diff --git a/Project.toml b/Project.toml
index e6900f3f..cf9bc29f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,6 +11,7 @@ FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GPLikelihoods = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
+IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
@@ -26,6 +27,7 @@ FastGaussQuadrature = "0.4"
 FillArrays = "0.12"
 ForwardDiff = "0.10"
 GPLikelihoods = "0.1, 0.2"
+IrrationalConstants = "0.1"
 PDMats = "0.11"
 Reexport = "1"
 SpecialFunctions = "1, 2"
diff --git a/examples/a-regression/Manifest.toml b/examples/a-regression/Manifest.toml
index 8db5fb5c..003eb0fd 100644
--- a/examples/a-regression/Manifest.toml
+++ b/examples/a-regression/Manifest.toml
@@ -1,16 +1,16 @@
 # This file is machine-generated - editing it directly is not advised
 
 [[AbstractFFTs]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+deps = ["ChainRulesCore", "LinearAlgebra"]
+git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "1.0.1"
+version = "1.1.0"
 
 [[AbstractGPs]]
 deps = ["ChainRulesCore", "Distributions", "FillArrays", "IrrationalConstants", "KernelFunctions", "LinearAlgebra", "Random", "RecipesBase", "Reexport", "Statistics", "StatsBase", "Test"]
-git-tree-sha1 = "e2af18922f65ea8cee7b8cd97a1668691f76f4b2"
+git-tree-sha1 = "821d37c2f571ed5f2dfa028f03e324abd12f9910"
 uuid = "99985d1d-32ba-4be9-9821-2ec096f28918"
-version = "0.5.3"
+version = "0.5.4"
 
 [[AbstractTrees]]
 git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
@@ -19,24 +19,24 @@ version = "0.3.4"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "3.3.1"
+version = "3.3.3"
 
 [[ApproximateGPs]]
-deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
+deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "IrrationalConstants", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
 path = "../.."
 uuid = "298c2ebc-0411-48ad-af38-99e88101b606"
-version = "0.2.3"
+version = "0.2.6"
 
 [[ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
 [[ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "e527b258413e0c6d4f66ade574744c94edef81f8"
+git-tree-sha1 = "1ee88c4c76caa995a885dc2f22a5d548dfbbc0ba"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.40"
+version = "3.2.2"
 
 [[Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
@@ -63,9 +63,9 @@ version = "0.4.1"
 
 [[CUDA]]
 deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
-git-tree-sha1 = "2c8329f16addffd09e6ca84c556e2185a4933c64"
+git-tree-sha1 = "5bd05cd090588389201f7e1c703d50ace07be861"
 uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
-version = "3.5.0"
+version = "3.6.4"
 
 [[Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
@@ -75,15 +75,21 @@ version = "1.16.1+1"
 
 [[ChainRules]]
 deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "RealDot", "Statistics"]
-git-tree-sha1 = "035ef8a5382a614b2d8e3091b6fdbb1c2b050e11"
+git-tree-sha1 = "c6366ec79d9e62cd11030bba0945712eb4013712"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.12.1"
+version = "1.17.0"
 
 [[ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
+git-tree-sha1 = "926870acb6cbcf029396f2f2de030282b6bc1941"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.11.1"
+version = "1.11.4"
+
+[[ChangesOfVariables]]
+deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
+git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.2"
 
 [[CodecZlib]]
 deps = ["TranscodingStreams", "Zlib_jll"]
@@ -117,9 +123,9 @@ version = "0.3.0"
 
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
+git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.40.0"
+version = "3.41.0"
 
 [[CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -143,9 +149,9 @@ version = "1.9.0"
 
 [[DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
+git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.10"
+version = "0.18.11"
 
 [[DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
@@ -160,6 +166,12 @@ uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
+[[DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
 [[DiffResults]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
@@ -168,25 +180,25 @@ version = "1.0.3"
 
 [[DiffRules]]
 deps = ["LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "3287dacf67c3652d3fed09f4c12c187ae4dbb89a"
+git-tree-sha1 = "9bc5dac3c8b6706b58ad5ce24cffd9861f07c94f"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.4.0"
+version = "1.9.0"
 
 [[Distances]]
-deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "837c83e5574582e07662bbbba733964ff7c26b9d"
+deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.6"
+version = "0.10.7"
 
