arXiv subjects

Suzie Brown

Publications and source records attributed to Suzie Brown.

3 recordsLinked to original sources

arXiv2023

Weak Convergence of Non-neutral Genealogies to Kingman's Coalescent

Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both applications. Under neutrality, when fitnesses of particles are independent from those of their parents, rescaled genealogies are known to converge to Kingman's coalescent. Recent work has established convergence under non-neutrality, but only for finite-dimensional distributions. We prove weak convergence of non-neutral genealogies on the space of càdlàg paths under standard assumptions, enabling analysis of the whole genealogical tree.

math.PR↗

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↗

arXiv2018

Reliability of Broadcast Communications Under Sparse Random Linear Network Coding

Ultra-reliable Point-to-Multipoint (PtM) communications are expected to become pivotal in networks offering future dependable services for smart cities. In this regard, sparse Random Linear Network Coding (RLNC) techniques have been widely employed to provide an efficient way to improve the reliability of broadcast and multicast data streams. This paper addresses the pressing concern of providing a tight approximation to the probability of a user recovering a data stream protected by this kind of coding technique. In particular, by exploiting the Stein--Chen method, we provide a novel and general performance framework applicable to any combination of system and service parameters, such as finite field sizes, lengths of the data stream and level of sparsity. The deviation of the proposed approximation from Monte Carlo simulations is negligible, improving significantly on the state of the art performance bounds.

cs.IT↗