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realised that it meant the _actual_ y value of the function at some chosen x. The only sense in which the word 'maximum' applies is for the sampling in step 2. The inclusion of a reference to a 'chosen x' would also make sense of the Markov Chain nature of this procedure (which was also puzzling me), because the next iteration of the chain is then seen to depend on the x derived from step 4 of the procedure from the previous iteration. This also makes sense of later comments about dependence.
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The motivation sentence that immediately follows the 4-step description also seems misleading. As specified, the probability of picking a point (or let's say a point within an interval of specific length in a slice) is greater the higher up the slice is, since the relevant length of each slice to be
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I found the initial description of slice sampling quite confusing. As I read the first of the numbered steps (1.Compute the maximum value of the distribution (i.e. its maximum y-position) ), I understood this to mean the mode of the PDF. It's only on working through the details much later on that I
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The example is close to being really helpful for understanding this method. There appears to be two steps to the algorithm, and it might be nice if the example followed that pattern including how the values are arrived at. It starts with x=0 and then does not go on from there with sepecific values.
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Maybe making a specific and a general example would be a good way to go? i.e. an example that starts at zero and then draws a value and takes a step... and then one that is just general. Thanks!
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I'm not an expert in this field and am loth to change it myself. Would very much appreciate an expert view.
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