torfjelde/Manifest.toml

## Manifest.toml
# This file is machine-generated - editing it directly is not advised

julia_version = "1.10.0"
manifest_format = "2.0"
project_hash = "a0590676db40552635a5877095b47d6a64ec5413"

[[deps.ADTypes]]
git-tree-sha1 = "41c37aa88889c171f1300ceac1313c06e891d245"
uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
version = "0.2.6"

[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.5.0"
weakdeps = ["ChainRulesCore", "Test"]

    [deps.AbstractFFTs.extensions]
    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
    AbstractFFTsTestExt = "Test"

[[deps.AbstractMCMC]]
deps = ["BangBang", "ConsoleProgressMonitor", "Distributed", "LogDensityProblems", "Logging", "LoggingExtras", "ProgressLogging", "Random", "StatsBase", "TerminalLoggers", "Transducers"]
git-tree-sha1 = "87e63dcb990029346b091b170252f3c416568afc"
uuid = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
version = "4.4.2"

[[deps.AbstractPPL]]
deps = ["AbstractMCMC", "DensityInterface", "Random", "Setfield", "SparseArrays"]
git-tree-sha1 = "caa9b62583577b0d6b222f11f54aa29fabbdb5ca"
uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
version = "0.6.2"

[[deps.AbstractTrees]]
git-tree-sha1 = "faa260e4cb5aba097a73fab382dd4b5819d8ec8c"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.4.4"

[[deps.Accessors]]
deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "LinearAlgebra", "MacroTools", "Test"]
git-tree-sha1 = "cb96992f1bec110ad211b7e410e57ddf7944c16f"
uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
version = "0.1.35"

    [deps.Accessors.extensions]
    AccessorsAxisKeysExt = "AxisKeys"
    AccessorsIntervalSetsExt = "IntervalSets"
    AccessorsStaticArraysExt = "StaticArrays"
    AccessorsStructArraysExt = "StructArrays"

    [deps.Accessors.weakdeps]
    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"

[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "cde29ddf7e5726c9fb511f340244ea3481267608"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.7.2"
weakdeps = ["StaticArrays"]

    [deps.Adapt.extensions]
    AdaptStaticArraysExt = "StaticArrays"

[[deps.AdvancedHMC]]
deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "ProgressMeter", "Random", "Requires", "Setfield", "SimpleUnPack", "Statistics", "StatsBase", "StatsFuns"]
git-tree-sha1 = "acbe805c3078ba0057bb56985248bd66bce016b1"
uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
version = "0.5.5"

    [deps.AdvancedHMC.extensions]
    AdvancedHMCCUDAExt = "CUDA"
    AdvancedHMCMCMCChainsExt = "MCMCChains"
    AdvancedHMCOrdinaryDiffEqExt = "OrdinaryDiffEq"

    [deps.AdvancedHMC.weakdeps]
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
    OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"

[[deps.AdvancedMH]]
deps = ["AbstractMCMC", "Distributions", "FillArrays", "LinearAlgebra", "LogDensityProblems", "Random", "Requires"]
git-tree-sha1 = "b2a1602952739e589cf5e2daff1274a49f22c9a4"
uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
version = "0.7.5"
weakdeps = ["DiffResults", "ForwardDiff", "MCMCChains", "StructArrays"]

    [deps.AdvancedMH.extensions]
    AdvancedMHForwardDiffExt = ["DiffResults", "ForwardDiff"]
    AdvancedMHMCMCChainsExt = "MCMCChains"
    AdvancedMHStructArraysExt = "StructArrays"

[[deps.AdvancedPS]]
deps = ["AbstractMCMC", "Distributions", "Libtask", "Random", "Random123", "StatsFuns"]
git-tree-sha1 = "4d73400b3583147b1b639794696c78202a226584"
uuid = "576499cb-2369-40b2-a588-c64705576edc"
version = "0.4.3"

[[deps.AdvancedVI]]
deps = ["Bijectors", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
git-tree-sha1 = "1f919a9c59cf3dfc68b64c22c453a2e356fca473"
uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
version = "0.2.4"

[[deps.ArgCheck]]
git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.3.0"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"

[[deps.Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"]
git-tree-sha1 = "9b9b347613394885fd1c8c7729bfc60528faa436"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.5.4"

[[deps.Arpack_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.1+1"

[[deps.ArrayInterface]]
deps = ["Adapt", "LinearAlgebra", "Requires", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "bbec08a37f8722786d87bedf84eae19c020c4efa"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "7.7.0"