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[Distributions]]
-deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "72dcda9e19f88d09bf21b5f9507a0bb430bce2aa"
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "6a8dc9f82e5ce28279b6e3e2cea9421154f5bd0d"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.24"
+version = "0.25.37"
 
 [[DocStringExtensions]]
 deps = ["LibGit2"]
@@ -229,9 +241,9 @@ version = "4.4.0+0"
 
 [[FastGaussQuadrature]]
 deps = ["LinearAlgebra", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "5829b25887e53fb6730a9df2ff89ed24baa6abf6"
+git-tree-sha1 = "58d83dd5a78a36205bdfddb82b1bb67682e64487"
 uuid = "442a2c76-b920-505d-bb47-c5924d526838"
-version = "0.4.7"
+version = "0.4.9"
 
 [[FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
@@ -264,10 +276,10 @@ uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
 [[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "ef3fec65f9db26fa2cf8f4133c697c5b7ce63c1d"
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "2b72a5624e289ee18256111657663721d59c143e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.22"
+version = "0.10.24"
 
 [[FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
@@ -293,34 +305,34 @@ uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
 version = "3.3.5+1"
 
 [[GPLikelihoods]]
-deps = ["Distributions", "Functors", "LinearAlgebra", "Random", "StatsFuns"]
-git-tree-sha1 = "bdfe8a65b3ca3aa92812d74138264570f33aa66e"
+deps = ["Distributions", "Functors", "InverseFunctions", "LinearAlgebra", "Random", "StatsFuns", "Test"]
+git-tree-sha1 = "ca3cc4ca49bf8dcf3f6e92f2e2fec8bdd8e8359c"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
-version = "0.2.4"
+version = "0.2.6"
 
 [[GPUArrays]]
 deps = ["Adapt", "LinearAlgebra", "Printf", "Random", "Serialization", "Statistics"]
-git-tree-sha1 = "7772508f17f1d482fe0df72cabc5b55bec06bbe0"
+git-tree-sha1 = "d9681e61fbce7dde48684b40bdb1a319c4083be7"
 uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
-version = "8.1.2"
+version = "8.1.3"
 
 [[GPUCompiler]]
 deps = ["ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
-git-tree-sha1 = "77d915a0af27d474f0aaf12fcd46c400a552e84c"
+git-tree-sha1 = "2cac236070c2c4b36de54ae9146b55ee2c34ac7a"
 uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
-version = "0.13.7"
+version = "0.13.10"
 
 [[GR]]
 deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
-git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
+git-tree-sha1 = "b9a93bcdf34618031891ee56aad94cfff0843753"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.62.1"
+version = "0.63.0"
 
 [[GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
+git-tree-sha1 = "f97acd98255568c3c9b416c5a3cf246c1315771b"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.62.0+0"
+version = "0.63.0+0"
 
 [[GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
@@ -353,9 +365,9 @@ version = "1.0.2"
 
 [[HTTP]]
 deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
-git-tree-sha1 = "14eece7a3308b4d8be910e265c724a6ba51a9798"
+git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "0.9.16"
+version = "0.9.17"
 
 [[HarfBuzz_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
@@ -371,9 +383,9 @@ version = "0.2.2"
 
 [[IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
+git-tree-sha1 = "006127162a51f0effbdfaab5ac0c83f8eb7ea8f3"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.3"
+version = "0.4.4"
 
 [[IfElse]]
 git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
@@ -392,9 +404,9 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "f0c6489b12d28fb4c2103073ec7452f3423bd308"
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.1"
+version = "0.1.2"
 
 [[IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
@@ -402,9 +414,9 @@ uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.1.1"
 
 [[IterTools]]
-git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
-version = "1.3.0"
+version = "1.4.0"
 
 [[IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -455,15 +467,15 @@ version = "3.100.1+0"
 
 [[LLVM]]
 deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
-git-tree-sha1 = "46092047ca4edc10720ecab437c42283cd7c44f3"
+git-tree-sha1 = "f8dcd7adfda0dddaf944e62476d823164cccc217"
 uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
-version = "4.6.0"
+version = "4.7.1"
 
