Related papers: Comparing Evolutionary Rates Using An Exact Test f…
In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…
This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error…
We present a comprehensive new framework for handling biologically accurate models of molecular evolution. This model provides a systematic framework for studying models of molecular evolution that implement heterogeneous rates,…
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
We consider the evolution of N bosons, where N is large, with two-body interactions of the form $N^{3\beta}v(N^\beta \cdot)$, $0\leq\beta\leq 1$. The parameter $\beta$ measures the strength of interactions. We compare the exact evolution…
The Full Counting Statistics (FCS) is studied for a one-dimensional system of non-interacting fermions with and without disorder. For two unbiased $L$ site lattices connected at time $t=0$, the charge variance increases as the natural…
Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular the fossilized…
We propose a novel formulation of deep networks that do not use dot-product neurons and rely on a hierarchy of voting tables instead, denoted as Convolutional Tables (CT), to enable accelerated CPU-based inference. Convolutional layers are…
Clinical prediction models enable healthcare professionals to estimate individual outcomes using patient characteristics. Current sample size guidelines for developing or updating models with continuous outcomes aim to minimise overfitting…
In outlier hypothesis testing, one aims to detect outlying sequences among a given set of sequences, where most sequences are generated i.i.d. from a nominal distribution while outlying sequences (outliers) are generated i.i.d. from a…
We consider finite-sample inference for a single regression coefficient in the fixed-design linear model $Y = Z\beta + bX + \varepsilon$, where $\varepsilon\in\mathbb{R}^n$ may exhibit complex dependence or heterogeneity. We develop a group…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
A procedure is described for estimating evolutionary rate matrices from observed site frequency data. The procedure assumes (1) that the data are obtained from a constant size population evolving according to a stationary Wright-Fisher…
In this paper, we propose semiparametric efficient estimators of genetic relatedness between two traits in a model-free framework. Most existing methods require specifying certain parametric models involving the traits and genetic variants.…
The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…