Related papers: Detecting random sets by samplings from their valu…
We address the problem of one dimensional segment detection and estimation, in a regression setup. At each point of a fixed or random design, one observes whether that point belongs to the unknown segment or not, up to some additional…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We study from a statistical mechanics viewpoint some of the simplest mathematical objects, finite pure sets. Starting from the empty set, new generations are produced step by step, sets of the next generation being those whose elements are…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
We study the amount of information that is contained in "random pictures", by which we mean the sample sets of a Boolean model. To quantify the notion "amount of information", two closely connected questions are investigated: on the one…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Researchers in psychology characterize decision-making as a process of eliminating options. While statistical modelling typically focuses on the eventual choice, we analyze consideration sets describing, for each survey participant, all…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Intuitively, sampling is likely to be more efficient for prevalence estimation, if the cases (or positives) have a relatively higher representation in the sample than in the population. In case the virus is transmitted via personal…