 [[LLVMExtra_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "6a2af408fe809c4f1a54d2b3f188fdd3698549d6"
+git-tree-sha1 = "62115afed394c016c2d3096c5b85c407b48be96b"
 uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
-version = "0.0.11+0"
+version = "0.0.13+1"
 
 [[LZO_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -564,10 +576,10 @@ uuid = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
 version = "2.9.4"
 
 [[LogExpFunctions]]
-deps = ["ChainRulesCore", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "6193c3815f13ba1b78a51ce391db8be016ae9214"
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.4"
+version = "0.3.6"
 
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -617,29 +629,29 @@ uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
 [[NNlib]]
 deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
-git-tree-sha1 = "5203a4532ad28c44f82c76634ad621d7c90abcbd"
+git-tree-sha1 = "afcfd88042cc5a62743c98ca311668ff5c03148a"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-version = "0.7.29"
+version = "0.7.32"
 
 [[NNlibCUDA]]
 deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
-git-tree-sha1 = "04490d5e7570c038b1cb0f5c3627597181cc15a9"
+git-tree-sha1 = "a2dc748c9f6615197b6b97c10bcce829830574c9"
 uuid = "a00861dc-f156-4864-bf3c-e6376f28a68d"
-version = "0.1.9"
+version = "0.1.11"
 
 [[NaNMath]]
-git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+git-tree-sha1 = "f755f36b19a5116bb580de457cda0c140153f283"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.5"
+version = "0.3.6"
 
 [[NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
 [[Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
-version = "1.3.5+0"
+version = "1.3.5+1"
 
 [[OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -647,9 +659,9 @@ uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
 [[OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
+git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "1.1.10+0"
+version = "1.1.13+0"
 
 [[OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
@@ -676,15 +688,15 @@ version = "8.44.0+0"
 
 [[PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "c8b8775b2f242c80ea85c83714c64ecfa3c53355"
+git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.3"
+version = "0.11.5"
 
 [[Parsers]]
 deps = ["Dates"]
-git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
+git-tree-sha1 = "d7fa6237da8004be601e19bd6666083056649918"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "2.1.2"
+version = "2.1.3"
 
 [[Pixman_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -704,21 +716,21 @@ version = "2.0.1"
 
 [[PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
-git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
+git-tree-sha1 = "68604313ed59f0408313228ba09e79252e4b2da8"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
-version = "1.0.15"
+version = "1.1.2"
 
 [[Plots]]
-deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
-git-tree-sha1 = "7dc03c2b145168f5854085a16d054429d612b637"
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
+git-tree-sha1 = "68e602f447344154f3b80f7d14bfb459a0f4dadf"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.23.5"
+version = "1.25.5"
 
 [[Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.2"
+version = "1.2.3"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -767,9 +779,9 @@ uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 version = "0.1.0"
 
 [[RecipesBase]]
-git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.2"
+version = "1.2.1"
 
 [[RecipesPipeline]]
 deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
@@ -784,9 +796,9 @@ version = "1.2.2"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+git-tree-sha1 = "8f82019e525f4d5c669692772a6f4b0a58b06a6a"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.1.3"
+version = "1.2.0"
 
 [[Rmath]]
 deps = ["Random", "Rmath_jll"]
@@ -843,36 +855,36 @@ version = "1.8.1"
 
 [[Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
+git-tree-sha1 = "7f5a513baec6f122401abfc8e9c074fdac54f6c1"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.4.0"
+version = "0.4.1"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
+git-tree-sha1 = "88a559da57529581472320892576a486fa2377b9"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.2.13"
+version = "1.3.1"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.2.0"
 
 [[StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
+git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.12"
+version = "0.33.14"
 
 [[StatsFuns]]
-deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.12"
+version = "0.9.14"
 
 [[StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
@@ -896,9 +908,9 @@ version = "1.0.1"
 
 [[Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
+git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.6.0"
+version = "1.6.1"
 
 [[Tar]]
 deps = ["ArgTools", "SHA"]
@@ -916,9 +928,9 @@ uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [[TimerOutputs]]
 deps = ["ExprTools", "Printf"]
-git-tree-sha1 = "7cb456f358e8f9d102a8b25e8dfedf58fa5689bc"
+git-tree-sha1 = "a5aed757f65c8a1c64503bc4035f704d24c749bf"
 uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
-version = "0.5.13"
+version = "0.5.14"
 
