Implied distributions in multiple change point problems

Aston, John A. D.; Peng, Jyh-Ying; Martin, Donald E. K.

doi:10.1007/s11222-011-9268-6

Cited by 8 publications

(12 citation statements)

References 30 publications

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“…This definition generalizes the changepoint-out-of the regime k CP = 1, considered by Aston, Peng, and Martin (2011). Under this changepoint definition, the changepoint problem becomes a waiting time distribution problem for runs in the underlying state sequence.…”

Section: Exact Changepoint Distributionsmentioning

confidence: 97%

“…For overviews of HMMs, we refer the reader to MacDonald and Zucchini (1997) and Cappé, Moulines, and Rydén (2005). The use of HMMs provides a sophisticated modeling framework for a variety of problems and applications including changepoint analysis (e.g., Chib 1998;Aston, Peng, and Martin 2011) and thus forms one of the many building blocks in our proposed methodology. Within a HMM framework, we have the observation process {Y t } t≥1 which is dependent on an underlying latent finite state Markov chain (MC), {X t } t≥0 ∈ X with | X | < ∞.…”

Section: Statistical Backgroundmentioning

confidence: 99%

“…A natural question to thus ask is whether it is possible to combine the two frameworks such that HMM-based changepoint methods can be applied within the LSW framework. The hybrid framework would thus allow us to consider changes in second-order structure through the LSW framework, while applying a multitude of existing HMM-based changepoint methods (e.g., Chib 1998, Aston, Peng, andMartin 2011;and Nam, Aston, and Johansen (2012)). Section 3 proposes a framework in which this can be achieved.…”

Section: Lsw Processesmentioning

confidence: 99%

See 2 more Smart Citations

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

Nam¹,

Aston

Eckley³

et al. 2015

Technometrics

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In oceanography, there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling. In particular, there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them. Such changes are associated with autocovariance changes. This article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application. More specifically, the framework considers time series under the locally stationary wavelet (LSW) framework, deriving a joint density for scale processes in the raw wavelet periodogram. By embedding this density within a hidden Markov model (HMM) framework, we consider changepoint characteristics under this multiscale setting. Such a methodology allows us to model changepoints and their uncertainty for a wide range of models, including piecewise second-order stationary processes, for example, piecewise moving average processes.

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Section: Exact Changepoint Distributionsmentioning

confidence: 97%

Section: Statistical Backgroundmentioning

confidence: 99%

Section: Lsw Processesmentioning

confidence: 99%

See 1 more Smart Citation

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

Nam¹,

Aston

Eckley³

et al. 2015

Technometrics

View full text Add to dashboard Cite

show abstract

“…Much of the inference and applications for HMMs such as estimating the underlying state sequence (Viterbi, 1967), parameter estimation (Baum et al, 1970) and changepoint inference (Chib (1998), Aston et al (2011), Nam et al (2012)), assume that the number of states the underlying Markov Chain (MC) can take, H, is known a priori. However, this is often not the case when presented with time series data.…”

Section: Introductionmentioning

confidence: 99%

Parallel sequential Monte Carlo samplers and estimation of the number of states in a Hidden Markov Model

2014

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The majority of modelling and inference regarding Hidden Markov Models (HMMs) assumes that the number of underlying states is known a priori. However, this is often not the case and thus determining the appropriate number of underlying states for a HMM is of considerable interest. This paper proposes the use of a parallel Sequential Monte Carlo samplers framework to approximate the posterior distribution of the number of states. This requires no additional computational effort if approximating parameter posteriors conditioned on the number of states is also necessary. The proposed methodology is evaluated on a comprehensive set of simulated data and shown to compare favorably with other state of the art methods. An application to business cycle analysis is also presented.

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“…The exact change point distributions computed via FMCI methodology (Aston et al. , 2011) already quantify the residual uncertainty given both the model parameters and the observed data.…”

Section: Introductionmentioning

confidence: 99%

Quantifying the uncertainty in change points

Nam

Aston

Johansen

2012

Journal Time Series Analysis

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a Quantifying the uncertainty in the location and nature of change points in time series is important in a variety of applications. Many existing methods for estimation of the number and location of change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst others require explicit simulation of large vectors of dependent latent variables. This article proposes methodology for approximating the full posterior distribution of various change point characteristics in the presence of parameter uncertainty. The methodology combines recent work on evaluation of exact change point distributions conditional on model parameters via finite Markov chain imbedding in a hidden Markov model setting, and accounting for parameter uncertainty and estimation via Bayesian modelling and sequential Monte Carlo. The combination of the two leads to a flexible and computationally efficient procedure, which does not require estimates of the underlying state sequence. We illustrate that good estimation of the posterior distributions of change point characteristics is provided for simulated data and functional magnetic resonance imaging data. We use the methodology to show that the modelling of relevant physical properties of the scanner can influence detection of change points and their uncertainty.

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Implied distributions in multiple change point problems

Cited by 8 publications

References 30 publications

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

Parallel sequential Monte Carlo samplers and estimation of the number of states in a Hidden Markov Model

Quantifying the uncertainty in change points

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