arXiv subjects

Meagan Carney

Publications and source records attributed to Meagan Carney.

11 recordsLinked to original sources

arXiv2026

Exploring Drivers of Extreme Housing Prices in Australia

In recent years Australia has observed a growing, unexplained resilience of increasing house price trends. Here, we seek to understand what is driving Australia's indestructible asset using insights from market experts. We construct a differential equation model of house price to develop intuition for its historical behaviour and responsiveness to changes in mortgage rates. Using this model, we identify a point of 'decoupling' between house price and mortgage rate in the system with supply limitations found to be the main driver for this change. From there, modern extreme value techniques are implemented on real-world data to investigate how the effectiveness of mortgage rate in moderating extreme house price has changed before and after this historical decoupling. We find that without an increase in the housing supply chain, through either deregulation or reduced competition with government building, an 11\% increase in mortgage rate will be needed to slow extreme housing costs.

q-fin.GN↗

arXiv2025

A novel statistical workflow for nonstationary modelling of successive Fr\'{e}chet extremes

Accurate estimation of the frequency and magnitude of successive extreme events in energy demand is critical for strategic resource planning. Traditional approaches based on extreme value theory (EVT) are typically limited to modelling isolated extreme events and struggle to capture the dynamics of temporally clustered extremes, such as those driven by prolonged extreme weather events. These limitations are exacerbated by the scarcity of historical data and computational costs of longrun simulations leading to high uncertainty in return level estimates for successive extremes. Here, we introduce a novel statistical framework leveraging recent theoretical advances in successive extreme value modelling in dynamical systems. Under reasonable assumptions of the time series data (e.g. the data follow a fat-tailed Fr\'{e}chet distribution), our tool allows for significantly more robust estimates of returns and magnitudes of successive extreme events compared to standard likelihood methods. We illustrate our statistical workflow on scenarios of forecasted gas supply levels from 2025 to 2050. Common measures of statistical accuracy are provided as benchmarks for comparison.

math.ST↗

arXiv2025

An Improved Autoencoder Conjugacy Network to Learn Chaotic Maps

We introduce a method for learning chaotic maps using an improved autoencoder neural network that incorporates a conjugacy layer in the latent space. The added conjugacy layer transforms nonlinear maps into a simple piecewise linear map (the tent map) whilst enforcing dynamical principles of well-known and defective conjugacy functions that increase the accuracy and stability of the learned solution. We demonstrate the method's effectiveness on both continuous and piecewise chaotic one-dimensional maps and numerically illustrate improved performance over related traditional and recently emerged deep learning architectures.

math.DS↗

arXiv2024

Modeling Multiday Extreme Precipitation Across Eastern Australia: A Dynamical Perspective

The purpose of this paper is to illustrate new techniques for computing multiday extreme precipitation taken from recent theoretical advancements in extreme value theory in the framework of dynamical systems, using historical precipitation data along the eastern coast of Australia as a case study. We explore the numerical pitfalls of applying standard extreme value techniques to model multiday extremes. Then, we illustrate that our data conforms to the appropriate setting for the application of recently derived extreme value distributions for runs of extremes in the dynamical framework and adapt these to the non-stationary setting. Finally, we use these distributions to make more informed predictions on the return times and magnitudes of consecutive daily extreme precipitation and find changes in the dependence of increasing consecutive daily rainfall extremes on the Southern Oscillation Index. Although our case study is focused on extreme precipitation across eastern Australia, we emphasize that these techniques can be used to model expected returns and magnitudes of consecutive extreme precipitation events across many locations.

math.DS↗

arXiv2023

Runs of Extremes of Observables on Dynamical Systems and Applications

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fréchet (fat-tailed) or Weibull (bounded) distribution. The motivation for this work was to give estimates of the probabilities of sustained periods of weather anomalies such as heat-waves, cold spells or prolonged periods of rainfall in climate models. Our predictions are borne out by numerical simulations and also analysis of rainfall and temperature data.

math.DS↗

arXiv2021

Hurricane Simulation and Nonstationary Extremal Analysis for a Changing Climate

Particularly important to hurricane risk assessment for coastal regions is finding accurate approximations of return probabilities of maximum windspeeds. Since extremes in maximum windspeed have a direct relationship to minimums in the central pressure, accurate windspeed return estimates rely heavily on proper modeling of the central pressure minima. Using the HURDAT2 database, we show that the central pressure minima of hurricane events can be appropriately modeled by a nonstationary extreme value distribution. We also provide and validate a Poisson distribution with a nonstationary rate parameter to model returns of hurricane events. Using our nonstationary models and numerical simulation techniques from established literature, we perform a simulation study to model returns of maximum windspeeds of hurricane events along the North Atlantic Coast. We show that our revised model agrees with current data and results in an expectation of higher maximum windspeeds for all regions along the coast with the highest maximum windspeeds occurring in the northern part of the coast.

