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 cs-677sp2010:slice-sampling [2014/12/11 16:46]ryancha cs-677sp2010:slice-sampling [2014/12/11 16:49] (current)ryancha Both sides previous revision Previous revision 2014/12/11 16:49 ryancha 2014/12/11 16:48 ryancha 2014/12/11 16:47 ryancha 2014/12/11 16:47 ryancha 2014/12/11 16:46 ryancha 2014/12/11 16:45 ryancha 2014/12/11 16:44 ryancha 2014/12/09 09:52 ryancha created Next revision Previous revision 2014/12/11 16:49 ryancha 2014/12/11 16:48 ryancha 2014/12/11 16:47 ryancha 2014/12/11 16:47 ryancha 2014/12/11 16:46 ryancha 2014/12/11 16:45 ryancha 2014/12/11 16:44 ryancha 2014/12/09 09:52 ryancha created Line 39: Line 39: *A candidate sample is selected uniformly from within this region. If the candidate sample lies inside of the slice, then it is accepted as the new sample. If it lies outside of the slice, the candidate point becomes the new boundary for the region. A new candidate sample is taken uniformly. The process repeats until the candidate sample is within the slice. (See diagram for a visual example). *A candidate sample is selected uniformly from within this region. If the candidate sample lies inside of the slice, then it is accepted as the new sample. If it lies outside of the slice, the candidate point becomes the new boundary for the region. A new candidate sample is taken uniformly. The process repeats until the candidate sample is within the slice. (See diagram for a visual example). - [[Image:​500px-slice.png|thumb|center|500pxFinding ​a sample given a set of slices (the slices are represented here as blue lines and correspond to the solid line slices in the previous graph of f(x) ). a) A width parameter ''​w''​ is set. b) A region of width ''​w''​ is identified around a given point $x_0$. c) The region is expanded by ''​w''​ until both endpoints are outside of the considered slice. d) $x_1$ is selected uniformly from the region. e) Since $x_1$ lies outside the considered slice, the region'​s left bound is adjusted to $x_1$. f) Another uniform sample $x$ is taken and accepted as the sample since it lies within the considered slice.]] + [[media:​cs-677sp10:​500px-slice.png]] + Finding ​a sample given a set of slices (the slices are represented here as blue lines and correspond to the solid line slices in the previous graph of f(x) ). a) A width parameter ''​w''​ is set. b) A region of width ''​w''​ is identified around a given point $x_0$. c) The region is expanded by ''​w''​ until both endpoints are outside of the considered slice. d) $x_1$ is selected uniformly from the region. e) Since $x_1$ lies outside the considered slice, the region'​s left bound is adjusted to $x_1$. f) Another uniform sample $x$ is taken and accepted as the sample since it lies within the considered slice. ==Multivariate Methods== ==Multivariate Methods==