ref.bib

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PHDTHESIS {Uppe97a,
    TITLE = "Theory and Algorithms for Hidden {M}arkov Models and Generalized Hidden {M}arkov Models",
    AUTHOR = "D. R. Upper",
    SCHOOL = "University of California",
    ADDRESS = "Berkeley",
    NOTE = "{P}ublished by University Microfilms Intl, Ann Arbor, Michigan",
    YEAR = 1997}

@ARTICLE {Blac57a,
    TITLE = "On the Identifiability Problem for Functions of {Markov} Chains",
    AUTHOR = "D. Blackwell and L. Koopmans",
    JOURNAL = "Ann. Math. Statist.",
    VOLUME = 28,     PAGES = 1011,
    YEAR = 1957}

@STRING{AnnMathStat = {Ann. Math. Stat.}}

@STRING{AppStat = {Appl. Stat.}}

@STRING{IEEEIT = {IEEE Trans. Inform. Theory}}

@STRING{IEEENN = {IEEE Trans. Neur. Net.}}

@STRING{JourAppProb = {Jour. Appl. Prob.}}

@STRING{PNAS = {Proc. Natl. Acad. Sci.}}

@STRING{PRA = {Phys. Rev. A}}

@STRING{PRE = {Phys. Rev. E}}

@STRING{PRL = {Phys. Rev. Lett.}}

@STRING{RMP = {Rev. Mod. Phys.}}

@BOOK{Abramowitz1965,
  title = {Handbook of Mathematical Functions},
  publisher = {Dover},
  year = {1965},
  author = {Milton~Abramowitz and Irene~A.~Stegun},
  address = {New York}
}

@ARTICLE{TWAnderson1957,
  author = {T.~W.~Anderson and Leo~A.~Goodman},
  title = {Statistical Inference About Markov Chains},
  journal = AnnMathStat,
  year = {1957},
  volume = {28},
  pages = {89 -- 110},
  number = {1},
  abstract = {Maximum likelihood estimates and their asymptotic distribution are
	obtained for the transition probabilities in a Markov chain of arbitrary
	order when there are repeated observations of the chain. Likelihood
	ratio tests and $\chi^2$-tests of the form used in contingency tables
	are obtained for testing the following hypotheses: (a) that the
	transition probabilities of a first order chain are constant, (b)
	that in case the transition probabilities are constant, they are
	specified numbers, and (c) that the process is a $u$th order Markov
	chain against the alternative it is $r$th but not $u$th order. In
	case $u = 0$ and $r = 1$, case (c) results in tests of the null
	hypothesis that observations at successive time points are statistically
	independent against the alternate hypothesis that observations are
	from a first order Markov chain. Tests of several other hypotheses
	are also considered. The statistical analysis in the case of a single
	observation of a long chain is also discussed. There is some discussion
	of the relation between likelihood ratio criteria and $\chi^2$-tests
	of the form used in contingency tables.},
  annote = {Markov Chain},
  keywords = {Markov Chain, Inference, Maximum Likelihood},
  pdf = {TWAnderson1957.pdf}
}

@ARTICLE{Avery1999,
  author = {Peter~J.~Avery and Daniel~A.~Henderson},
  title = {Fitting Markov Chain Models to Discrete State Series Such as {DNA}
	Sequences},
  journal = AppStat,
  year = {1999},
  volume = {48},
  pages = {53 -- 61},
  number = {1},
  abstract = {Discrete state series such as DNA sequences can often be modelled
	by Markov chains. The analysis of such series is discussed in the
	context of log-linear models. The data produce contingency tables
	with similar margins due to the dependence of the observations.
	However, despite the unusual structure of the tables, the analysis
	is equivalent to that for data from multinomial sampling. The reason
	why the standard number of degrees of freedom is correct is explained
	by using theoretical arguments and the asymptotic distribution of
	the deviance is verified empirically. Problems involved with fitting
	high order Markov chain models, such as reduced power and computational
	expense, are also discussed.},
  annote = {Markov Chain},
  keywords = {Markov Chain, Inference},
  pdf = {\Avery1999.pdf}
}

@BOOK{Baldi2001,
  title = {Bioinformatics: The Machine Learning Approach},
  publisher = {MIT Press},
  year = {2001},
  author = {Pierre~Baldi and S{\o}ren~Brunak},
  address = {Cambridge}
}

