Registers are increasingly important sources of data to be analyzed. Examples include registers of congenital abnormalities, supermarket purchases, or traffic violations. In such registers, records are created when a relevant event is observed, and they contain the features characterizing the event. Understanding the structure of associations among the features is of primary interest. However, the registers often do not contain cases in which no feature is present and therefore, standard multiplicative or log-linear models may not be applicable.
In a seminal paper, Robins (1998) introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. He established identification of MSM parameters under a sequential randomization assumption (SRA), which rules out unmeasured confounding of treatment assignment over time.
A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse-Bayes technique with prior-predictive tail probabilities to define replication success. The method gives rise to a quantitative measure for replication success, called the sceptical p-value. The sceptical p-value integrates traditional significance of both the original and replication study with a comparison of the respective effect sizes.
The asymptotics of the second-largest eigenvalue in random regular graphs (also referred to as the "Alon conjecture") have been computed by Joel Friedman in his celebrated 2004 paper. Recently, a new proof of this result has been given by Charles Bordenave, using the non-backtracking operator and the Ihara-Bass formula. In the same spirit, we have been able to translate Bordenave's ideas to bipartite biregular graphs in order to calculate the asymptotical value of the second-largest pair of eigenvalues, and obtained a similar spectral gap result.
This talk presents a variational framework for the asymptotic analysis of empirical risk minimization in general settings. In its most general form the framework concerns a two-stage inference procedure. In the first stage of the procedure, an average loss criterion is used to fit the trajectory of an observed dynamical system with a trajectory of a reference dynamical system. In the second stage of the procedure, a parameter estimate is obtained from the optimal trajectory of the reference system.
Non-Gaussian spatial data arise in a number of disciplines. Examples include spatial data on disease incidences (counts), and satellite images of ice sheets (presence-absence). Spatial generalized linear mixed models (SGLMMs), which build on latent Gaussian processes or Markov random fields, are convenient and flexible models for such data and are used widely in mainstream statistics and other disciplines. For high-dimensional data, SGLMMs present significant computational challenges due to the large number of dependent spatial random effects.
Hawkes processes has been a popular point process model for capturing mutual excitation of discrete events. In the network setting, this can capture the mutual influence between nodes, which has a wide range of applications in neural science, social networks, and crime data analysis. In this talk, I will present a statistical change-point detection framework to detect in real-time, a change in the influence using streaming discrete events.
R. A. Fisher, the father of modern statistics, proposed the idea of fiducial inference in the 1930's. While his proposal led to some interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher's approach because it went against the ideas of statistical inference of the time.
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs.
We study maximum likelihood estimation for exponential families that are multivariate totally positive of order two (MTP2). Such distributions appear in the context of ferromagnetism in the Ising model and various latent models, as for example Brownian motion tree models used in phylogenetics. We show that maximum likelihood estimation for MTP2 exponential families is a convex optimization problem. For quadratic exponential families such as Ising models and Gaussian graphical models, we show that MTP2 implies sparsity of the underlying graph without the need of a tuning parameter.