Related papers: Overdispersed and Markovian Children
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…
In this article I present results from a statistical study of prime numbers that shows a behaviour that is not compatible with the thesis that they are distributed randomly. The analysis is based on studying two arithmetical progressions…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
Comparing the differences in outcomes (that is, in "dependent variables") between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to "independent…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…
This paper studies the trade-off between two different kinds of pure exploration: breadth versus depth. The most biased coin problem asks how many total coin flips are required to identify a "heavy" coin from an infinite bag containing both…
We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset…
We highlight a pitfall when applying stochastic variational inference to general Bayesian networks. For global random variables approximated by an exponential family distribution, natural gradient steps, commonly starting from a unit length…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x)…
When numbers are added in base $b$ in the usual way, carries occur. If two random, independent 1-digit numbers are added, then the probability of a carry is $\frac{b-1}{2b}$. Other choices of digits lead to less carries. In particular, if…
The statistics of outbreaks in a model for the propagation of meningococcal diseases is analyzed, taking into account the possibility that the population is fragmented into weakly connected patches. It is shown that, depending on the size…
A growing literature provides evidence on multigenerational inequality -- the extent to which socio-economic advantages persist across three or more generations. This chapter reviews its main findings and implications. Most studies find…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
Following Fisher, it is widely believed that randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." In particular, it is said to control for known and unknown…
Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…
We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the…