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- Slice_sampling abstract "Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution. The method is based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function.To visualize this motivation, imagine printing out a simple bell curve and throwing darts at it. Assume that the darts are uniformly distributed around the board. Now take off all of the darts that are outside the curve (i.e. perform rejection sampling). The x-positions of the remaining darts will be distributed according to the bell curve. This is because there is the most room for the darts to land where curve is highest and thus the probability density is greatest.Slice sampling, in its simplest form, samples uniformly from underneath the curve f(x) without the need to reject any points, as follows:Choose a starting value x0 for which f(x0)>0.Sample a y value uniformly between 0 and f(x0).Draw a horizontal line across the curve at this y position.Sample a point (x,y) from the line segments within the curve.Repeat from step 2 using the new x value.The motivation here is that one way to sample a point uniformly from within an arbitrary curve is first to draw thin uniform-height horizontal slices across the whole curve. Then, we can sample a point within the curve by randomly selecting a slice that falls at or below the curve at the x-position from the previous iteration, then randomly picking an x-position somewhere along the slice. By using the x-position from the previous iteration of the algorithm, in the long run we select slices with probabilities proportional to the lengths of their segments within the curve.Generally, the trickiest part of this algorithm is finding the bounds of the horizontal slice, which involves inverting the function describing the distribution being sampled from. This is especially problematic for multi-modal distributions, where the slice may consist of multiple discontiguous parts. It is often possible to use a form of rejection sampling to overcome this, where we sample from a larger slice that is known to include the desired slice in question, and then discard points outside of the desired slice.Note also that this algorithm can be used to sample from the area under any curve, regardless of whether the function integrates to 1. In fact, scaling a function by a constant has no effect on the sampled x-positions. This means that the algorithm can be used to sample from a distribution whose probability density function is only known up to a constant (i.e. whose normalizing constant is unknown), which is common in computational statistics.".
- Slice_sampling thumbnail Some_probability_distribution.png?width=300.
- Slice_sampling wikiPageExternalLink slice.html.
- Slice_sampling wikiPageID "7149788".
- Slice_sampling wikiPageRevisionID "596660559".
- Slice_sampling hasPhotoCollection Slice_sampling.
- Slice_sampling subject Category:Markov_chain_Monte_Carlo.
- Slice_sampling subject Category:Non-uniform_random_numbers.
- Slice_sampling type Abstraction100002137.
- Slice_sampling type Amount105107765.
- Slice_sampling type Attribute100024264.
- Slice_sampling type Magnitude105090441.
- Slice_sampling type Non-uniformRandomNumbers.
- Slice_sampling type Number105121418.
- Slice_sampling type Property104916342.
- Slice_sampling comment "Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution. The method is based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function.To visualize this motivation, imagine printing out a simple bell curve and throwing darts at it. Assume that the darts are uniformly distributed around the board.".
- Slice_sampling label "Slice sampling".
- Slice_sampling label "Выборка по уровням".
- Slice_sampling label "スライスサンプリング".
- Slice_sampling sameAs スライスサンプリング.
- Slice_sampling sameAs m.0h6w_v.
- Slice_sampling sameAs Q4128565.
- Slice_sampling sameAs Q4128565.
- Slice_sampling sameAs Slice_sampling.
- Slice_sampling wasDerivedFrom Slice_sampling?oldid=596660559.
- Slice_sampling depiction Some_probability_distribution.png.
- Slice_sampling isPrimaryTopicOf Slice_sampling.