    [deps.ArrayInterface.extensions]
    ArrayInterfaceBandedMatricesExt = "BandedMatrices"
    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
    ArrayInterfaceCUDAExt = "CUDA"
    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
    ArrayInterfaceTrackerExt = "Tracker"

    [deps.ArrayInterface.weakdeps]
    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[deps.Atomix]]
deps = ["UnsafeAtomics"]
git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be"
uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
version = "0.1.0"

[[deps.AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.1"

[[deps.AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "16351be62963a67ac4083f748fdb3cca58bfd52f"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.7"

[[deps.BangBang]]
deps = ["Compat", "ConstructionBase", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables"]
git-tree-sha1 = "7aa7ad1682f3d5754e3491bb59b8103cae28e3a3"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.40"

    [deps.BangBang.extensions]
    BangBangChainRulesCoreExt = "ChainRulesCore"
    BangBangDataFramesExt = "DataFrames"
    BangBangStaticArraysExt = "StaticArrays"
    BangBangStructArraysExt = "StructArrays"
    BangBangTypedTablesExt = "TypedTables"

    [deps.BangBang.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[deps.Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[deps.Bijectors]]
deps = ["ArgCheck", "ChainRules", "ChainRulesCore", "ChangesOfVariables", "Compat", "Distributions", "Functors", "InverseFunctions", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "MappedArrays", "Random", "Reexport", "Requires", "Roots", "SparseArrays", "Statistics"]
git-tree-sha1 = "199dc2c4151db557549a0ad8888ce1a60337ff42"
uuid = "76274a88-744f-5084-9051-94815aaf08c4"
version = "0.13.8"

    [deps.Bijectors.extensions]
    BijectorsDistributionsADExt = "DistributionsAD"
    BijectorsForwardDiffExt = "ForwardDiff"
    BijectorsLazyArraysExt = "LazyArrays"
    BijectorsReverseDiffExt = "ReverseDiff"
    BijectorsTrackerExt = "Tracker"
    BijectorsZygoteExt = "Zygote"

    [deps.Bijectors.weakdeps]
    DistributionsAD = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.BitFlags]]
git-tree-sha1 = "2dc09997850d68179b69dafb58ae806167a32b1b"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.8"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+1"

[[deps.CEnum]]
git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.5.0"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
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[[deps.Calculus]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
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[[deps.ChainRules]]
deps = ["Adapt", "ChainRulesCore", "Compat", "Distributed", "GPUArraysCore", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "SparseInverseSubset", "Statistics", "StructArrays", "SuiteSparse"]
git-tree-sha1 = "213f001d1233fd3b8ef007f50c8cab29061917d8"
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[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra"]
git-tree-sha1 = "ad25e7d21ce10e01de973cdc68ad0f850a953c52"
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weakdeps = ["SparseArrays"]

    [deps.ChainRulesCore.extensions]
    ChainRulesCoreSparseArraysExt = "SparseArrays"

[[deps.ChangesOfVariables]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "2fba81a302a7be671aefe194f0525ef231104e7f"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.8"
weakdeps = ["InverseFunctions"]

    [deps.ChangesOfVariables.extensions]
    ChangesOfVariablesInverseFunctionsExt = "InverseFunctions"

[[deps.Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "Random", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "9ebb045901e9bbf58767a9f34ff89831ed711aae"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.15.7"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "59939d8a997469ee05c4b4944560a820f9ba0d73"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.4"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "67c1f244b991cad9b0aa4b7540fb758c2488b129"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.24.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
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[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"
weakdeps = ["SpecialFunctions"]

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
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[[deps.Combinatorics]]
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version = "1.0.2"

[[deps.CommonSolve]]
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[[deps.CommonSubexpressions]]
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[[deps.Compat]]
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weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
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[[deps.CompositionsBase]]
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weakdeps = ["InverseFunctions"]

    [deps.CompositionsBase.extensions]
    CompositionsBaseInverseFunctionsExt = "InverseFunctions"

[[deps.ConcreteStructs]]
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[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
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[[deps.ConsoleProgressMonitor]]
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[[deps.ConstructionBase]]
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weakdeps = ["IntervalSets", "StaticArrays"]

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    ConstructionBaseStaticArraysExt = "StaticArrays"

