slice sampler
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2018 ◽  
Vol 55 (4) ◽  
pp. 1186-1202
Author(s):  
Daniel Rudolf ◽  
Mario Ullrich

Abstract Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler, and random walk Metropolis algorithm are popular tools to simulate such Markov chains. We develop a general approach to compare the efficiency of these sampling procedures by the use of a partial ordering of their Markov operators, the covariance ordering. In particular, we show that the hit-and-run and the simple slice sampler are more efficient than a hybrid slice sampler based on hit-and-run, which, itself, is more efficient than a (lazy) random walk Metropolis algorithm.


2017 ◽  
Vol 47 (4) ◽  
pp. 1-32
Author(s):  
Mohammad Rostami ◽  
Mohd Bakri Adam Yahya ◽  
Mohamed Hisham Yahya ◽  
Noor Akma Ibrahim

2016 ◽  
Author(s):  
Silvan C. Quax ◽  
Thomas C. van Koppen ◽  
Pasi Jylänki ◽  
Serge O. Dumoulin ◽  
Marcel A.J. van Gerven

AbstractFunctional magnetic resonance imaging (FMRI) allows to non-invasively measure human brain activity at the millimeter scale. As such, it is widely used in computational neuroimaging studies that aim to build models to predict stimulus-induced neural responses in visual cortex. A popular method is population receptive field (PRF) mapping, which is able to characterize responses to a large range of stimuli. For each voxel, the PRF method estimates the best fitting receptive field properties (such as location and size in the visual field) using a coarse–to–fine approach which minimizes, but not eliminates, the risk of returning a local minimum. Here, we provide a Bayesian approach to the PRF method based on the slice sampler. Using this approach, we provide estimates of receptive field properties while at the same time being able to quantify their uncertainty. We test the performance of conventional and Bayesian approaches on simulated and empirical data.


Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. F373-F386 ◽  
Author(s):  
Whitney Trainor-Guitton ◽  
G. Michael Hoversten

Traditional deterministic geophysical inversion algorithms are not designed to provide a robust evaluation of uncertainty that reflects the limitations of the geophysical technique. Stochastic inversions, which do provide a sampling-based measure of uncertainty, are computationally expensive and not straightforward to implement for nonexperts (nonstatisticians). Our results include stochastic inversion for magnetotelluric and controlled source electromagnetic data. Two Markov Chain sampling algorithms (Metropolis-Hastings and Slice Sampler) can significantly decrease the computational expense compared to using either sampler alone. The statistics of the stochastic inversion allow for (1) variances that better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques and (2) models defined by the median and modes of parameter probability density functions, which produce amplitude and phase data that are consistent with the observed data. In general, parameter error estimates from the covariance matrix significantly underestimate the true parameter error, whereas the parameter variance derived from Markov chains accurately encompass the error.


Author(s):  
Christian P. Robert ◽  
George Casella
Keyword(s):  

2002 ◽  
Vol 18 (2) ◽  
pp. 257-280 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal
Keyword(s):  

2000 ◽  
pp. 123-130
Author(s):  
Gareth Roberts ◽  
Jeffrey Rosenthal

Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal
Keyword(s):  

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