Related papers: On sequential selection and a first passage proble…
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a…
We revisit the problem of maximising the expected length of increasing subsequence that can be selected from a marked Poisson process by an online strategy. Resorting to a natural size variable, the problem is represented in terms of a…
The Poisson compound decision problem is a long-standing problem in statistics, where empirical Bayes methodologies are commonly used to estimate Poisson's means in static or batch domains. In this paper, we study the Poisson compound…
The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here…
Let $v_n$ be the maximum expected length of an increasing subsequence, which can be selected by an online nonanticipating policy from a random sample of size $n$. Refining known estimates, we obtain an asymptotic expansion of $v_n$ up to a…
We study an edge-weighted online stochastic \emph{Generalized Assignment Problem} with \emph{unknown} Poisson arrivals. In this model, we consider a bipartite graph that contains offline bins and online items, where each offline bin is…
The online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the…
We study the online stochastic matching problem. Consider a bipartite graph with offline vertices on one side, and with i.i.d.online vertices on the other side. The offline vertices and the distribution of online vertices are known to the…
We introduce the problem of Poisson sampling over joins: compute a sample of the result of a join query by conceptually performing a Bernoulli trial for each join tuple, using a non-uniform and tuple-specific probability. We propose an…
This work investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one "most informative"…
In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the…
Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…
Queuing systems with an unlimited number of devices with an incoming nonstationary Poisson flow and a random flow controlled by a Markov chain are investigated. The inexpediency of ap-proximation of the birth process by Poisson flows in…
This paper deals with the problem of model selection for a general class of integer-valued time series. We propose a penalized criterion based on the Poisson quasi-likelihood of the model. Under certain regularity conditions, the…