@ARTICLE{Berry1990,
  author = {K.J. Berry and {P.W. Mielke, Jr.} and G.W. Cran},
  title = {Algorithm {AS R83}: A Remark on Algorithm {AS 109} (Inverse of the
	Incomplete Beta Function Ratio)},
  journal = AppStat,
  year = {1990},
  volume = {39},
  pages = {309-310},
  number = {2},
  owner = {admin},
  timestamp = {2007.02.13}
}

@ARTICLE{Billingsley1961a,
  author = {Patrick~Billingsley},
  title = {Statistical Methods in Markov Chains},
  journal = AnnMathStat,
  year = {1961},
  volume = {32},
  pages = {12 -- 40},
  number = {1},
  abstract = {This paper is an expository survey of the mathematical aspects of
	statistical inference as it applies to finite Markov chains, the
	problem being to draw inferences about the transition probabilities
	from one long, unbroken observation $\{x_1, x_2, \cdots, x_n\}$
	on the chain. The topics covered include Whittle's formula, chi-square
	and maximum-likelihood methods, estimation of parameters, and multiple
	Markov chains. At the end of the paper it is briefly indicated how
	these methods can be applied to a process with an arbitrary state
	space or a continuous time parameter. Section 2 contains a simple
	proof of Whittle's formula; Section 3 provides an elementary and
	self-contained development of the limit theory required for the
	application of chi-square methods to finite chains. In the remainder
	of the paper, the results are accompanied by references to the literature,
	rather than by complete proofs. As is usual in a review paper, the
	emphasis reflects the author's interests. Other general accounts
	of statistical inference on Markov processes will be found in Grenander
	[53], Bartlett [9] and [10], Fortet [35], and in my monograph [18].
	I would like to thank Paul Meier for a number of very helpful discussions
	on the topics treated in this paper, particularly those of Section
	3.},
  annote = {Markov Chain},
  keywords = {Markov Chain, Inference, Maximum Likelihood},
  pdf = {Billingsley1961.pdf}
}

@ARTICLE{Chatfield1973,
  author = {Christopher Chatfield},
  title = {Statistical Inference Regarding Markov Chain Models},
  journal = AppStat,
  year = {1973},
  volume = {22},
  pages = {7-20},
  number = {1},
  abstract = {The paper reviews different techniques for examining sequential dependencies
	in a series of observations each of which can have c possible outcomes.
	The relationship between the likelihood ratio test and information
	theory is described. The paper also considers how the techniques
	need to be modified in situations where two successive outcomes
	are always different.},
  annote = {Markov Chain},
  keywords = {Markov Chains, Information Theory, Inference, Likelihood Ratio, Model
	Comparison},
  pdf = {\Chatfield1973.pdf}
}

@BOOK{Cover1991,
  title = {Elements of Information Theory},
  publisher = {Wiley-Interscience},
  year = {1991},
  author = {Thomas~M.~Cover and Joy~A.~Thomas},
  address = {New York}
}

@ARTICLE{Cran1977,
  author = {G.W. Cran and K.J. Martin and G.E. Thomas},
  title = {Remark {AS R19} and Algorithm {AS 109}--A Remark on Algorithms {AS
	63} (The Incomplete Integral) and {AS 64} (Inverse of the Incomplete
	Beta Function Ratio)},
  journal = AppStat,
  year = {1977},
  volume = {26},
  pages = {111-114},
  number = {1},
  owner = {admin},
  timestamp = {2007.02.13}
}

@ARTICLE{Crutchfield1994,
  author = {James~P.~Crutchfield},
  title = {The Calculi of Emergence: Computation, Dynamics, and Induction},
  journal = {Physica D},
  year = {1994},
  volume = {75},
  pages = {11-54},
  abstract = {Defining structure and detecting the emergence of complexity in nature
	are inherently subjective, though essential, scientific activities.
	Despite the difficulties, these problems can be analyzed in terms
	of how model-building observers infer from measurements the computational
	capabilities embedded in nonlinear processes. An observer's notion
	of what is ordered, what is random, and what is complex in its environment
	depends directly on its computational resources: the amount of raw
	measurement data, of memory, and of time available for estimation
	and inference. The discovery of structure in an environment depends
	more critically and subtlely, though, on how those resources are
	organized. The descriptive power of the observer's chosen (or implicit)
	computational model class, for example, can be an overwhelming determinant
	in finding regularity in data. This paper presents an overview of
	an inductive framework -- hierarchical epsilon machine reconstruction
	-- in which the emergence of complexity is associated with the innovation
	of new computational model classes. Complexity metrics for detecting
	structure and quantifying emergence, along with an analysis of the
	constraints on the dynamics of innovation, are outlined. Illustrative
	examples are drawn from the onset of unpredictability in nonlinear
	systems, finitary nondeterministic processes, and cellular automata
	pattern recognition. They demonstrate how finite inference resources
	drive the innovation of new structures and so lead to the emergence
	of complexity.},
  pdf = {\Crutchfield1994.pdf}
}

