Biomedical subjects

Kevin Judd

Publications and source records attributed to Kevin Judd.

6 recordsLinked to original sources

PubMed2006

Degeneracy of time series models: the best model is not always the correct model.

There are a number of good techniques for finding, in some sense, the best model of a deterministic system given a time series of observations. We examine a problem called model degeneracy, which has the consequence that even when a perfect model of a system exists, one does not find it using the best techniques currently available. The problem is illustrated using global polynomial models and the theory of Grobner bases.

Algorithms↗

PubMed2005

Constructing dynamical systems with specified symbolic dynamics.

In this paper we demonstrate how to construct signals (time series) of continuous-time dynamical systems that exhibit a given symbolic dynamics. This is achieved without construction of the ordinary differential equations that generate the flow. This construction is of theoretical interest and is useful as a source of dynamical data that can be used to test various data analysis algorithms.

Algorithms↗

PubMed2004

Estimating a generating partition from observed time series: symbolic shadowing.

We propose a deterministic algorithm for approximating a generating partition from a time series using tessellations. Using data generated by Hénon and Ikeda maps, we demonstrate that the proposed method produces partitions that uniquely encode all the periodic points up to some order, and provide good estimates of the metric and topological entropies. The algorithm gives useful results even with a short noisy time series.

Journal Article↗

PubMed2003

Chaotic-time-series reconstruction by the Bayesian paradigm: right results by wrong methods.

Recently, papers have appeared that champion the Bayesian approach to the analysis of experimental data. From reading these papers, the physicist could be forgiven for believing that Bayesian methods reveal deep truths about physical systems and are the correct paradigm for the analysis of all experimental data. This paper makes a contrary argument and is deliberately provocative. It is argued that the Bayesian approach to reconstruction of chaotic time series is fundamentally flawed, and the apparent successes result not from any degree of correctness of the paradigm, but by an accidental and unintended property of an algorithm. We also argue that (non-Bayesian) shadowing techniques provide all the information the erroneous Bayesian methods obtain, but much more efficiently, and also provide a wealth of additional useful information.

Journal Article↗

PubMed2002

Modeling continuous processes from data.

Experimental and simulated time series are necessarily discretized in time. However, many real and artificial systems are more naturally modeled as continuous-time systems. This paper reviews the major techniques employed to estimate a continuous vector field from a finite discrete time series. We compare the performance of various methods on experimental and artificial time series and explore the connection between continuous (differential) and discrete (difference equation) systems. As part of this process we propose improvements to existing techniques. Our results demonstrate that the continuous-time dynamics of many noisy data sets can be simulated more accurately by modeling the one-step prediction map than by modeling the vector field. We also show that radial basis models provide superior results to global polynomial models.

Journal Article↗

PubMed2002

Starting a canine program.

If it is done properly, a program of canine patrols in a healthcare setting can produce a number of benefits, not the least of which is a decline in criminal activity. In this article, the author shares his experiences in developing and implementing a successful program.

Animals↗