[[deps.Contour]]
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[[deps.Crayons]]
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[[deps.DataAPI]]
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[[deps.DataStructures]]
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[[deps.Dates]]
deps = ["Printf"]
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[[deps.DefineSingletons]]
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[[deps.DelimitedFiles]]
deps = ["Mmap"]
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[[deps.DensityInterface]]
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[[deps.DiffResults]]
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version = "1.1.0"

[[deps.DiffRules]]
deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
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[[deps.Distances]]
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weakdeps = ["ChainRulesCore", "SparseArrays"]

    [deps.Distances.extensions]
    DistancesChainRulesCoreExt = "ChainRulesCore"
    DistancesSparseArraysExt = "SparseArrays"

[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
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## mixture-sampler-shared.jl
using Distributions, LinearAlgebra, AdvancedMH, AdvancedHMC, AbstractMCMC, MCMCTempering, ForwardDiff
using Setfield: Setfield
using LogDensityProblems: LogDensityProblems
using Random: Random

# Source: https://turinglang.org/MCMCTempering.jl/dev/getting-started/
# Make `AdvancedMH` compatible with `MCMCTempering`.
MCMCTempering.getparams_and_logprob(transition::AdvancedMH.Transition) = transition.params, transition.lp
function MCMCTempering.setparams_and_logprob!!(transition::AdvancedMH.Transition, params, lp)
    return AdvancedMH.Transition(params, lp)
end

# Make `AdvancedHMC` compatible with `MCMCTempering`.
# Provides a convenient way of "mutating" (read: reconstructing) types with different values
# for specified fields; see usage below.
function MCMCTempering.getparams_and_logprob(state::AdvancedHMC.HMCState)
    t = state.transition
    return t.z.θ, t.z.ℓπ.value
end
function MCMCTempering.setparams_and_logprob!!(model, state::AdvancedHMC.HMCState, params, logprob)
    # NOTE: Need to recompute the gradient because it might be used in the next integration step.
    hamiltonian = AdvancedHMC.Hamiltonian(state.metric, model)
    return Setfield.@set state.transition.z = AdvancedHMC.phasepoint(
        hamiltonian, params, state.transition.z.r;
        ℓκ=state.transition.z.ℓκ
    )
end

# For post-processing.
function MCMCTempering.getparams_and_logprob(t::AdvancedHMC.Transition)
    return t.z.θ, t.z.ℓπ.value
end

# Implement a `MixtureSampler`.
struct MixtureSampler{S,Ws} <: AbstractMCMC.AbstractSampler
    samplers::S
    weights::Ws
end

struct MixtureState{Ss,S}
    states::Ss
    current::S
end

# Initial step.
function AbstractMCMC.step(
    rng::Random.AbstractRNG,
    model::AbstractMCMC.LogDensityModel,
    sampler::MixtureSampler;
    kwargs...
)
    transition_and_state_initials = map(sampler.samplers) do s
        AbstractMCMC.step(rng, model, s; kwargs...)
    end

    # Sample a transition using the weights.
    idx = rand(rng, Categorical(sampler.weights))
    state_initial = MixtureState(map(last, transition_and_state_initials), last(transition_and_state_initials[idx]))
    transition_initial = first(transition_and_state_initials[idx])

    return transition_initial, state_initial
end

# Subsequent iterations.
function AbstractMCMC.step(
    rng::Random.AbstractRNG,
    model::AbstractMCMC.LogDensityModel,
    sampler::MixtureSampler,
    state::MixtureState;
    kwargs...
)
    # Sample the sampler using the weights.
    idx = rand(rng, Categorical(sampler.weights))
    sampler_inner = sampler.samplers[idx]

    # Update the state we're going to use from the current state.
    state_inner = state.states[idx]
    state_inner_updated = if state_inner === state.current
        state_inner
    else
        # Updates `state_inner` using `state.current`.
        MCMCTempering.state_from(model, state_inner, state.current)
    end

    # Step the inner sampler.
    transition_inner, state_inner_current = AbstractMCMC.step(rng, model, sampler_inner, state_inner_updated; kwargs...)

    state_new = Setfield.@set(state.states[idx] = state_inner_current)
    return transition_inner, Setfield.@set(state_new.current = state_inner_current)
end

## mixture-sampler-with-turing.jl
using LinearAlgebra
using Turing

# Include the implementation of `MixtureSampler` and the necessary sampling methods.
include("mixture-sampler-shared.jl")

# Model.
@model function demo()
    x ~ MixtureModel(
        MvNormal,
        [([-10], I), ([10], I)],  # parameters
        [0.5, 0.5]              # weights
    )
end

