arXiv subjects

Michael LuValle

Publications and source records attributed to Michael LuValle.

5 recordsLinked to original sources

arXiv2024

Chaotic uncertainty and statistical inference for natural chaotic systems: Choosing predictors for multiple season ahead prediction of precipitation, Extended and Annotated

Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In such systems the chaoticity, amplifying error exponentially fast, is so confounded with the boundary condition fluctuations and the measurement error, that it is impossible to consistently estimate the trajectory of the system much less predict it. Although asymptotic theory exists for estimating the conditional predictive distributions, it is hard to find where this theory has been applied. Here the theory is reviewed, and applied to identifying useful predictive variables for simultaneous multiseason prediction of precipitation with potentially useful updating possible. This is done at two locations, one midocean the other landlocked. The method appears to show promise for fast exploration of variables for multiseason prediction.

nlin.CD↗

arXiv2024

Learning tapestries, a statistical learning substrate for open chaotic systems measured with error

The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of representing measured data from large open chaotic systems subject to error as collections of threads of plausible pseudo future histories to enable statistical analysis is described. This representation provides asymptotically consistent predictive distributions, for use in developing predictive likelihood methods which: 1. provide a framework for variable selection, 2. provide a framework for Bayesian updating, so for example 4 season ahead predictions learn naturally as the 3rd season ahead is measured. 3. allows examination of conditional scenarios along the future histories for planning purposes. 4. allows the ranking of variable, delay combinations with higher signal to noise ratio. The method is tested for learning and variable selection by examining its behavior in predicting 9 years across 4 seasons of climate variables, including local temperature and rainfall measurements at two locations, predicting up to 4 seasons ahead.

stat.AP↗

arXiv2020

Statistical inference for Axiom A attractors

From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying theory that can be used not only for predicting those systems a short time ahead, but also as a basis for statistical inference about their dynamics. The method is applied to prediction of 3 different systems. The statistical inference aspect can be applied to explore and enhance computer models of such systems which in turn can provide feedback for even better prediction and more precise inference.

stat.AP↗

arXiv2019

Asymptotically consistent prediction of extremes in chaotic systems:1 stationary case

In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of the extreme behaviors of interest. For clarity, in this paper we confine ourselves to the case where the chaotic system to be predicted is stationary so theory for asymptotic consistency can be easily illuminated. We will start with a simple case, where the attractor of the chaotic system is of known dimension so the answer is clear from prior work. Some extension will be made to stationary chaotic system with higher dimension where a number of empirical results will be described and a theoretical framework proposed to help explain them.

stat.AP↗

arXiv2019

Statistical Failure Mechanism Analysis of Earthquakes Revealing Time Relationships

If we assume that earthquakes are chaotic, and influenced locally then chaos theory suggests that there should be a temporal association between earthquakes in a local region that should be revealed with statistical examination. To date no strong relationship has been shown (refs not prediction). However, earthquakes are basically failures of structured material systems, and when multiple failure mechanisms are present, prediction of failure is strongly inhibited without first separating the mechanisms. Here we show that by separating earthquakes statistically, based on their central tensor moment structure, along lines first suggested by a separation into mechanisms according to depth of the earthquake, a strong indication of temporal association appears. We show this in earthquakes above 200 Km along the pacific ring of fire, with a positive association in time between earthquakes of the same statistical type and a negative association in time between earthquakes of different types. Whether this can reveal either useful mechanistic information to seismologists, or can result in useful forecasts remains to be seen.

stat.AP↗