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src/bounds/ellipsoid.jl

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where `size(center) == (N,)` and `size(A) == (N,N)`.
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This implementation follows the algorithm presented in Mukherjee et al. (2006).[^1]
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This implementation follows the algorithm presented in Mukherjee et al. (2006).[^2]
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[^1]: Pia Mukherjee, et al., 2006, ApJ 638 L51 ["A Nested Sampling Algorithm for Cosmological Model Selection"](https://iopscience.iop.org/article/10.1086/501068)
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[^2]: Pia Mukherjee, et al., 2006, ApJ 638 L51 ["A Nested Sampling Algorithm for Cosmological Model Selection"](https://iopscience.iop.org/article/10.1086/501068)
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"""
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mutable struct Ellipsoid{T} <: AbstractBoundingSpace{T}
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center::Vector{T}

src/bounds/multiellipsoid.jl

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Bounds.MultiEllipsoid([T=Float64], ndims)
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Bounds.MultiEllipsoid(::AbstractVector{Ellipsoid})
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Use multiple [`Ellipsoid`](@ref)s in an optimal clustering to bound prior space. This implementation follows the MultiNest implementation outlined in Feroz et al. (2008,2009).[^1][^2] For more details about the bounding algorithm, see the extended help (`??Bounds.MultiEllipsoid`)
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Use multiple [`Ellipsoid`](@ref)s in an optimal clustering to bound prior space. This implementation follows the MultiNest implementation outlined in Feroz et al. (2008,2009).[^3][^4] For more details about the bounding algorithm, see the extended help (`??Bounds.MultiEllipsoid`)
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[^1]: Feroz and Hobson, 2008, MNRAS 384, 2 ["Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses"](https://academic.oup.com/mnras/article/384/2/449/1023701)
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[^2]: Feroz et al., 2009, MNRAS 398, 4 ["MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics"](https://academic.oup.com/mnras/article/398/4/1601/981502)
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[^3]: Feroz and Hobson, 2008, MNRAS 384, 2 ["Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses"](https://academic.oup.com/mnras/article/384/2/449/1023701)
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[^4]: Feroz et al., 2009, MNRAS 398, 4 ["MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics"](https://academic.oup.com/mnras/article/398/4/1601/981502)
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## Extended help
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src/proposals/Proposals.jl

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"""
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Proposals.RWalk(;ratio=0.5, walks=25, scale=1)
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Propose a new live point by random walking away from an existing live point. This follows the algorithm outlined in Skilling (2006).[^1]
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Propose a new live point by random walking away from an existing live point. This follows the algorithm outlined in Skilling (2006).[^5]
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[^1]: Skilling, 2006, Bayesian Anal. 1(4), ["Nested sampling for general Bayesian computation"](https://projecteuclid.org/journals/bayesian-analysis/volume-1/issue-4/Nested-sampling-for-general-Bayesian-computation/10.1214/06-BA127.full)
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[^5]: Skilling, 2006, Bayesian Anal. 1(4), ["Nested sampling for general Bayesian computation"](https://projecteuclid.org/journals/bayesian-analysis/volume-1/issue-4/Nested-sampling-for-general-Bayesian-computation/10.1214/06-BA127.full)
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## Parameters
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- `ratio` is the target acceptance ratio
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Propose a new live point by random staggering away from an existing live point.
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This differs from the random walk proposal in that the step size here is exponentially adjusted
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to reach a target acceptance rate _during_ each proposal, in addition to _between_
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proposals. This follows the algorithm outlined in Skilling (2006).[^1]
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proposals. This follows the algorithm outlined in Skilling (2006).[^5]
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[^1]: Skilling, 2006, Bayesian Anal. 1(4), ["Nested sampling for general Bayesian computation"](https://projecteuclid.org/journals/bayesian-analysis/volume-1/issue-4/Nested-sampling-for-general-Bayesian-computation/10.1214/06-BA127.full)
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[^5]: Skilling, 2006, Bayesian Anal. 1(4), ["Nested sampling for general Bayesian computation"](https://projecteuclid.org/journals/bayesian-analysis/volume-1/issue-4/Nested-sampling-for-general-Bayesian-computation/10.1214/06-BA127.full)
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## Parameters
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- `ratio` is the target acceptance ratio
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Proposals.Slice(;slices=5, scale=1)
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Propose a new live point by a series of random slices away from an existing live point.
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This is a standard _Gibbs-like_ implementation where a single multivariate slice is a combination of `slices` univariate slices through each axis. This follows the algorithm outlined in Neal (2003).[^1]
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This is a standard _Gibbs-like_ implementation where a single multivariate slice is a combination of `slices` univariate slices through each axis. This follows the algorithm outlined in Neal (2003).[^6]
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[^1]: Neal, 2003, Ann. Statist. 31(3), ["Slice Sampling"](https://projecteuclid.org/journals/annals-of-statistics/volume-31/issue-3/Slice-sampling/10.1214/aos/1056562461.full)
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[^6]: Neal, 2003, Ann. Statist. 31(3), ["Slice Sampling"](https://projecteuclid.org/journals/annals-of-statistics/volume-31/issue-3/Slice-sampling/10.1214/aos/1056562461.full)
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## Parameters
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- `slices` is the minimum number of slices
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"""
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Proposals.RSlice(;slices=5, scale=1)
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Propose a new live point by a series of random slices away from an existing live point. This is a standard _random_ implementation where each slice is along a random direction based on the provided axes. This more closely matches the PolyChord implementation outlined in Handley et al. (2015a,b).[^1][^2]
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Propose a new live point by a series of random slices away from an existing live point. This is a standard _random_ implementation where each slice is along a random direction based on the provided axes. This more closely matches the PolyChord implementation outlined in Handley et al. (2015a,b).[^7][^8]
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[^1]: Handley, et al., 2015a, MNRAS 450(1), ["polychord: nested sampling for cosmology"](https://academic.oup.com/mnrasl/article/450/1/L61/986122)
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[^2]: Handley, et al., 2015b, MNRAS 453(4), ["polychord: next-generation nested sampling"](https://academic.oup.com/mnras/article/453/4/4384/2593718)
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[^7]: Handley, et al., 2015a, MNRAS 450(1), ["polychord: nested sampling for cosmology"](https://academic.oup.com/mnrasl/article/450/1/L61/986122)
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[^8]: Handley, et al., 2015b, MNRAS 453(4), ["polychord: next-generation nested sampling"](https://academic.oup.com/mnras/article/453/4/4384/2593718)
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## Parameters
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- `slices` is the minimum number of slices

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