Related papers: Exchangeable min-id sequences: Characterization, e…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is…
The transition law of every exchangeable Feller process on the space of countable graphs is determined by a $\sigma$-finite measure on the space of $\{0,1\}\times\{0,1\}$-valued arrays. In discrete-time, this characterization amounts to a…
We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily…
We develop constructions for exchangeable sequences of point processes that are rendered conditionally-i.i.d. negative binomial processes by a (possibly unknown) random measure called the base measure. Negative binomial processes are useful…
For regime-switching diffusions processes with singular drifts, we introduce integrability conditions involving a nice reference probability measure and the $Q$-matrix of the jump part to study the existence of the invariant probability…
We call a random point measure infinitely ramified if for every $n\in \mathbb N$, it has the same distribution as the $n$-th generation of some branching random walk. On the other hand, branching L\'evy processes model the evolution of a…
An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on inter-relationships between different…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…
Nested nonparametric processes are vectors of random probability measures widely used in the Bayesian literature to model the dependence across distinct, though related, groups of observations. These processes allow a two-level clustering,…
A length-$n$ random sequence $X_1,\ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
This paper studies new classes of infinitely divisible distributions on R^d. Firstly, the connecting classes with a continuous parameter between the Jurek class and the class of selfdecomposable distributions are revisited. Secondly, the…
We argue for the use of separate exchangeability as a modeling principle in Bayesian nonparametric (BNP) inference. Separate exchangeability is de facto widely applied in the Bayesian parametric case, e.g., it naturally arises in simple…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in [0,1]^\N: \sum_{i\ge 1} x_i=1\}$ with GEM…