math.DS↗

arXiv2020

Sources and Sinks of Rare Trajectories in 2-Dimensional Velocity Fields Identified by Importance Sampling

We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed 2-dimensional flow of the atmosphere from wind velocity fields provided by the Portable University Model of the Atmosphere. Motivated by extreme value theory, we consider an observable $ϕ(x) = -\log(d(x,γ))$ maximized at the center $γ$ of a chosen target coherent set, where it is rare for a particle to transition. We illustrate that importance sampling maximizing this observable provides an enriched data set of trajectories that experience such a rare event. Backwards reconstruction of these trajectories provides valuable information on initial conditions and most likely paths a trajectory will take. With this information, we are able to obtain more accurate estimates of rare transition probabilities compared to those of standard integration techniques.

nlin.CD↗

arXiv2020

Extremes and extremal indices for level set observables on hyperbolic systems

Consider an ergodic measure preserving dynamical system $(T,X,μ)$, and an observable $ϕ:X\to\mathbb{R}$. For the time series $X_n(x)=ϕ(T^{n}(x))$, we establish limit laws for the maximum process $M_n=\max_{k\leq n}X_k$ in the case where $ϕ$ is an observable maximized on a curve or submanifold, and $(T,X,μ)$ is a hyperbolic dynamical system. Such observables arise naturally in weather and climate applications. We consider the extreme value laws and extremal indices for these observables on Anosov diffeomorphisms, Sinai dispersing billiards and coupled expanding maps. In particular we obtain clustering and nontrivial extremal indices due to self intersection of submanifolds under iteration by the dynamics, not arising from any periodicity.

math.DS↗

arXiv2020

Analysis and Simulation of Extremes and Rare Events in Complex Systems

Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and climate forecasting has often turned to simulations of climate models to make better predictions of rare weather events. However very long simulations of complex models, in order to obtain accurate probability estimates, may be prohibitively slow. It is an important scientific problem to develop probabilistic and dynamical techniques to estimate the probabilities of rare events accurately from limited data. In this paper we compare four modern methods of estimating the probability of rare events: the generalized extreme value (GEV) method from classical extreme value theory; two importance sampling techniques, genealogical particle analysis (GPA) and the Giardina-Kurchan-Lecomte-Tailleur (GKLT) algorithm; as well as brute force Monte Carlo (MC). With these techniques we estimate the probabilities of rare events in three dynamical models: the Ornstein-Uhlenbeck process, the Lorenz '96 system and PlaSim (a climate model). We keep the computational effort constant and see how well the rare event probability estimation of each technique compares to a gold standard afforded by a very long run control. Somewhat surprisingly we find that classical extreme value theory methods outperform GPA, GKLT and MC at estimating rare events.

stat.ME↗

arXiv2017

Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems

We show that a compound Poisson distribution holds for scaled exceedances of observables $ϕ$ uniquely maximized at a periodic point $ζ$ in a variety of two-dimensional hyperbolic dynamical systems with singularities $(M,T,μ)$, including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form $ϕ(z)=-\ln d(z,ζ)$ where $d$ is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index $θ$. We calculate $θ$ in terms of the derivative of the map $T$. Furthermore if we define $M_n=\max\{ϕ,\ldots,ϕ\circ T^n\}$ and $u_n (τ)$ by $\lim_{n\to \infty} nμ(ϕ>u_n (τ) )=τ$ the maximal process satisfies an extreme value law of form $μ(M_n \le u_n)=e^{-θτ}$. These results generalize to a broader class of functions maximized at $ζ$, though the formulas regarding the parameters in the distribution need to be modified.

math.DS↗

arXiv2016

Dynamical Borel-Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems

We consider implications of dynamical Borel-Cantelli lemmas for rates of growth of Birkhoff sums of non-integrable observables $φ(x) = d(x,p)^{-k}$, $k>0$, on ergodic dynamical systems $(T,X,μ)$ where $μ(X) = 1$. Some general results are given as well as some more concrete examples involving non-uniformly expanding maps, intermittent type maps as well as uniformly hyperbolic systems.

math.DS↗