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54
How Many Iterations in the Gibbs Sampler?
 In Bayesian Statistics 4
, 1992
"... When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easilyimplemented metho ..."
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Cited by 155 (6 self)
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When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easilyimplemented method for determining the total number of iterations required, and also the number of initial iterations that should be discarded to allow for "burnin". The method uses only the Gibbs iterates themselves, and does not, for example, require external specification of characteristics of the posterior density. Here the method is described for the situation where one long run is generated, but it can also be easily applied if there are several runs from different starting points. It also applies more generally to Markov chain Monte Carlo schemes other than the Gibbs sampler. It can also be used when several quantiles are to be estimated, when the quantities of interest are probabilities rath...
Mixed memory Markov models: decomposing complex stochastic processes as mixtures of simpler ones
, 1998
"... . We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple ..."
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Cited by 76 (1 self)
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. We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an ExpectationMaximization (EM) procedure. We derive a set of generalized BaumWelch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes. Keywords: Markov models, mixture models, discrete time series 1. Introduction The modeling of time series is a fundamental problem in machine learning, with widespread applications. These include speech recognition (Rabiner, 1989), natu...
Computer Intrusion: Detecting Masquerades
"... Abstract. Masqueraders in computer intrusion detection are people who use somebody else’s computer account. We investigate a number of statistical approaches for detecting masqueraders. To evaluate them, we collected UNIX command data from 50 users and then contaminated the data with masqueraders. ..."
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Cited by 73 (1 self)
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Abstract. Masqueraders in computer intrusion detection are people who use somebody else’s computer account. We investigate a number of statistical approaches for detecting masqueraders. To evaluate them, we collected UNIX command data from 50 users and then contaminated the data with masqueraders. The experiment was blinded. We show results from six methods, including two approaches from the computer science community.
Driving with Knowledge from the Physical World
 In Proc. of KDD 2011
"... This paper presents a Cloudbased system computing customized and practically fast driving routes for an end user using (historical and realtime) traffic conditions and driver behavior. In this system, GPSequipped taxicabs are employed as mobile sensors constantly probing the traffic rhythm of a c ..."
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Cited by 68 (13 self)
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This paper presents a Cloudbased system computing customized and practically fast driving routes for an end user using (historical and realtime) traffic conditions and driver behavior. In this system, GPSequipped taxicabs are employed as mobile sensors constantly probing the traffic rhythm of a city and taxi drivers’ intelligence in choosing driving directions in the physical world. Meanwhile, a Cloud aggregates and mines the information from these taxis and other sources from the Internet, like Web maps and weather forecast. The Cloud builds a model incorporating day of the week, time of day, weather conditions, and individual driving strategies (both of the taxi drivers and of the end user for whom the route is being computed). Using this model, our system predicts the traffic conditions of a future time (when the computed route is actually driven) and performs a selfadaptive driving direction service for a particular user. This service gradually learns a user’s driving behavior from the user’s GPS logs and customizes the fastest route for the user with the help of the Cloud. We evaluate our service using a realworld dataset generated by over 33,000 taxis over a period of 3 months in Beijing. As a result, our service accurately estimates the travel time of a route for a user; hence finding the fastest route customized for the user.
The mixture transition distribution model for highorder Markov chains and nonGaussian time series
 Statistical Science
, 2002
"... Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA seq ..."
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Cited by 31 (2 self)
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Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA sequences and social behavior. Here we review the MTD model and the developments since 1985. We first introduce the basic principle and then we present several extensions, including general state spaces and spatial statistics. Following that, we review methods for estimating the model parameters. Finally, a review of different types of applications shows the practical interest of the MTD model. Key words and phrases: Mixture transition distribution (MTD) model, Markov chains, highorder dependences, time series, GMTD model, EM algorithm,
A Hybrid Highorder Markov Chain Model for Computer Intrusion Detection
, 1999
"... A hybrid model based mostly on a highorder Markovchain and occasionally on an independence model is proposed for pro#ling the commandsequence of a computer user in order to identify a "signature behavior" for that user. Based on the model, an estimation procedure for such a signature beh ..."
