Statistical inference and Monte Carlo algorithms

Casella, George; Ferrándiz, Juan; Peña, Daniel; Insua, David Rı́os; Bernardo, José M.; Garcı́a-López, Pedro; González, A. Gustavo; Berger, James O.; Dawid, A. P.; DiCiccio, Thomas J.; Wells, Martin T.; Gustafson, Paul; Wasserman, L. H.; George, Edward I.; Liu, Jun S.; Meng, Xiao‐Li; Philippe, Anne; Schafer, Joseph L.; Strawderman, Robert L.

doi:10.1007/bf02562621

Cited by 29 publications

(17 citation statements)

References 38 publications

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“…New realizations are kept or discarded according to the Metropolis criterion in a Markov chain. This results in a sample of DEM(T) solutions that is representative of the actual probability distribution of the DEM(T) (see, e.g., Smith & Roberts 1993;Casella 1996). MCMC methods are described in detail in the astronomical literature by Kashyap & Drake (1998), van Dyk et al (2001, von Hippel et al (2006), and others.…”

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confidence: 99%

Coronal Heat: Solar Loop Temperatures from TRACE Triple-Filter Data

Schmelz

Kashyap

Weber

2007

ApJ

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The Transition Region and Coronal Explorer (TRACE) has state-of-the-art spatial resolution and shows the most detailed images of coronal loops ever observed. The temperatures of these loops are primarily derived from the 171 to 195 filter ratio, with data from the third filter at 284 used by several authors to improve theÅ A precision of the derived temperatures. Most of these studies assume that the plasma is isothermal and model the loops primarily as uniform temperature structures with footpoint-dominated heating. However, these triple-filter data are insufficient to constrain the plasma temperature and cannot be used to determine the isothermality or otherwise of coronal loop structures. We show this explicitly by constructing differential emission measures with these same triple-filter data using a sophisticated Markov-chain Monte Carlo-based reconstruction algorithm. We find that these TRACE data cannot, in general, limit the temperature distribution for coronal loop plasma. In other words, many different temperature distributions (isothermal, broad, sloped, etc.) can reproduce the observed fluxes, and the TRACE coronal data alone cannot determine which of these distributions represents the actual coronal plasma.

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confidence: 99%

Coronal Heat: Solar Loop Temperatures from TRACE Triple-Filter Data

Schmelz

Kashyap

Weber

2007

ApJ

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“…Whereas the approach of Bartolucci & Besag applies, in theory, to any probability model, it presupposes that the full conditionals are compatible with a valid joint distribution. For conditionals that are not derived from a known, though possibly unnormalised, joint distribution, compatibility must be checked; see for example Casella (1996) and Arnold et al (2001 (1996). Kaiser & Cressie (2000) consider the question of defining Markov random fields with arbitrary conditionals, and give necessary and sufficient conditions which such conditionals must fulfil.…”

Section: Discussionmentioning

confidence: 99%

Efficient recursions for general factorisable models

Reeves¹,

Pettitt²

2004

Biometrika

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SummaryLet n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r + 1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(S r+1 ) computations, as opposed to O(S n ) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

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“…Notice that in both MM PF and MKF the updated state estimates and posterior mode probabilities are calculated before the resampling step, because resampling brings extra variation to the current samples ( [30], [26], pp. 103).…”

Section: The Mixture Kalman Filter Algorithmmentioning

confidence: 99%

Joint target tracking and classification with particle filtering and mixture Kalman filtering using kinematic radar information

Angelova

Mihaylova

2006

Digital Signal Processing

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This paper considers the problem of joint maneuvering target tracking and classification. Based on recently proposed Monte Carlo techniques, a multiple model (MM) particle filter and a mixture Kalman filter (MKF) are designed for two-class identification of air targets: commercial and military aircraft. The classification task is carried out by processing radar measurements only, no class (feature) measurements are used. A speed likelihood function for each class is defined using a prior information about speed constraints. Class-dependent speed likelihoods are calculated through the state estimates of each class-dependent tracker. They are combined with the kinematic measurement likelihoods in order to improve the classification process. The two designed estimators are compared and evaluated over rather complex target scenarios. The results demonstrate the usefulness of the proposed scheme for the incorporation of additional speed information. Both filters illustrate the opportunity of the particle filtering and mixture Kalman filtering to incorporate constraints in a natural way, providing reliable tracking and correct classification. Future observations contain valuable information about the current state of the dynamic systems. In the framework of the MKF, an algorithm for delayed estimation is designed for improving the current modal state estimate. It is used as an additional, more reliable information in resolving complicated classification situations.

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Statistical inference and Monte Carlo algorithms

Abstract: This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other.

Cited by 29 publications

References 38 publications

Coronal Heat: Solar Loop Temperatures from TRACE Triple-Filter Data

Coronal Heat: Solar Loop Temperatures from TRACE Triple-Filter Data

Efficient recursions for general factorisable models

Joint target tracking and classification with particle filtering and mixture Kalman filtering using kinematic radar information

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