@ARTICLE{Crutchfield1997,
  author = {James~P.~Crutchfield and David~P.~Feldman},
  title = {Statistical Complexity of Simple One-Dimensional Spin Systems},
  journal = PRE,
  year = {1997},
  volume = {55},
  pages = {R1239 -- R1242},
  number = {2},
  abstract = {We present exact results for two complementary measures of spatial
	structure generated by one-dimensional spin systems with finite-range
	interactions. The first, excess entropy, measures the apparent spatial
	memory stored in configurations. The second, statistical complexity,
	measures the amount of memory needed to optimally predict the chain
	of spin values in configurations. These statistics capture distinct
	properties and are different from existing thermodynamic quantities.},
  pdf = {\Crutchfield1997.pdf}
}

@ARTICLE{Crutchfield1983,
  author = {J.~P.~Crutchfield and N.~H.~Packard},
  title = {Symbolic Dynamics of Noisy Chaos},
  journal = {Physica D},
  year = {1983},
  volume = {7D},
  pages = {201 -- 223},
  abstract = {One model of randomness observed in physical systems is that low-dimensional
	deterministic chaotic attractors underly the observations. A phenomenological
	theory of chaotic dynamics requires an accounting of the information
	flow from the observed system to the observer, the amount of information
	available in observations, and just how this information affects
	predictions of the system's future behavior. In an effort to develop
	such a description, we discuss the information theory of highly
	discretized observations of random behavior. Metric entropy and
	topological entropy are well-defined invariant measures of such
	an attractor's "level of chaos", and are computable using symbolic
	dynamics. Real physical systems that display low dimensional dynamics
	are, however, inevitably coupled to high-dimensional randomness,
	e.g. thermal noise. We investigate the effects of such fluctuations
	coupled to deterministic chaotic systems, in particular, the metric
	entropy's response to the fluctuations. We find that the entropy
	increases with a power law in the noise level, and that the convergence
	of the entropy and the effect of fluctuations can be cast as a scaling
	theory. We also argue that in addition to the metric entropy, there
	is a second scaling invariant quantity that characterizes a deterministic
	system with added fluctuations: I0, the maximum average information
	obtainable about the initial condition that produces a particular
	sequence of measurements (or symbols).},
  annote = {SMS},
  keywords = {Chaos, Sumbolic Dynamics, Noise, Partitions},
  pdf = {\Crutchfield1983.pdf}
}

@ARTICLE{Crutchfield1982,
  author = {J. P. Crutchfield and N. H. Packard},
  title = {Symbolic Dynamics of One-Dimensional Maps: Entropies, Finite Precision,
	and Noise},
  journal = {Int. J. Theo. Phys.},
  year = {1982},
  volume = {21},
  pages = {433 - 466},
  abstract = {In the study of nonlinear physical systems, one encounters apparently
	random or chaotic behavior, although the systems may be completely
	deterministic. Applying techniques from symbolic dynamics to maps
	of the interval, we compute two measures of chaotic behavior commonly
	employed in dynamical systems theory: the topological and metric
	entropies. For the quadratic logistic equation, we find that the
	metric entropy converges very slowly in comparison to maps which
	are strictly hyperbolic. The effects of finite precision arithmetic
	and external noise on chaotic behavior are characterized with the
	symbolic dynamics entropies. Finally, we discuss the relationship
	of these measures of chaos to algorithmic complexity, and use algorithmic
	information theory as a framework to discuss the construction of
	models for chaotic dynamics.},
  annote = {SMS},
  keywords = {Chaos, Symbolic Dyanamics, Entropy, Stochastic}
}

@BOOK{Durbin1998,
  title = {Biological Sequence Analysis},
  publisher = {Camridge University Press},
  year = {1998},
  author = {R.~Durbin and S.~Eddy and A.~Krogh and G.~Mitchison},
  address = {Cambridge}
}

@BOOK{BLHao1998,
  title = {Applied Symbolic Dynamics and Chaos},
  publisher = {World Scientific},
  year = {1998},
  author = {Bai-Lin~Hao and Wei-Mou~Zheng}
}

