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We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
We discuss uniform sampling algorithms that are based on stochastic growth methods, using sampling of extreme configurations of polymers in simple lattice models as a motivation. We shall show how a series of clever enhancements to a…
We establish the limiting distribution of $\frac{{(\log \log x)}^{1/4}}{\sqrt{x}} \sum_{n\le x}\alpha(n)$ where $\alpha$ is a Steinhaus random multiplicative function, answering a question of Harper. The distributional convergence is proved…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
State-of-the-art parallel sorting algorithms for distributed-memory architectures are based on computing a balanced partitioning via sampling and histogramming. By finding samples that partition the sorted keys into evenly-sized chunks,…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
Revision of the paper previously entitled "Learning a Machine for the Decision in a Partially Observable Markov Universe" In this paper, we are interested in optimal decisions in a partially observable universe. Our approach is to directly…
In this paper we survey and further study partial sums of a stationary process via approximation with a martingale with stationary differences. Such an approximation is useful for transferring from the martingale to the original process the…
This paper derives the asymptotic behavior of realized power variation of pure-jump It\^{o} semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated…
We analyze the convergence rate of the randomized Newton-like method introduced by Qu et. al. (2016) for smooth and convex objectives, which uses random coordinate blocks of a Hessian-over-approximation matrix $\bM$ instead of the true…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…