 [[TranscodingStreams]]
 deps = ["Random", "Test"]
@@ -944,6 +956,11 @@ git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"
 
+[[Unzip]]
+git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.1.2"
+
 [[Wayland_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
@@ -951,10 +968,10 @@ uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.19.0+0"
 
 [[Wayland_protocols_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
-git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.18.0+4"
+version = "1.23.0+0"
 
 [[XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
@@ -1112,9 +1129,9 @@ version = "1.5.0+0"
 
 [[Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "0fc9959bcabc4668c403810b4e851f6b8962eac9"
+git-tree-sha1 = "78da1a0a69bcc86b33f7cb07bc1566c926412de3"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.29"
+version = "0.6.33"
 
 [[ZygoteRules]]
 deps = ["MacroTools"]
diff --git a/examples/b-classification/Manifest.toml b/examples/b-classification/Manifest.toml
index 67972d0f..b05c2b14 100644
--- a/examples/b-classification/Manifest.toml
+++ b/examples/b-classification/Manifest.toml
@@ -1,37 +1,37 @@
 # This file is machine-generated - editing it directly is not advised
 
 [[AbstractFFTs]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+deps = ["ChainRulesCore", "LinearAlgebra"]
+git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "1.0.1"
+version = "1.1.0"
 
 [[AbstractGPs]]
 deps = ["ChainRulesCore", "Distributions", "FillArrays", "IrrationalConstants", "KernelFunctions", "LinearAlgebra", "Random", "RecipesBase", "Reexport", "Statistics", "StatsBase", "Test"]
-git-tree-sha1 = "e2af18922f65ea8cee7b8cd97a1668691f76f4b2"
+git-tree-sha1 = "821d37c2f571ed5f2dfa028f03e324abd12f9910"
 uuid = "99985d1d-32ba-4be9-9821-2ec096f28918"
-version = "0.5.3"
+version = "0.5.4"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "3.3.1"
+version = "3.3.3"
 
 [[ApproximateGPs]]
-deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
+deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "IrrationalConstants", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
 path = "../.."
 uuid = "298c2ebc-0411-48ad-af38-99e88101b606"
-version = "0.2.3"
+version = "0.2.6"
 
 [[ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
 [[ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "e527b258413e0c6d4f66ade574744c94edef81f8"
+git-tree-sha1 = "d0d82f1c0b651173a4f839d84f662d03f3417740"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.40"
+version = "4.0.0"
 
 [[Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
@@ -53,15 +53,21 @@ version = "1.16.1+1"
 
 [[ChainRules]]
 deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "RealDot", "Statistics"]
-git-tree-sha1 = "035ef8a5382a614b2d8e3091b6fdbb1c2b050e11"
+git-tree-sha1 = "c6366ec79d9e62cd11030bba0945712eb4013712"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.12.1"
+version = "1.17.0"
 
 [[ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
+git-tree-sha1 = "926870acb6cbcf029396f2f2de030282b6bc1941"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.11.1"
+version = "1.11.4"
+
+[[ChangesOfVariables]]
+deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
+git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.2"
 
 [[ColorSchemes]]
 deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
@@ -89,9 +95,9 @@ version = "0.3.0"
 
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
+git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.40.0"
+version = "3.41.0"
 
 [[CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -115,9 +121,9 @@ version = "1.9.0"
 
 [[DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
+git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.10"
+version = "0.18.11"
 
 [[DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
@@ -132,6 +138,12 @@ uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
+[[DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
 [[DiffResults]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
@@ -140,25 +152,25 @@ version = "1.0.3"
 
 [[DiffRules]]
 deps = ["LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "3287dacf67c3652d3fed09f4c12c187ae4dbb89a"
+git-tree-sha1 = "9bc5dac3c8b6706b58ad5ce24cffd9861f07c94f"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.4.0"
+version = "1.9.0"
 
 [[Distances]]
-deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "837c83e5574582e07662bbbba733964ff7c26b9d"
+deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.6"
+version = "0.10.7"
 
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[Distributions]]
-deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "72dcda9e19f88d09bf21b5f9507a0bb430bce2aa"
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "6a8dc9f82e5ce28279b6e3e2cea9421154f5bd0d"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.24"
+version = "0.25.37"
 
