Related papers: Posterior bounds on divergence time of two sequenc…
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
The central limit theorem is one of the most fundamental results in probability and has been successfully extended to locally dependent data and strongly-mixing random fields. In this paper, we establish its rate of convergence for…
Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general…
In a variety of problems in pure and applied probability, it is of relevant to study the large exceedance probabilities of the perpetuity sequence $Y_n := B_1 + A_1 B_2 + \cdots + (A_1 \cdots A_{n-1}) B_n$, where $(A_i,B_i) \subset…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…
In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by $L$-divergence and rare…
Neural Temporal Difference (TD) Learning is an approximate temporal difference method for policy evaluation that uses a neural network for function approximation. Analysis of Neural TD Learning has proven to be challenging. In this paper we…
In this short note, a correction is made to the recently proposed solution [1] to a 1D biased diffusion model for linear DNA translocation and a new analysis will be given to the data in [1]. It was pointed out [2] by us recently that this…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
Consider a one-dimensional stepping stone model with colonies of size $M$ and per-generation migration probability $\nu$, or a voter model on $\mathbb{Z}$ in which interactions occur over a distance of order $K$. Sample one individual at…
A complete time-parameterized statistical model quantifying the divergent evolution of protein structures in terms of the patterns of conservation of their secondary structures is inferred from a large collection of protein 3D structure…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
Divergence time estimation requires the reconciliation of two major sources of data. These are fossil and/or biogeographic evidence that give estimates of the absolute age of nodes (ancestors) and molecular estimates that give us estimates…
The Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. There are $n$ sites (or loci), a finite number of letters (or alleles) at every…
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…