Related papers: Empirical Process Results for Exchangeable Arrays
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
The exchange algorithm is one of the most popular extensions of the Metropolis--Hastings algorithm to sample from doubly-intractable distributions. However, the theoretical exploration of the exchange algorithm is very limited. For example,…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
Trait allocations are a class of combinatorial structures in which data may belong to multiple groups and may have different levels of belonging in each group. Often the data are also exchangeable, i.e., their joint distribution is…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models - called conjugate…
In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…
In an array of random variables, each row can be regarded as a single, sequence-valued random variable. In this way, the array is seen as a sequence of sequences. Such an array is said to be row exchangeable if each row is an exchangeable…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over…
Failure times of a machinery cannot always be assumed independent and identically distributed, e.g. if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a…
Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to…
We consider long-range dependent data. It is shown that the bootstrapped empirical process of these data converges to a semi-degenerate limit. The random part of this limit is always Gaussian. Thus the bootstrap might fail when the original…
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
When using dyadic data (i.e., data indexed by pairs of units), researchers typically assume a linear model, estimate it using Ordinary Least Squares and conduct inference using ``dyadic-robust" variance estimators. The latter assumes that…
This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an…
In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
We investigate the asymptotic properties of the integrated periodogram calculated from a sequence of indicator functions of dependent extremal events. An event in Euclidean space is extreme if it occurs far away from the origin. We use a…
We reconsider the immediate exchange model and define a more general class of models where mass is split, exchanged and merged. We relate the splitting process to the symmetric inclusion process via thermalization and from that obtain…