 [[DocStringExtensions]]
 deps = ["LibGit2"]
@@ -196,9 +208,9 @@ version = "4.4.0+0"
 
 [[FastGaussQuadrature]]
 deps = ["LinearAlgebra", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "5829b25887e53fb6730a9df2ff89ed24baa6abf6"
+git-tree-sha1 = "58d83dd5a78a36205bdfddb82b1bb67682e64487"
 uuid = "442a2c76-b920-505d-bb47-c5924d526838"
-version = "0.4.7"
+version = "0.4.9"
 
 [[FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
@@ -208,9 +220,9 @@ version = "0.12.7"
 
 [[FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
-git-tree-sha1 = "8b3c09b56acaf3c0e581c66638b85c8650ee9dca"
+git-tree-sha1 = "b374f22e8565a01d6e5db1e8640c3c5e3fe7d564"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.8.1"
+version = "2.9.0"
 
 [[FixedPointNumbers]]
 deps = ["Statistics"]
@@ -231,10 +243,10 @@ uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
 [[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "ef3fec65f9db26fa2cf8f4133c697c5b7ce63c1d"
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "2b72a5624e289ee18256111657663721d59c143e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.22"
+version = "0.10.24"
 
 [[FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
@@ -260,22 +272,22 @@ uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
 version = "3.3.5+1"
 
 [[GPLikelihoods]]
-deps = ["Distributions", "Functors", "LinearAlgebra", "Random", "StatsFuns"]
-git-tree-sha1 = "bdfe8a65b3ca3aa92812d74138264570f33aa66e"
+deps = ["Distributions", "Functors", "InverseFunctions", "LinearAlgebra", "Random", "StatsFuns", "Test"]
+git-tree-sha1 = "ca3cc4ca49bf8dcf3f6e92f2e2fec8bdd8e8359c"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
-version = "0.2.4"
+version = "0.2.6"
 
 [[GR]]
 deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
-git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
+git-tree-sha1 = "b9a93bcdf34618031891ee56aad94cfff0843753"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.62.1"
+version = "0.63.0"
 
 [[GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
+git-tree-sha1 = "f97acd98255568c3c9b416c5a3cf246c1315771b"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.62.0+0"
+version = "0.63.0+0"
 
 [[GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
@@ -308,9 +320,9 @@ version = "1.0.2"
 
 [[HTTP]]
 deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
-git-tree-sha1 = "14eece7a3308b4d8be910e265c724a6ba51a9798"
+git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "0.9.16"
+version = "0.9.17"
 
 [[HarfBuzz_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
@@ -326,9 +338,9 @@ version = "0.2.2"
 
 [[IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
+git-tree-sha1 = "006127162a51f0effbdfaab5ac0c83f8eb7ea8f3"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.3"
+version = "0.4.4"
 
 [[IfElse]]
 git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
@@ -347,9 +359,9 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "f0c6489b12d28fb4c2103073ec7452f3423bd308"
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.1"
+version = "0.1.2"
 
 [[IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
@@ -357,9 +369,9 @@ uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.1.1"
 
 [[IterTools]]
-git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
-version = "1.3.0"
+version = "1.4.0"
 
 [[IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -503,10 +515,10 @@ uuid = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
 version = "2.9.4"
 
 [[LogExpFunctions]]
-deps = ["ChainRulesCore", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "6193c3815f13ba1b78a51ce391db8be016ae9214"
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.4"
+version = "0.3.6"
 
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -555,18 +567,18 @@ uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
 version = "7.8.2"
 
 [[NaNMath]]
-git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+git-tree-sha1 = "f755f36b19a5116bb580de457cda0c140153f283"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.5"
+version = "0.3.6"
 
 [[NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
 [[Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
-version = "1.3.5+0"
+version = "1.3.5+1"
 
 [[OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -574,9 +586,9 @@ uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
 [[OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
+git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "1.1.10+0"
+version = "1.1.13+0"
 
 [[OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
@@ -586,9 +598,9 @@ version = "0.5.5+0"
 
