Are different slices of fixed income markets more dependent during times of crisis than during normal times? We call this increase in dependence during times of crisis credit contagion, and define this concept through a local correlation function very similar to the usual correlation coefficient. Surprisingly, an analysis of bond yield spreads and credit default swap premia suggests that fixed income markets have not experienced credit contagion during crises like the Panic of 2008. Instead, these measures of credit risk have tended to become less correlated or even conditionally uncorrelated during crises---a concept we call credit confusion.

Maximum likelihood estimators have traditionally dominated discrete inference for a long time. In this work we apply statistical decision theory to derive a new contender that minimizes a posterior generalized Hamming loss: the centroid estimator. The centroid estimator is formally characterized as a solution to a discrete optimization problem having posterior marginal distributions as inputs. We discuss both specific constraints of interest and broad conditions under which this optimization problem becomes tractable and provide further generalizations to centroid estimation. We illustrate centroid estimation with simple applications to stochastic grammar parsing, reconstruction of ancestral states given a phylogeny, and RNA secondary structure prediction. Finally, we offer a few concluding remarks and directions for future work.

We consider modeling dependent high throughput expression data arising from different molecular interrogation technologies. Dependence between molecules is introduced via the explicit consideration of informative prior information associated with available pathways, representing known biochemical regulatory processes. The important features of the proposed methodology are the ease of representing typical prior information on the nature of dependencies, model-based parsimonious representation of the signal as an ordinal outcome, and the use of coherent probabilistic schemes over both, structure and strength of the conjectured dependencies. As part of the inference we reduce the recorded data to a trinary response representing underexpression, average expression and overexpression. Inference in the described model is implemented through Markov chain Monte Carlo (MCMC) simulation, including posterior simulation over conditional dependence and independence. The latter involves a variable dimensional parameter space. We use a reversible jump MCMC scheme. The motivating example are data from ovarian cancer patients.

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, since commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this paper, we focus on hypothesis tests of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such hypothesis tests have correct Type I error for large samples. Our main result is that for a surprisingly large class of commonly used regression models, standard regression-based hypothesis tests (but using robust variance estimators) are guaranteed to have correct Type I error for large samples, even when the models are incorrec! tly specified. To the best of our knowledge, this robustness of such model-based hypothesis tests to incorrectly specified models was previously unknown for Poisson regression models and for other commonly used models we consider. Our results have practical implications for understanding the reliability of commonly used, model-based tests for analyzing randomized trials.

We will introduce general notions of stochastic derivatives on stochastic processes. We will first show how the tools from Malliavin Calculus allow to study these objects. The involved techniques yield applications on various structures of the processes under study: gradient diffusions, asymptotic expansions of fractional SDE. Second, we will extend ODE on stochastic processes through these derivatives. We will focus on the relationships between these stochastic equations and various PDE, including the Navier-Stokes equation.

We consider a stable Gaussian autoregressive process and wish to estimate its mean, variance and autoregression coefficient based on rounded-off observations. We present a law of large numbers, uniform in the parameters which is the decisive step towards establishing consistency of the corresponding maximum likelihood estimates.

Wireless Sensor Networks (WSN) are a new technology with many applications, including environmental monitoring, habitat monitoring, surveillance, and health care. In many applications, each sensor records a signal (temperature, vibration, etc) emitted from a target, makes a decision about the target's presence, and then transmits either the signal or the decision to a central node. Transmission of decisions instead of signals offers significant savings in communication costs, but binary decisions are unreliable in noisy environments. We develop a new algorithm to improve reliability of binary decisions, the Local Vote Decision Fusion (LVDF). Using LVDF, we develop new data fusion algorithms for target detection (making a network-level decision about the presence of a target), target localization (estimating the target's position), and target tracking (estimating trajectories of multiple moving targets over time). We apply our framework based on binary corrected decisions to two case studies -- an experiment involving tracking people and a project of tracking zebras. Our tracking approach based on corrected decisions exhibits a competitive performance even compared to maximum likelihood estimation based on the signals themselves. Motivated by the success of the LVDF algorithm in WSNs, we are currently developing a general classification framework for based on data fusion from correlated classifiers

Abstract: This talk will be based on lecture notes by Géard Ben Arous of NYU. I will begin by discussing the continuous-time random walk (CTRW) on Z^d, which is a simple random walk that waits for a random time at each step. The waiting times we consider are sampled from a heavy-tailed distribution. With appropriate scaling of the CTRW, we obtain another process, called the fractional kinetic process, which is Brownian motion with a time change given by the inverse of an alpha-stable subordinator which is independent of the Brownian motion. We will then introduce the Bouchaud trap model, which generalizes the CTRW by adding dependence between the steps of the random walker and the waiting times. We will look at the scaling limit of this model and see some surprising results.