# HACK: This is a temporary workaround for the fact that `MixtureModel` doesn't have a `bijector` method.
function Bijectors.bijector(d::MixtureModel)
    # Only okay to do if all the components have the same bijector.
    b = bijector(first(components(d)))
    if any(!=(b) ∘ bijector, components(d))
        throw(ArgumentError("All components must have the same bijector."))
    end
    return b
end

# Instantiate the model.
model = demo()
# Convert into a `LogDensityFunction` so we can pass directly to AdvancedHMC.jl, etc.
target_model = DynamicPPL.LogDensityFunction(model);
# Link because we need to work in unconstrained space.
# For this particular model, it's not actually necessary, but in general it is.
# NOTE: This will cause the resulting parameters to be in unconstrained space, not the original space.
# But we can easily map this back after sampling.
DynamicPPL.link!!(target_model.varinfo, target_model.model);

# Now we're ready to sample.
num_iterations = 10_000
num_adapts = 1000
num_chains = 4

# First we run a few preliminary chains with HMC so we can determine relevant modes.
num_preliminary_iterations = 1000 # use fewer iterations for preliminary chains
sampler_preliminary = AdvancedHMC.NUTS(0.8)

chains_preliminary = sample(
    target_model,
    sampler_preliminary,
    MCMCSerial(),
    num_preliminary_iterations,
    num_chains;
    n_adapts=num_adapts
);
# Use means and variances of the chains to construct a proposal distribution.
means = map(chains_preliminary) do chain
    mean(MCMCTempering.getparams, chain)
end
variances = map(chains_preliminary) do chain
    var(map(MCMCTempering.getparams, chain))
end
proposal_components = map(means, variances) do μ, σ²
    MvNormal(μ, Diagonal(σ²))
end
# Mixture proposal of the HMC chains.
proposal = MixtureModel(proposal_components)

# Construct MH sampler which uses our specified proposal distribution.
proposal_mh = StaticProposal(proposal);
sampler_mh = MetropolisHastings(proposal_mh);

# Construct HMC sampler which we'll use for the "local" exploration.
sampler_hmc = AdvancedHMC.NUTS(0.8);

# Mixture sampler.
proposal_portion = 0.1  # this parameter might need some tweaking depending on the problem
sampler = MixtureSampler([sampler_mh, sampler_hmc], [proposal_portion, 1 - proposal_portion]);

# Sample.
chains = sample(
    target_model,
    sampler,
    MCMCSerial(),
    num_iterations,
    num_chains;
    4;
    n_adapts=num_adapts,
);
chain = reduce(vcat, chains);
mean(first ∘ MCMCTempering.getparams, chain)

using StatsPlots
plot(map(first ∘ MCMCTempering.getparams, chain), label="")
density(map(first ∘ MCMCTempering.getparams, chain), label="")

## mixuter-sampler.jl
# Include the implementation of `MixtureSampler` and the necessary sampling methods.
include("mixture-sampler-shared.jl")

# Define the target distribution.
target_distribution = MixtureModel(
    MvNormal,
    [([-10], I), ([10], I)],  # parameters
    [0.5, 0.5]              # weights
);

# Implement LogDensityProblems.jl-interface for `Distribution`.
struct DistributionLogDensity{D<:Distribution}
    d::D
end

LogDensityProblems.logdensity(d::DistributionLogDensity, x) = loglikelihood(d.d, x)
LogDensityProblems.dimension(d::DistributionLogDensity) = length(d.d)
LogDensityProblems.capabilities(::Type{<:DistributionLogDensity}) = LogDensityProblems.LogDensityOrder{0}()

# Wrap our target distribution.
target_model = DistributionLogDensity(target_distribution);

# Now we can sample!
# MH sampler.
proposal_mh = StaticProposal(target_distribution);  # we're cheating
sampler_mh = MetropolisHastings(proposal_mh);

# HMC sampler.
sampler_hmc = AdvancedHMC.HMC(1e-2, 32);

# Mixture sampler.
sampler = MixtureSampler([sampler_mh, sampler_hmc], [0.1, 0.9]);

# Sample.
chain = sample(target_model, sampler, 1000; n_adapts=0);
mean(first ∘ MCMCTempering.getparams, chain)

using StatsPlots
plot(map(first ∘ MCMCTempering.getparams, chain), label="")