 [[Optim]]
 deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
-git-tree-sha1 = "35d435b512fbab1d1a29138b5229279925eba369"
+git-tree-sha1 = "916077e0f0f8966eb0dc98a5c39921fdb8f49eb4"
 uuid = "429524aa-4258-5aef-a3af-852621145aeb"
-version = "1.5.0"
+version = "1.6.0"
 
 [[Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -609,15 +621,15 @@ version = "8.44.0+0"
 
 [[PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "c8b8775b2f242c80ea85c83714c64ecfa3c53355"
+git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.3"
+version = "0.11.5"
 
 [[ParameterHandling]]
 deps = ["ChainRulesCore", "Compat", "InverseFunctions", "IterTools", "LinearAlgebra", "LogExpFunctions", "SparseArrays", "Test"]
-git-tree-sha1 = "603fde842910e6d33bfce2ce7d0e0a0851d8e21e"
+git-tree-sha1 = "1e38f118bf4c0428b64f39a0722446f17e95f82a"
 uuid = "2412ca09-6db7-441c-8e3a-88d5709968c5"
-version = "0.4.0"
+version = "0.4.2"
 
 [[Parameters]]
 deps = ["OrderedCollections", "UnPack"]
@@ -627,9 +639,9 @@ version = "0.12.3"
 
 [[Parsers]]
 deps = ["Dates"]
-git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
+git-tree-sha1 = "d7fa6237da8004be601e19bd6666083056649918"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "2.1.2"
+version = "2.1.3"
 
 [[Pixman_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -649,15 +661,15 @@ version = "2.0.1"
 
 [[PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
-git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
+git-tree-sha1 = "68604313ed59f0408313228ba09e79252e4b2da8"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
-version = "1.0.15"
+version = "1.1.2"
 
 [[Plots]]
-deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
-git-tree-sha1 = "7dc03c2b145168f5854085a16d054429d612b637"
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
+git-tree-sha1 = "68e602f447344154f3b80f7d14bfb459a0f4dadf"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.23.5"
+version = "1.25.5"
 
 [[PositiveFactorizations]]
 deps = ["LinearAlgebra"]
@@ -667,9 +679,9 @@ version = "0.2.4"
 
 [[Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.2"
+version = "1.2.3"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -702,9 +714,9 @@ uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 version = "0.1.0"
 
 [[RecipesBase]]
-git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.2"
+version = "1.2.1"
 
 [[RecipesPipeline]]
 deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
@@ -719,9 +731,9 @@ version = "1.2.2"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+git-tree-sha1 = "8f82019e525f4d5c669692772a6f4b0a58b06a6a"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.1.3"
+version = "1.2.0"
 
 [[Rmath]]
 deps = ["Random", "Rmath_jll"]
@@ -778,36 +790,36 @@ version = "1.8.1"
 
 [[Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
+git-tree-sha1 = "b4912cd034cdf968e06ca5f943bb54b17b97793a"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.4.0"
+version = "0.5.1"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
+git-tree-sha1 = "88a559da57529581472320892576a486fa2377b9"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.2.13"
+version = "1.3.1"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.2.0"
 
 [[StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
+git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.12"
+version = "0.33.14"
 
 [[StatsFuns]]
-deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.12"
+version = "0.9.14"
 
 [[StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
@@ -831,9 +843,9 @@ version = "1.0.1"
 
 [[Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
+git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.6.0"
+version = "1.6.1"
 
 [[Tar]]
 deps = ["ArgTools", "SHA"]
@@ -872,6 +884,11 @@ git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"
 
+[[Unzip]]
+git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.1.2"
+
 [[Wayland_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
@@ -879,10 +896,10 @@ uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.19.0+0"
 
 [[Wayland_protocols_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
-git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.18.0+4"
+version = "1.23.0+0"
 
 [[XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
@@ -1034,9 +1051,9 @@ version = "1.5.0+0"
 
 [[Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "0fc9959bcabc4668c403810b4e851f6b8962eac9"
+git-tree-sha1 = "78da1a0a69bcc86b33f7cb07bc1566c926412de3"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.29"
+version = "0.6.33"
 