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Cited by 28 (3 self)
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A hybrid model based mostly on a highorder Markovchain and occasionally on an independence model is proposed for pro#ling the commandsequence of a computer user in order to identify a "signature behavior" for that user. Based on the model, an estimation procedure for such a signature behavior driven by Maximum Likelihood #ML# considerations is devised. The formal ML estimates are numerically intractable, but the MLoptimization problem can be substituted by a linear inverse problem with positivity constraints #LININPOS#, for which the EM algorithm can be used as an equation solver to produce an approximate MLestimate. A user's commandsequence is then compared to his and others' estimated signaturebehavior in real time, by means of statistical hypothesis testing. A form of the likelihoodratio test is used to test if a given sequence of commands is from the proclaimed user, with the alternative hypothesis being masquerader user. Data from a reallife experiment, conducted at a research lab, is used to assess the method. Key Words: Anomaly Detection; Unix; Mixture Transition Distribution #MTD#; LININPOS; EM. 1
Discrete variate time series
 In Handbook of Statistics, C.Raoand D.Shanbhag,Eds.,ElsevierScience,Amsterdam,573–606. MR1973555
, 2003
"... Modelling discrete variate time series is the most challenging and, as yet, least well developed of all areas of research in time series. The fact that variate values are integer renders most traditional representations of dependence either impossible or impractical. In the last two decades there ha ..."
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Cited by 21 (0 self)
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Modelling discrete variate time series is the most challenging and, as yet, least well developed of all areas of research in time series. The fact that variate values are integer renders most traditional representations of dependence either impossible or impractical. In the last two decades there have been a number of imaginative attempts to develop a
The double chain Markov model
 Comm Stat Theor Meths
, 1999
"... Among the class of discrete time Markovian processes, two models are widely used, the Markov chain and the Hidden Markov Model. A major di erence between these two models lies in the relation between successive outputs of the observed variable. In a visible Markov chain, these are directly correlate ..."
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Cited by 19 (2 self)
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Among the class of discrete time Markovian processes, two models are widely used, the Markov chain and the Hidden Markov Model. A major di erence between these two models lies in the relation between successive outputs of the observed variable. In a visible Markov chain, these are directly correlated while in hidden models they are not. However, in some situations it is possible to observe both a hidden Markov chain and a direct relation between successive observed outputs. Unfortunately, the use of either a visible or a hidden model implies the suppression of one of these hypothesis. This paper presents a Markovian model called the Double Chain Markov Model which takes into account the main features of both visible and hidden models. Its main purpose is the modeling of nonhomogeneous timeseries. It is very exible and can be estimated with traditional methods. The model is applied on a sequence of wind speeds and it appears to
Highorder extensions of the double chain Markov model
 Stoch. Models
, 2002
"... The Double Chain Markov Model is a fully Markovian model for the representation of timeseries in random environment. In this article, we showthat it can handle transitions of highorder between both a set of obsevations and a set of hidden states. In order to reduce the number of parameters, each t ..."
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Cited by 13 (4 self)
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The Double Chain Markov Model is a fully Markovian model for the representation of timeseries in random environment. In this article, we showthat it can handle transitions of highorder between both a set of obsevations and a set of hidden states. In order to reduce the number of parameters, each transition matrix can be replaced by a Mixture Transition Model. We provide a complete derivation of the algorithms needed to compute the model. Three applications, the analysis of a sequence of DNA, the song of the wood pewee and the behavior of young monkeys, show that this model is of great interest for the representation of data which can be decomposed
Estimation of the Mixture Transition Distribution Model
, 1999
"... This paper introduces a new iterative algorithm for the estimation of the Mixture Transition Distribution model (MTD). It does not require the use of any speci c external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results s ..."
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Cited by 12 (4 self)
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This paper introduces a new iterative algorithm for the estimation of the Mixture Transition Distribution model (MTD). It does not require the use of any speci c external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results show that this new algorithm performs at least as good or better than other methods. The choice of initial values is also discussed. The MTD model was designed for the modeling of highorder Markov chains and already proved to be a useful tool for the analysis of di erenttypes of timeseries such as wind speeds and wind directions. In this paper, we also propose to use this it for the modeling of onedimensional spatial data. An application using a DNA sequence shows that this approach