Biomedical Engineering Reference
In-Depth Information
integrated primer on chaotic dynamics besides. Ruelle's little topic (16) is
much
more subtle than it looks, full of deep insights. The SFI proceedings volumes
(233,234) are very worthwhile. The journals
Physica D
,
Physical Review E
, and
Chaos
often have new developments.
From the statistical wing, one of the best recent textbooks is (55); there are
many, many others. That by Durbin and Koopman (60) is particularly strong on
the state-space point of view. The one by (235) Azencott and Dacunha-Castelle
is admirably clear on both the aims of time series analysis, and the statistical
theory underlying classical methods; unfortunately it typography is less easy to
read than it should be. (236) provides a comprehensive and up-to-date view of
the statistical theory for modern models, including strongly nonlinear and non-
Gaussian models. While many of the results are directly useful in application,
the proofs rely on advanced theoretical statistics, in particular the geometric
approach pioneered by the Japanese school of Amari et al. (237). This
informa-
tion geometry
has itself been applied by Ay to the study of complex systems
(238,239).
At the interface between the statistical and the dynamical points of view,
there is an interesting conference proceedings (240) and a useful topic by Tong
(241). Pearson's topic (242) on discrete-time models is very good on many im-
portant issues related to model selection, and exemplifies the habit of control
theorists of cheerful stealing whatever seems helpful.
Filtering
. Linear filters are well-described by many textbooks in control
theory (e.g., (243)), signal processing, time series analysis (e.g., (55)), and sto-
chastic dynamics (e.g., (58)).
(89) provides a readable introduction to optimal nonlinear estimation, draws
interesting analogies to nonequilibrium statistical mechanics and turbulence,
and
describes a reasonable approximation scheme. (90) is an up-to-date textbook,
covering both linear and nonlinear methods, and including a concise exposition
of the essential parts of stochastic calculus. The website run by R.W.R. Darling,
www.nonlinearfiltering.webhop.net, provides a good overview and extensive
pointers to the literature.
Symbolic Dynamics and Hidden Markov Models
. On symbolic dynam-
ics, formal languages and hidden Markov models generally, see (10). (198) is a
good first course on formal languages and automata theory. Charniak is a very
readable introduction to grammatical inference. (244) is an advanced treatment
of symbolic dynamics emphasizing applications; by contrast, (116) focuses on
algebraic, pure-mathematical aspects of the subject. (163) is good on the sto-
chastic properties of symbolic-dynamical representations. Gershenfeld (245)
gives a good motivating discussion of hidden Markov models, as does Baldi and
Brunak (95), while (94) describes advanced methods related to statistical signal
processing. Open-source code for reconstructing causal-state models from state
is available from http://bactra.org/CSSR.
