Related papers: Approximate sampling formulae for general finite-a…
In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
Model selection is critical in the modern statistics and machine learning community. However, most existing works do not apply to heavy-tailed data, which are commonly encountered in real applications, such as the single-cell multiomics…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…
This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion…
Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
A Y-linked two-sex branching process with mutations and blind choice of males is a suitable model for analyzing the evolution of the number of carriers of an allele and its mutations of a Y-linked gene. Considering a two-sex monogamous…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
The dynamics of tumour evolution are not well understood. In this paper we provide a statistical framework for evaluating the molecular variation observed in different parts of a colorectal tumour. A multi-sample version of the Ewens…