Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications

Lockhart, Richard; O'Reilly, Federico J.; Stephens, M. A.

doi:10.1093/biomet/asm065

Cited by 25 publications

(24 citation statements)

References 11 publications

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“…More general approaches to conditional sampling given sufficient statistics are found in Lindqvist and Taraldsen [22] and Lockhardt et al [18]. The methods given there may well be applied to a large class of NHPP models.…”

Section: Discussionmentioning

confidence: 99%

“…., X n on [0, ] given n j=1 X j = s. The main reason for this is that there is no simple expression for the probability density of n j=1 X j . Inspired by, for example, Lockhart et al [18] and Diaconis and Sturmfels [19], we shall use a slightly modified Gibbs sampler algorithm to simulate the desired samples.…”

Section: The Log-linear Law Casementioning

confidence: 99%

“…As regards maximum likelihood estimation of b, looking at the likelihood function (18), it is seen that we can use the same expression for the maximum likelihood estimatorb as for the time-censored cases, just replacing by t n .…”

Section: Processes With Failure Censoringmentioning

confidence: 99%

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Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

Lindqvist

Rannestad

2010

Appl. Stochastic Models Bus. Ind.

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Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness-offit for the power law and the log-linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log-linear case seems to be less known. A data example, as well as simulations, are considered.

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Section: Discussionmentioning

confidence: 99%

Section: The Log-linear Law Casementioning

confidence: 99%

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Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

Lindqvist

Rannestad

2010

Appl. Stochastic Models Bus. Ind.

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“…The distributions were calculated across all subjects and separately for each group. To statistically test the distributions for each interaction, one-and two-sample bootstrapping of the mean was performed using all 10,000 samples generated by the Gibbs sampling (Lockhart et al, 2007). Sampling with replacement was performed for 100,000 iterations per connection and group.…”

Section: Wildenberg Et Almentioning

confidence: 99%

Altered Connectivity of the Balance Processing Network After Tongue Stimulation in Balance-Impaired Individuals

Wildenberg

Tyler²,

Danilov³

et al. 2013

Brain Connectivity

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Some individuals with balance impairment have hypersensitivity of the motion-sensitive visual cortices (hMT + ) compared to healthy controls. Previous work showed that electrical tongue stimulation can reduce the exaggerated postural sway induced by optic flow in this subject population and decrease the hypersensitive response of hMT + . Additionally, a region within the brainstem (BS), likely containing the vestibular and trigeminal nuclei, showed increased optic flow-induced activity after tongue stimulation. The aim of this study was to understand how the modulation induced by tongue stimulation affects the balance-processing network as a whole and how modulation of BS structures can influence cortical activity. Four volumes of interest, discovered in a general linear model analysis, constitute major contributors to the balance-processing network. These regions were entered into a dynamic causal modeling analysis to map the network and measure any connection or topology changes due to the stimulation. Balance-impaired individuals had downregulated response of the primary visual cortex (V1) to visual stimuli but upregulated modulation of the connection between V1 and hMT + by visual motion compared to healthy controls ( p £ 1E-5). This upregulation was decreased to near-normal levels after stimulation. Additionally, the region within the BS showed increased response to visual motion after stimulation compared to both prestimulation and controls. Stimulation to the tongue enters the central nervous system at the BS but likely propagates to the cortex through supramodal information transfer. We present a model to explain these brain responses that utilizes an anatomically present, but functionally dormant pathway of information flow within the processing network.

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“…Given the importance of the Gamma distribution in statistical practice, several authors have addressed the problem of testing if this model is the underlying distribution of a random sample. For instance, Lockhart et al (2007) used conditionally sufficient samples to obtain exact versions of some tests based on the empirical distribution function. Wilding and Mudholkar (2008) proposed a test based on the characteristic independence of the mean and the coefficient of variation.…”

Section: Introductionmentioning

confidence: 99%