital-microfluidic LoC platforms. © 2007 IEEE.

A model of sequential heart and composite tissue allotransplant in rats.

BACKGROUND: Some of the 600,000 patients with solid organ allotransplants need reconstruction with a composite tissue allotransplant, such as the hand, abdominal wall, or face. The aim of this study was to develop a rat model for assessing the effects of a secondary composite tissue allotransplant on a primary heart allotransplant. METHODS: Hearts of Wistar Kyoto rats were harvested and transplanted heterotopically to the neck of recipient Fisher 344 rats. The anastomoses were performed between the donor brachiocephalic artery and the recipient left common carotid artery, and between the donor pulmonary artery and the recipient external jugular vein. Recipients received cyclosporine A for 10 days only. Heart rate was assessed noninvasively. The sequential composite tissue allotransplant consisted of a 3 x 3-cm abdominal musculocutaneous flap harvested from Lewis rats and transplanted to the abdomen of the heart allotransplant recipients. The abdominal flap vessels were connected to the femoral vessels. No further immunosuppression was administered following the composite tissue allotransplant. Ten days after composite tissue allotransplantation, rejection of the heart and abdominal flap was assessed histologically. RESULTS: The rat survival rate of the two-stage transplant surgery was 80 percent. The transplanted heart rate decreased from 150 +/- 22 beats per minute immediately after transplant to 83 +/- 12 beats per minute on day 20 (10 days after stopping immunosuppression). CONCLUSIONS: This sequential allotransplant model is technically demanding. It will facilitate investigation of the effects of a secondary composite tissue allotransplant following primary solid organ transplantation and could be useful in developing future immunotherapeutic strategies.

The ocean sampling day consortium.

Ocean Sampling Day was initiated by the EU-funded Micro B3 (Marine Microbial Biodiversity, Bioinformatics, Biotechnology) project to obtain a snapshot of the marine microbial biodiversity and function of the world's oceans. It is a simultaneous global mega-sequencing campaign aiming to generate the largest standardized microbial data set in a single day. This will be achievable only through the coordinated efforts of an Ocean Sampling Day Consortium, supportive partnerships and networks between sites. This commentary outlines the establishment, function and aims of the Consortium and describes our vision for a sustainable study of marine microbial communities and their embedded functional traits.