@ARTICLE{Katz1981,
  author = {Richard~W.~Katz},
  title = {On Some Criteria for Estimating the Order of a Markov Chain},
  journal = {Technometrics},
  year = {1981},
  volume = {23},
  pages = {243 -- 249},
  number = {3},
  abstract = {Tong (1975) has proposed a procedure for estimating the order of a
	Markov chain based on Akaike's information criterion (AIC). In this
	paper, the asymptotic distribution of the AIC estimator is derived
	and it is shown that the estimator is inconsistent. As an alternative
	to the AIC procedure, the Bayesian information criterion (BIC) proposed
	by Schwarz (1978) is shown to be consistent. These two procedures
	yield different estimated orders when applied to specific samples
	of meteorological observations. For parameters based on these meteorological
	examples, the AIC and BIC procedures are compared by means of simulation
	for finite samples. The results obtained have practical implications
	concerning whether, in the routine fitting of precipitation data,
	it is necessary to consider higher than first-order Markov chains.},
  annote = {Markov Chain},
  keywords = {Markov Chain, Information Criteria, AIC, BIC, Model Comparison},
  pdf = {\Katz1981.pdf}
}

@ARTICLE{JSLiu1999,
  author = {Jun~S.~Liu and Charles~E.~Lawrence},
  title = {Bayesian Inference on Biopolymer Models},
  journal = {Bioinformatics},
  year = {1999},
  volume = {15},
  pages = {38 -- 52},
  number = {1},
  annote = {Markov Chain},
  keywords = {Markov Chain, Bayes, Inference, Dirichlet, Bioinformatics, Model Comparison},
  pdf = {\JSLiu1999.pdf}
}

@BOOK{MacKay2003,
  opttitle = {Information Theory, Inference, and Learning Algorithms},
  publisher = {Cambridge University Press},
  year = {2003},
  author = {D. MacKay},
  address = {Cambridge},
  keywords = {Information Theory, Inference, Bayes, Type Theory, Neural Networks}
}

@ARTICLE{MacKay1994,
  author = {David~J.~C.~MacKay and Linda~C.~Bauman~Peto},
  title = {A Hierarchical Dirichlet Language Model},
  journal = {Nat. Lang. Eng.},
  year = {1994},
  volume = {1},
  number = {1},
  abstract = {We discuss a hierarchical probabilistic model whose predictions are
	similar to those of the popular language modelling procedure known
	as `smoothing'. A number of interesting differences from smoothing
	emerge. The insights gained from a probabilistic view of this problem
	point towards new directions for language modelling. The ideas of
	this paper are also applicable to other problems such as the modelling
	of triphomes in speech, and DNA and protein sequences in molecular
	biology. The new algorithm is compared with smoothing on a two million
	word corpus. The methods prove to be about equally accurate, with
	the hierarchical model using fewer computational resources.},
  annote = {Markov Chain, Inference},
  keywords = {Inference, Markov Chain, Dirichlet, Bayesian},
  pdf = {MacKay1994.pdf}
}

@ARTICLE{Majumder1973,
  author = {K.L. Majumder and G.P. Bhattacharjee},
  title = {Algorithm {AS 64}: Inverse of the Incomplete Beta Function Ratio},
  journal = AppStat,
  year = {1973},
  volume = {22},
  pages = {411-414},
  number = {3},
  owner = {admin},
  timestamp = {2007.02.13}
}

@ARTICLE{Majumder1973a,
  author = {K.L. Majumder and G.P. Bhattacharjee},
  title = {Algorithm {AS 63}: The Incomplete Beta Integral},
  journal = AppStat,
  year = {1973},
  volume = {22},
  pages = {409-411},
  number = {3},
  owner = {admin},
  timestamp = {2007.02.13}
}

@ARTICLE{Menendez1999,
  author = {M.~L.~Men{\'e}ndez and D.~Morales and L.~Pardo and K.~Zografos},
  title = {Statistical Inference for Finite Markov Chains Based on Divergences},
  journal = {Stat. Prob. Lett.},
  year = {1999},
  volume = {41},
  pages = {9 --17},
  number = {1},
  abstract = {We consider statistical data forming sequences of states of stationary
	finite irreducible Markov chains, and draw statistical inference
	about the transition matrix. The inference consists in estimation
	of parameters of transition probabilities and testing simple and
	composite hypotheses about them. The inference is based on statistics
	which are suitable weighted sums of normed -divergences of theoretical
	row distributions, evaluated at suitable points, and observed empirical
	row distributions. The asymptotic distribution of minimum -divergence
	estimators is obtained, as well as critical values of asymptotically
	a-level tests.},
  annote = {Markov},
  keywords = {Markov Chain, Inference, Minimum Distance, Divergence Statistics},
  pdf = {\Menendez1999.pdf}
}

