Related papers: On Poisson approximations for the Ewens sampling f…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
When mutations are rampant, quasispecies theory or Eigen's model predicts that the fittest type in a population may not dominate. Beyond a critical mutation rate, the population may even be delocalized completely from the peak of the…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting,…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry…
Given data drawn from an unknown distribution, $D$, to what extent is it possible to ``amplify'' this dataset and output an even larger set of samples that appear to have been drawn from $D$? We formalize this question as follows: an…
The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
Stirling numbers of the first kind are common in number theory and combinatorics; through Ewen's sampling formula, these numbers enter into the calculation of several population genetics statistics, such as Fu's Fs. In previous papers we…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
Experimental studies often fail to appropriately account for the number of collected samples within a fixed time interval for functional responses. Data of this nature appropriately falls under an Infill Asymptotic domain that is…
We consider Gaussian approximation in a variant of the classical Johnson--Mehl birth-growth model with random growth speed. Seeds appear randomly in $\mathbb{R}^d$ at random times and start growing instantaneously in all directions with a…
We show that the number of cycles in a random permutation chosen according to generalized Ewens measure is normally distributed and compute asymptotic estimates for the mean and variance.
We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \to \infty$, that the random rule has a…
For an integer $n\geq1$, consider a random partition $\Pi_{n}$ of $\{1,\ldots,n\}$ into $K_{n}$ partition sets with $K_{r,n}$ partition subsets of size $r=1,\ldots,n$, and assume $\Pi_{n}$ distributed according to the Ewens-Pitman model…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
The Waxman-Peck theory of the population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central aim is the calculation of the probability density with respect to…