arXiv subjects

Angus Lewis

Publications and source records attributed to Angus Lewis.

4 recordsLinked to original sources

arXiv2025

Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo, can be computationally challenging when the populations that are being modelled grow exponentially or the time series is long. Instead, we derive a Gaussian approximation for the transition function of the process that leads to a Kalman filtering algorithm that runs in a time independent of the population sizes. We also develop a hybrid approach for when populations are smaller and the approximation is less applicable. We investigate the performance of our approximation and algorithms to both a simple and a complex epidemic model, finding good adherence to the true posterior distributions in both cases with large computational speed-ups in most cases. We also apply our method to a COVID-19 dataset with time dependent parameters where exact methods are intractable due to the population sizes involved.

stat.ME↗

arXiv2025

Weak convergence of quasi-birth-and-death processes with rational arrival process components to fluid queues

In this paper we construct a new approximation to a fluid queue as a quasi-birth-and-death process with rational arrival process components (QBD-RAP) and prove its convergence. Fluid queues are stochastic processes that move linearly at a rate governed by the state of a continuous-time Markov chain (CTMC), and are widely used to model telecommunications, power, risk, and storage systems. A key motivating application is to fluid-fluid queues, whose analysis proceeds via operator-analytic expressions involving the generator of the underlying fluid queue; these expressions are differential operators that are not, in general, readily computable, so approximation is needed. Existing approximations with a probabilistic interpretation guarantee valid probabilities but require a fine discretisation to be accurate, while methods such as the Discontinuous Galerkin approach are more accurate at a given discretisation level but can produce negative mass or probabilities exceeding one. Our (QBD-RAP) approximation addresses this. Because the QBD-RAP is itself a stochastic process, the approximation it produces automatically retains the defining properties of a probability, while promising improved numerical accuracy over existing probabilistic schemes for a given discretisation level. We prove that the generator of the QBD-RAP converges to the generator of the fluid queue, which is, to our knowledge, the first generator-theoretic convergence result for a process with rational arrival process components. The proof introduces a new technique for the analysis of RAP-modulated processes, analysing the generator via bases of conditional residual time distributions rather than the orbit process used in prior RAP analyses, and along the way establishes that the phase process of the QBD-RAP and of the fluid queue share the same distribution.

math.PR↗

arXiv2020

Bayesian estimation of trend components within Markovian regime-switching models for wholesale electricity prices: an application to the South Australian wholesale electricity market

We discuss and extend methods for estimating Markovian-Regime-Switching (MRS) and trend models for wholesale electricity prices. We argue the existing methods of trend estimation used in the electricity price modelling literature either require an ambiguous definition of an extreme price, or lead to issues when implementing model selection [23]. The first main contribution of this paper is to design and infer a model which has a model-based definition of extreme prices and permits the use of model selection criteria. Due to the complexity of the MRS models inference is not straightforward. In the existing literature an approximate EM algorithm is used [26]. Another contribution of this paper is to implement exact inference in a Bayesian setting. This also allows the use of posterior predictive checks to assess model fit. We demonstrate the methodologies with South Australian electricity market.

stat.ME↗

arXiv2019

Estimation of Markovian-regime-switching models with independent regimes

Markovian-regime-switching (MRS) models are commonly used for modelling economic time series, including electricity prices where independent regime models are used, since they can more accurately and succinctly capture electricity price dynamics than dependent regime MRS models can. We can think of these independent regime MRS models for electricity prices as a collection of independent AR(1) processes, of which only one process is observed at each time; which is observed is determined by a (hidden) Markov chain. Here we develop novel, computationally feasible methods for MRS models with independent regimes including forward, backward and EM algorithms. The key idea is to augment the hidden process with a counter which records the time since the hidden Markov chain last visited each state that corresponding to an AR(1) process.

stat.ME↗