arXiv subjects

Jere Koskela

Publications and source records attributed to Jere Koskela.

26 records · Page 2Linked to original sources

arXiv2020

Simple conditions for convergence of sequential Monte Carlo genealogies with applications

We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman coalescent. Sequential Monte Carlo algorithms are popular methods for approximating integrals in problems such as non-linear filtering and smoothing which employ this type of particle system. Their performance depends strongly on the properties of the induced genealogical process. We verify the conditions of our main result for standard sequential Monte Carlo algorithms with a broad class of low-variance resampling schemes, as well as for conditional sequential Monte Carlo with multinomial resampling.

stat.CO↗

arXiv2020

Statistical tools for seed bank detection

In this article, we derive statistical tools to analyze and distinguish the patterns of genetic variability produced by classical and recent population genetic models related to seed banks. In particular, we are concerned with models described by the Kingman coalescent (K), models exhibiting so-called weak seed banks described by a time-changed Kingman coalescent (W), models with so-called strong seed bank described by the seed bank coalescent (S) and the classical two-island model by Wright, described by the structured coalescent (TI). As the presence of a (strong) seed bank should stratify a population, we expect it to produce a signal roughly comparable to the presence of population structure. We begin with a brief analysis of Wright's $F_{ST}$, which is a classical but crude measure for population structure, followed by a derivation of the expected site frequency spectrum (SFS) in the infinite sites model based on 'phase-type distribution calculus' as recently discussed by Hobolth et al. (2019). Both the $F_{ST}$ and the SFS can be readily computed under various population models, they discard statistical signal. Hence we also derive exact likelihoods for the full sampling probabilities, which can be achieved via recursions and a Monte Carlo scheme both in the infinite alleles and the infinite sites model. We employ a pseudo-marginal Metropolis-Hastings algorithm of Andrieu and Roberts (2009) to provide a method for simultaneous model selection and parameter inference under the so-called infinitely-many sites model, which is the most relevant in real applications. It turns out that this full likelihood method can reliably distinguish among the model classes (K, W), (S) and (TI) on the basis of simulated data even from moderate sample sizes. It is also possible to infer mutation rates, and in particular determine whether mutation is taking place in the (strong) seed bank.

q-bio.PE↗

arXiv2019

Robust model selection between population growth and multiple merger coalescents

We study the effect of biological confounders on the model selection problem between Kingman coalescents with population growth, and Xi-coalescents involving simultaneous multiple mergers. We use a low dimensional, computationally tractable summary statistic, dubbed the singleton-tail statistic, to carry out approximate likelihood ratio tests between these model classes. The singleton-tail statistic has been shown to distinguish between them with high power in the simple setting of neutrally evolving, panmictic populations without recombination. We extend this work by showing that cryptic recombination and selection do not diminish the power of the test, but that misspecifying population structure does. Furthermore, we demonstrate that the singleton-tail statistic can also solve the more challenging model selection problem between multiple mergers due to selective sweeps, and multiple mergers due to high fecundity with moderate power of up to 30%.

q-bio.PE↗

arXiv2018

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. We also show that products of discrete net and Dirichlet mixture model priors satisfy our conditions, again under an identifiability assumption. This generalises known results by incorporating jumps into previous work on unit diffusions with uniformly Lipschitz drift coefficients.

math.ST↗

arXiv2018

Multi-locus data distinguishes between population growth and multiple merger coalescents

We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with population growth, and use this function to construct a hypothesis test between these model classes. The null and alternative sampling distributions of the statistic are intractable, but its low dimensionality renders them amenable to Monte Carlo estimation. We construct kernel density estimates of the sampling distributions based on simulated data, and show that the resulting hypothesis test dramatically improves on the statistical power of a current state-of-the-art method. A key reason for this improvement is the use of multi-locus data, in particular averaging observed site frequency spectra across unlinked loci to reduce sampling variance. We also demonstrate the robustness of our method to nuisance and tuning parameters. Finally we show that the same kernel density estimates can be used to conduct parameter estimation, and argue that our method is readily generalisable for applications in model selection, parameter inference and experimental design.

q-bio.PE↗

arXiv2017

Bayesian non-parametric inference for $Λ$-coalescents: consistency and a parametric method

We investigate Bayesian non-parametric inference of the $Λ$-measure of $Λ$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for posterior consistency when observations form a time series, and prove that any non-trivial prior is inconsistent when all observations are contemporaneous. We then show that the likelihood given a data set of size $n \in \mathbb{N}$ is constant across $Λ$-measures whose leading $n - 2$ moments agree, and focus on inferring truncated sequences of moments. We provide a large class of functionals which can be extremised using finite computation given a credible region of posterior truncated moment sequences, and a pseudo-marginal Metropolis-Hastings algorithm for sampling the posterior. Finally, we compare the efficiency of the exact and noisy pseudo-marginal algorithms with and without delayed acceptance acceleration using a simulation study.

stat.ME↗

arXiv2017

Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green's functions in Nagasawa's formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence the difficulty in designing SMC proposals in high dimension is greatly reduced. We illustrate our method on estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.

stat.CO↗

arXiv2015

Computational inference beyond Kingman's coalescent

Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently, more general $Λ$- and $Ξ$-coalescents have been observed to provide better modelling fits to some genetic data sets. We derive families of approximate CSDs for finite sites $Λ$- and $Ξ$-coalescents, and use them to obtain "approximately optimal" IS and PAC algorithms for $Λ$-coalescents, yielding substantial gains in efficiency over existing methods.

math.PR↗