@ARTICLE{JRissanen1984,
  author = {Rissanen, J.},
  title = {Universal coding, information, prediction, and estimation},
  journal = IEEEIT,
  year = {1984},
  volume = {30},
  pages = {629--636},
  number = {4},
  abstract = {A connection between universal codes and the problems of prediction
	and statistical estimation is established. A known lower bound for
	the mean length of universal codes is sharpened and generalized,
	and optimum universal codes constructed. The bound is defined to
	give the information in strings relative to the considered class
	of processes. The earlier derived minimum description length criterion
	for estimation of parameters, including their number, is given a
	fundamental information, theoretic justification by showing that
	its estimators achieve the information in the strings. It is also
	shown that one cannot do prediction in Gaussian autoregressive moving
	average (ARMA) processes below a bound, which is determined by the
	information in the data.},
  issn = {0018-9448},
  keywords = {Information theory, Parameter estimation, Prediction methods, Source
	coding, MDL},
  owner = {admin},
  pdf = {\JRissanen1984.pdf},
  timestamp = {2007.02.27}
}

@ARTICLE{Samengo2002,
  author = {Ines Samengo},
  title = {Estimating Probabilities from Experimental Frequencies},
  journal = PRE,
  year = {2002},
  volume = {65},
  pages = {46124},
  abstract = {Estimating the probability distribution q governing the behavior of
	a certain variable by sampling its value a finite number of times
	most typically involves an error. Successive measurements allow
	the construction of a histogram, or frequency count f, of each of
	the possible outcomes. In this work, the probability that the true
	distribution be q, given that the frequency count f was sampled,
	is studied. Such a probability may be written as a Gibbs distribution.
	A thermodynamic potential, which allows an easy evaluation of the
	mean Kullback-Leibler divergence between the true and measured distribution,
	is defined. For a large number of samples, the expectation value
	of any function of q is expanded in powers of the inverse number
	of samples. As an example, the moments, the entropy, and the mutual
	information are analyzed.},
  annote = {Entropy},
  keywords = {Time Series, Bayesian, Entropy, Kolmogorov, Estimation},
  pdf = {\Samengo2002.pdf}
}

@ARTICLE{HTong1975,
  author = {H.~Tong},
  title = {Determination of the Order of a Markov Chain by Akaike's Information
	Criterion},
  journal = JourAppProb,
  year = {1975},
  volume = {12},
  pages = {488 -- 497},
  number = {3},
  abstract = {Using Akaike's information criterion, we have presented an objective
	procedure for the determination of the order of an ergodic Markov
	chain with a finite number of states. The procedure exploits the
	asymptotic properties of the maximum likelihood ratio statistics
	and Kullback and Leibler's mean information for the discrimination
	between two distributions. Numerical illustrations are given, using
	data from Bartlett (1966), Good and Gover (1967) and some weather
	records.},
  annote = {Markov Chain},
  keywords = {Markov Chain, Inference, Model Comparison, Information Criteria, AIC},
  pdf = {Tong1975.pdf}
}

@ARTICLE{VVapnik1999,
  author = {Vapnik, V.N.},
  title = {An overview of statistical learning theory},
  journal = IEEENN,
  year = {1999},
  volume = {10},
  pages = {988--999},
  number = {5},
  abstract = {Statistical learning theory was introduced in the late 1960's. Until
	the 1990's it was a purely theoretical analysis of the problem of
	function estimation from a given collection of data. In the middle
	of the 1990's new types of learning algorithms (called support vector
	machines) based on the developed theory were proposed. This made
	statistical learning theory not only a tool for the theoretical
	analysis but also a tool for creating practical algorithms for estimating
	multidimensional functions. This article presents a very general
	overview of statistical learning theory including both theoretical
	and algorithmic aspects of the theory. The goal of this overview
	is to demonstrate how the abstract learning theory established conditions
	for generalization which are more general than those discussed in
	classical statistical paradigms and how the understanding of these
	conditions inspired new algorithmic approaches to function estimation
	problems},
  issn = {1045-9227},
  keywords = {estimation theory, generalisation (artificial intelligence), learning
	(artificial intelligence), statistical analysis, function estimation,
	generalization conditions, multidimensional function estimation,
	statistical learning theory, support vector machines},
  owner = {admin},
  pdf = {\VVapnik1999.pdf},
  timestamp = {2007.02.27}
}