## Project.toml
[deps]
AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
AdvancedHMC = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
AdvancedMH = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
LogDensityProblemsAD = "996a588d-648d-4e1f-a8f0-a84b347e47b1"
MCMCTempering = "ce233488-44ea-4441-b732-192676ce2298"
Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
	using Distributions, LinearAlgebra, AdvancedMH, AdvancedHMC, AbstractMCMC, MCMCTempering, ForwardDiff
	using Setfield: Setfield
	using LogDensityProblems: LogDensityProblems
	using Random: Random

	# Source: https://turinglang.org/MCMCTempering.jl/dev/getting-started/
	# Make `AdvancedMH` compatible with `MCMCTempering`.
	MCMCTempering.getparams_and_logprob(transition::AdvancedMH.Transition) = transition.params, transition.lp
	function MCMCTempering.setparams_and_logprob!!(transition::AdvancedMH.Transition, params, lp)
	return AdvancedMH.Transition(params, lp)
	end

	# Make `AdvancedHMC` compatible with `MCMCTempering`.
	# Provides a convenient way of "mutating" (read: reconstructing) types with different values
	# for specified fields; see usage below.
	function MCMCTempering.getparams_and_logprob(state::AdvancedHMC.HMCState)
	t = state.transition
	return t.z.θ, t.z.ℓπ.value
	end
	function MCMCTempering.setparams_and_logprob!!(model, state::AdvancedHMC.HMCState, params, logprob)
	# NOTE: Need to recompute the gradient because it might be used in the next integration step.
	hamiltonian = AdvancedHMC.Hamiltonian(state.metric, model)
	return Setfield.@set state.transition.z = AdvancedHMC.phasepoint(
	hamiltonian, params, state.transition.z.r;
	ℓκ=state.transition.z.ℓκ
	)
	end

	# For post-processing.
	function MCMCTempering.getparams_and_logprob(t::AdvancedHMC.Transition)
	return t.z.θ, t.z.ℓπ.value
	end

	# Implement a `MixtureSampler`.
	struct MixtureSampler{S,Ws} <: AbstractMCMC.AbstractSampler
	samplers::S
	weights::Ws
	end

	struct MixtureState{Ss,S}
	states::Ss
	current::S
	end

	# Initial step.
	function AbstractMCMC.step(
	rng::Random.AbstractRNG,
	model::AbstractMCMC.LogDensityModel,
	sampler::MixtureSampler;
	kwargs...
	)
	transition_and_state_initials = map(sampler.samplers) do s
	AbstractMCMC.step(rng, model, s; kwargs...)
	end

	# Sample a transition using the weights.
	idx = rand(rng, Categorical(sampler.weights))
	state_initial = MixtureState(map(last, transition_and_state_initials), last(transition_and_state_initials[idx]))
	transition_initial = first(transition_and_state_initials[idx])

	return transition_initial, state_initial
	end

	# Subsequent iterations.
	function AbstractMCMC.step(
	rng::Random.AbstractRNG,
	model::AbstractMCMC.LogDensityModel,
	sampler::MixtureSampler,
	state::MixtureState;
	kwargs...
	)
	# Sample the sampler using the weights.
	idx = rand(rng, Categorical(sampler.weights))
	sampler_inner = sampler.samplers[idx]

	# Update the state we're going to use from the current state.
	state_inner = state.states[idx]
	state_inner_updated = if state_inner === state.current
	state_inner
	else
	# Updates `state_inner` using `state.current`.
	MCMCTempering.state_from(model, state_inner, state.current)
	end

	# Step the inner sampler.
	transition_inner, state_inner_current = AbstractMCMC.step(rng, model, sampler_inner, state_inner_updated; kwargs...)

	state_new = Setfield.@set(state.states[idx] = state_inner_current)
	return transition_inner, Setfield.@set(state_new.current = state_inner_current)
	end
	using LinearAlgebra
	using Turing

	# Include the implementation of `MixtureSampler` and the necessary sampling methods.
	include("mixture-sampler-shared.jl")

	# Model.
	@model function demo()
	x ~ MixtureModel(
	MvNormal,
	[([-10], I), ([10], I)], # parameters
	[0.5, 0.5] # weights
	)
	end

	# HACK: This is a temporary workaround for the fact that `MixtureModel` doesn't have a `bijector` method.
	function Bijectors.bijector(d::MixtureModel)
	# Only okay to do if all the components have the same bijector.
	b = bijector(first(components(d)))
	if any(!=(b) ∘ bijector, components(d))
	throw(ArgumentError("All components must have the same bijector."))
	end
	return b
	end

