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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,
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
A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability
 Statist. Prob. Letters
, 1997
"... We consider Bayesian nonparametric inference for continuousvalued partially exchangeable data, when the partition of the observations into groups is unknown. This includes changepoint problems and mixture models. As the prior, we consider a mixture of products of Dirichlet processes. We show that ..."
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Cited by 10 (3 self)
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We consider Bayesian nonparametric inference for continuousvalued partially exchangeable data, when the partition of the observations into groups is unknown. This includes changepoint problems and mixture models. As the prior, we consider a mixture of products of Dirichlet processes. We show that the discreteness of the Dirichlet process can have a large effect on inference (posterior distributions and Bayes factors), leading to conclusions that can be different from those that result from a reasonable parametric model. When the observed data are all distinct, the effect of the prior on the posterior is to favor more evenly balanced partitions, and its effect on Bayes factors is to favor more groups. In a hierarchical model with a Dirichlet process as the secondstage prior, the prior can also have a large effect on inference, but in the opposite direction, towards more unbalanced partitions. (~) 1997 Elsevier Science B.V.
The Mixture Transition Distribution (MTD) Model for HighOrder Markov Chains and NonGaussian Time Series
, 1999
"... The Mixture Transition Distribution model (MTD) was introduced by Raftery (1985) 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 direction, DNA and social beha ..."
Abstract

Cited by 5 (1 self)
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The Mixture Transition Distribution model (MTD) was introduced by Raftery (1985) 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 direction, DNA and social behavior. Here we review the MTD model and the developments since 1985. We rst introduce the basic principle and then we present several extensions including general state spaces and spatial statistics. We then review methods for estimating the model parameters. Finally, a review
USE OF CUMULATIVE SUMS FOR DETECTION OF CHANGEPOINTS IN THE RATE PARAMETER OF A POISSON PROCESS
, 2004
"... This paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. W ..."
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Cited by 1 (0 self)
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This paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example.
Bayesian Simultaneous Variable and Transformation Selection in Linear Regression
, 1999
"... We suggest a method for simultaneous variable and transformation selection based on posterior probabilities. A simultaneous approach avoids the problem that the order in which variable and transformation selection are performed might influence the choice of variables and transformations. The simulta ..."
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Cited by 1 (0 self)
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We suggest a method for simultaneous variable and transformation selection based on posterior probabilities. A simultaneous approach avoids the problem that the order in which variable and transformation selection are performed might influence the choice of variables and transformations. The simultaneous approach also allows for consideration of all possible models. We use a changepoint model, or "changepoint transformation," which can yield more interpretable models and transformations than the standard BoxTidwell approach. We also address the problem of model uncertainty in the selection of models. By averaging over models, we account for the uncertainty inherent in inference based on a single model chosen from the set of all possible models. We use a Markov chain Monte Carlo model composition (MC 3 ) method which allows us to average over linear regression models when the space of all possible models is very large. This considers the selection of variables and transformations a...
Abstract Event Detection from Time Series Data
"... In the past few years there has been increased interest in using datamining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, whic ..."
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In the past few years there has been increased interest in using datamining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, which is then mined for interesting episodes. In some cases the rule for determining when a sensor reading should generate an event is well known. However, if the phenomenon is illunderstood, stating such a rule is difficult. Detection of events in such an environment is the focus of this paper. Consider a dynamic phenomenon whose behavior changes enough over time to be considered a qualitatively significant change. The problem we investigate is of identifying the time points at which the behavior change occurs. In the statistics literature this has been called the changepoint detection problem. The standard approach has been to (a) upriori determine the number of changepoints that are to be discovered, and (b) decide the function that will be used for curve fitting in the interval between successive changepoints. In this paper we generalize along both these dimensions. We propose an iterative algorithm that fits a model to a time segment, and uses a likelihood criterion to determine if the segment should be partitioned further, i.e. if it contains a new changepoint. In this paper we present algorithms for both the batch and incremental versions of the problem, and evaluate their behavior with synthetic and real data. Finally, we present initial results comparing the changepoints detected by the batch algorithm with those detected by people using visual inspection. 1
Covariance Models for Latent Structure in Longitudinal Data
"... We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the crosssectional mean and the influe ..."
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We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the crosssectional mean and the influence of covariates on the mean. Such analyses are particularly important in policyrelated studies, in which the heterogeneity of the population is of interest. We describe several traditional approaches to this modeling and introduce a flexible, parsimonious class of covariance models appropriate to such analyses. This class, while rooted in the tradition of mixed effects and random coefficient models, merges several disparate modeling philosophies into what we view as a hybrid approach to longitudinal data modeling. We discuss the implications of this approach and its alternatives especially on model interpretation. We compare several implementations of this class to more commonly employed mixed effects models to describe the strengths and limitations of each. These alternatives are compared in an application to longterm trends in wage inequality for young workers. The findings provide additional guidance for the model formulation process in both statistical and substantive senses.
Investigating Purchasing . . . Markov, MTD and MTDg Models
 FORTHCOMING IN EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 2003
"... In the past, several authors have found evidence for the existence of a priority pattern of acquisition for durable goods, as well as for financial services. Its usefulness lies in the fact that if the position of a particular customer in this acquisition sequence is known, one can predict what serv ..."
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In the past, several authors have found evidence for the existence of a priority pattern of acquisition for durable goods, as well as for financial services. Its usefulness lies in the fact that if the position of a particular customer in this acquisition sequence is known, one can predict what service will be acquired next by that customer. In this paper, we analyse purchase sequences of financial services to identify crossselling opportunities as part of a CRM (customer relationship management). Hereby, special attention is paid to transitions, which might encourage bank or insurance only customers to become financial services customers. We introduce the Mixture Transition Distribution model (MTD) as a parsimonious alternative to the Markov model for use in the analysis of marketing problems. An interesting extension on the MTD model is the MTDg model, which is able to represent situations where the relationship between each lag and the current state differs. We illustrate the MTD and MTDg model on acquisition sequences of customers of a major financialservices company and compare the fit of these models with that of the corresponding Markov model. Our results are in favor of the MTD and MTDg models. Therefore, the MTD as well as the MTDg transition matrices are investigated in order to reveal crosssell opportunities. The results are of great value to the product managers as they clarify the customer flows among product groups. In some cases, the lagspecific transition matrices of the MTDg model are better for the guidance of crosssell actions than the general transition matrix of the MTD model.
BY
, 2010
"... To my grandparents and my parents The climate and earth sciences have recently undergone a rapid transformation from a datapoor to a datarich environment. In particular, climate and ecosystem related observations from remote sensors on satellites, as well as outputs of climate or earth system mode ..."
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To my grandparents and my parents The climate and earth sciences have recently undergone a rapid transformation from a datapoor to a datarich environment. In particular, climate and ecosystem related observations from remote sensors on satellites, as well as outputs of climate or earth system models from largescale computational platforms, provide terabytes of temporal, spatial and spatiotemporal data. These massive and informationrich datasets offer huge potential for advancing the science of land cover change, climate change and anthropogenic impacts. One important area where remote sensing data can play a key role is in the study of land cover change. Specifically, the conversion of natural land cover into humandominated cover types continues to be a change of global proportions with many unknown environmental consequences. In addition, being able to assess the carbon risk of changes in forest cover is of critical importance for both economic and scientific reasons. In fact, changes in forests account for as much as 20 % of the greenhouse gas emissions