@ARTICLE{Vitanyi2000,
  author = {Paul M.B. Vit{\'a}nyi and Ming Li},
  title = {Minimum Description Length Induction, Bayesianism, and Kolmogorov
	Complexity},
  journal = IEEEIT,
  year = {2000},
  volume = {46(2)},
  pages = {446},
  abstract = {The relationship between the Bayesian approach and the minimum description
	length approach is established. We sharpen and clarify the general
	modeling principles minimum description length (MDL) and minimum
	message length (MML), abstracted as the ideal MDL principle and
	defined from Bayes’s rule by means of Kolmogorov complexity. The
	basic condition under which the ideal principle should be applied
	is encapsulated as the fundamental inequality, which in broad terms
	states that the principle is valid when the data are random, relative
	to every contemplated hypothesis and also these hypotheses are random
	relative to the (universal) prior. The ideal principle states that
	the prior probability associated with the hypothesis should be given
	by the algorithmic universal probability, and the sum of the log
	universal probability of the model plus the log of the probability
	of the data given the model should be minimized. If we restrict
	the model class to finite sets then application of the ideal principle
	turns into Kolmogorov’s minimal sufficient statistic. In general,
	we show that data compression is almost always the best strategy,
	both in model selection and prediction.},
  keywords = {Bayes’s Rule, Data Compression,Kolmogorov Complexity, MDL, MML, Model
	Selection, Prediction, Randomness Test, Universal Distribution.},
  pdf = {\Vitanyi2000.pdf}
}

@BOOK{Wilks1962,
  title = {Mathematical Statistics},
  publisher = {John Wiley \& Sons, Inc.},
  year = {1962},
  author = {Samuel~S.~Wilks},
  address = {New York}
}

@ARTICLE{Wolpert1995,
  author = {David~H.~Wolpert and David~R.~Wolf},
  title = {Estimating Functions of Probability Distributions from a Finite Set
	of Samples},
  journal = PRE,
  year = {1995},
  volume = {52},
  pages = {6841},
  abstract = {This paper addresses the problem of estimating a function of a probability
	distribution from a finite set of samples of that distribution.
	A Bayesian analysis of this problem is presented, the optimal properties
	of the Bayes estimators are discussed, and as an example of the
	formalism, closed form expressions for the Bayes estimators for
	the moments of the Shannon entropy function are derived. Then numerical
	results are presented that compare the Bayes estimator to the frequency-counts
	estimator for the Shannon entropy. We also present the closed form
	estimators, all derived elsewhere, for the mutual information, Chi-square
	covariance, and some other statistics.},
  annote = {Markov Chain},
  keywords = {Inference, Bayesian, Multinomial, Entropy, Dirichlet},
  pdf = {\Wolpert1995.pdf}
}

@ARTICLE{Young1994,
  author = {Karl~Young and James~P.~Crutchfield},
  title = {Fluctuation Spectroscopy},
  journal = {Chaos, Solitons, and Fractals},
  year = {1994},
  volume = {4},
  pages = {5 -- 39},
  number = {1},
  abstract = {We review the thermodynamics of estimating the statistical fluctuations
	of an observed process. Since any statistical analysis involves
	a choice of model class--either explicitly or implicitly --we demonstrate
	the benefits of a careful choice. For each of three classes a particular
	model is reconstructed from data streams generated by four sample
	processes. Then each estimated model's thermodynamic structure is
	used to estimate the typical behavior and the magnitude of deviations
	for the observed system. These are then compared to the known fluctuation
	properties. The type of analysis advocated here, which uses estimated
	model class information, recovers the correct statistical structure
	of these processes from simulated data. The current alternative--direct
	estimation of the Renyi entropy from time series histograms--uses
	neither prior nor reconstructed knowledge of the model class. And,
	in most cases, it fails to recover the proeess's statistical structure
	from finite data--unpredictability is overestimated. In this analysis,
	we introduce the fluctuation complexity as a measure of a process's
	total range of allowed statistical variation. It is a new and complementary
	characteristic in that it differs from the process's information
	production rate and its memory capacity.},
  annote = {CMG},
  keywords = {Chaos, Inference, Type Theory, Thermodynamics},
  pdf = {\Young1994.pdf}
}

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