deletions | additions       diff --git a/Slice_Sampling_Slice_sampling_is__.md b/Slice_Sampling_Slice_sampling_is__.md  index a210158..2f3ce32 100644  --- a/Slice_Sampling_Slice_sampling_is__.md  +++ b/Slice_Sampling_Slice_sampling_is__.md 
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Slice sampling in particular possesses several very desirable properties \cite{murray2009elliptical}. It allows us to sample from integrals that are _proportional_ to our underlying distribution. There is no assumption that our probability mass sums to one. Consequently our intractable denominator above is of no concern -- we simply proceed using the scaled posterior.  Additionally, slice sampling has no free parameters. This is useful from a practical perspective, as it removes the need to spend time tuning and updating hyper-parameters for more complex models. It also impacts on performance; the more general Metropolis-Hastings model is highly sensitive to step-size parameters, which means unless we get it right we're going to perform very poorly on evaluation. In contrast, slice sampling adjusts the step-size to match the local shape of the density function. There are several modified slice-samplers which are heavily parallelisable \cite{Tran_2015}.  SS as parallel MCMC \cite{Tran_2015} In our analysis we use the following slice-sampling algorithm, iteratively tuning on each subsequent weight-parameter.