	# Instantiate the model.
	model = demo()
	# Convert into a `LogDensityFunction` so we can pass directly to AdvancedHMC.jl, etc.
	target_model = DynamicPPL.LogDensityFunction(model);
	# Link because we need to work in unconstrained space.
	# For this particular model, it's not actually necessary, but in general it is.
	# NOTE: This will cause the resulting parameters to be in unconstrained space, not the original space.
	# But we can easily map this back after sampling.
	DynamicPPL.link!!(target_model.varinfo, target_model.model);

	# Now we're ready to sample.
	num_iterations = 10_000
	num_adapts = 1000
	num_chains = 4

	# First we run a few preliminary chains with HMC so we can determine relevant modes.
	num_preliminary_iterations = 1000 # use fewer iterations for preliminary chains
	sampler_preliminary = AdvancedHMC.NUTS(0.8)

	chains_preliminary = sample(
	target_model,
	sampler_preliminary,
	MCMCSerial(),
	num_preliminary_iterations,
	num_chains;
	n_adapts=num_adapts
	);
	# Use means and variances of the chains to construct a proposal distribution.
	means = map(chains_preliminary) do chain
	mean(MCMCTempering.getparams, chain)
	end
	variances = map(chains_preliminary) do chain
	var(map(MCMCTempering.getparams, chain))
	end
	proposal_components = map(means, variances) do μ, σ²
	MvNormal(μ, Diagonal(σ²))
	end
	# Mixture proposal of the HMC chains.
	proposal = MixtureModel(proposal_components)

	# Construct MH sampler which uses our specified proposal distribution.
	proposal_mh = StaticProposal(proposal);
	sampler_mh = MetropolisHastings(proposal_mh);

	# Construct HMC sampler which we'll use for the "local" exploration.
	sampler_hmc = AdvancedHMC.NUTS(0.8);

	# Mixture sampler.
	proposal_portion = 0.1 # this parameter might need some tweaking depending on the problem
	sampler = MixtureSampler([sampler_mh, sampler_hmc], [proposal_portion, 1 - proposal_portion]);

	# Sample.
	chains = sample(
	target_model,
	sampler,
	MCMCSerial(),
	num_iterations,
	num_chains;
	4;
	n_adapts=num_adapts,
	);
	chain = reduce(vcat, chains);
	mean(first ∘ MCMCTempering.getparams, chain)

	using StatsPlots
	plot(map(first ∘ MCMCTempering.getparams, chain), label="")
	density(map(first ∘ MCMCTempering.getparams, chain), label="")
	# Include the implementation of `MixtureSampler` and the necessary sampling methods.
	include("mixture-sampler-shared.jl")

	# Define the target distribution.
	target_distribution = MixtureModel(
	MvNormal,
	[([-10], I), ([10], I)], # parameters
	[0.5, 0.5] # weights
	);

	# Implement LogDensityProblems.jl-interface for `Distribution`.
	struct DistributionLogDensity{D<:Distribution}
	d::D
	end

	LogDensityProblems.logdensity(d::DistributionLogDensity, x) = loglikelihood(d.d, x)
	LogDensityProblems.dimension(d::DistributionLogDensity) = length(d.d)
	LogDensityProblems.capabilities(::Type{<:DistributionLogDensity}) = LogDensityProblems.LogDensityOrder{0}()

	# Wrap our target distribution.
	target_model = DistributionLogDensity(target_distribution);

	# Now we can sample!
	# MH sampler.
	proposal_mh = StaticProposal(target_distribution); # we're cheating
	sampler_mh = MetropolisHastings(proposal_mh);

	# HMC sampler.
	sampler_hmc = AdvancedHMC.HMC(1e-2, 32);

	# Mixture sampler.
	sampler = MixtureSampler([sampler_mh, sampler_hmc], [0.1, 0.9]);

	# Sample.
	chain = sample(target_model, sampler, 1000; n_adapts=0);
	mean(first ∘ MCMCTempering.getparams, chain)

	using StatsPlots
	plot(map(first ∘ MCMCTempering.getparams, chain), label="")
	[deps]
	AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
	AdvancedHMC = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
	AdvancedMH = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
	Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
	ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
	LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
	LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
	LogDensityProblemsAD = "996a588d-648d-4e1f-a8f0-a84b347e47b1"
	MCMCTempering = "ce233488-44ea-4441-b732-192676ce2298"
	Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
	StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
	Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"