 [[ZygoteRules]]
 deps = ["MacroTools"]
diff --git a/examples/c-comparisons/Manifest.toml b/examples/c-comparisons/Manifest.toml
index de5d6de3..ee971d03 100644
--- a/examples/c-comparisons/Manifest.toml
+++ b/examples/c-comparisons/Manifest.toml
@@ -1,37 +1,37 @@
 # This file is machine-generated - editing it directly is not advised
 
 [[AbstractFFTs]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+deps = ["ChainRulesCore", "LinearAlgebra"]
+git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "1.0.1"
+version = "1.1.0"
 
 [[AbstractGPs]]
 deps = ["ChainRulesCore", "Distributions", "FillArrays", "IrrationalConstants", "KernelFunctions", "LinearAlgebra", "Random", "RecipesBase", "Reexport", "Statistics", "StatsBase", "Test"]
-git-tree-sha1 = "e2af18922f65ea8cee7b8cd97a1668691f76f4b2"
+git-tree-sha1 = "821d37c2f571ed5f2dfa028f03e324abd12f9910"
 uuid = "99985d1d-32ba-4be9-9821-2ec096f28918"
-version = "0.5.3"
+version = "0.5.4"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "3.3.1"
+version = "3.3.3"
 
 [[ApproximateGPs]]
-deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
+deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "IrrationalConstants", "KLDivergences", "LinearAlgebra", "PDMats", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
 path = "../.."
 uuid = "298c2ebc-0411-48ad-af38-99e88101b606"
-version = "0.2.3"
+version = "0.2.6"
 
 [[ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
 [[ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "e527b258413e0c6d4f66ade574744c94edef81f8"
+git-tree-sha1 = "d0d82f1c0b651173a4f839d84f662d03f3417740"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.40"
+version = "4.0.0"
 
 [[Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
@@ -53,15 +53,21 @@ version = "1.16.1+1"
 
 [[ChainRules]]
 deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "RealDot", "Statistics"]
-git-tree-sha1 = "035ef8a5382a614b2d8e3091b6fdbb1c2b050e11"
+git-tree-sha1 = "c6366ec79d9e62cd11030bba0945712eb4013712"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.12.1"
+version = "1.17.0"
 
 [[ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
+git-tree-sha1 = "926870acb6cbcf029396f2f2de030282b6bc1941"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.11.1"
+version = "1.11.4"
+
+[[ChangesOfVariables]]
+deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
+git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.2"
 
 [[ColorSchemes]]
 deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
@@ -89,9 +95,9 @@ version = "0.3.0"
 
 [[Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
+git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.40.0"
+version = "3.41.0"
 
 [[CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -115,9 +121,9 @@ version = "1.9.0"
 
 [[DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
+git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.10"
+version = "0.18.11"
 
 [[DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
@@ -132,6 +138,12 @@ uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
+[[DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
 [[DiffResults]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
@@ -140,25 +152,25 @@ version = "1.0.3"
 
 [[DiffRules]]
 deps = ["LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "3287dacf67c3652d3fed09f4c12c187ae4dbb89a"
+git-tree-sha1 = "9bc5dac3c8b6706b58ad5ce24cffd9861f07c94f"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.4.0"
+version = "1.9.0"
 
 [[Distances]]
-deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "837c83e5574582e07662bbbba733964ff7c26b9d"
+deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.6"
+version = "0.10.7"
 
 [[Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[Distributions]]
-deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "72dcda9e19f88d09bf21b5f9507a0bb430bce2aa"
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "6a8dc9f82e5ce28279b6e3e2cea9421154f5bd0d"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.24"
+version = "0.25.37"
 
 [[DocStringExtensions]]
 deps = ["LibGit2"]
@@ -196,9 +208,9 @@ version = "4.4.0+0"
 
 [[FastGaussQuadrature]]
 deps = ["LinearAlgebra", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "5829b25887e53fb6730a9df2ff89ed24baa6abf6"
+git-tree-sha1 = "58d83dd5a78a36205bdfddb82b1bb67682e64487"
 uuid = "442a2c76-b920-505d-bb47-c5924d526838"
-version = "0.4.7"
+version = "0.4.9"
 
 [[FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
@@ -208,9 +220,9 @@ version = "0.12.7"
 
 [[FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
-git-tree-sha1 = "8b3c09b56acaf3c0e581c66638b85c8650ee9dca"
+git-tree-sha1 = "b374f22e8565a01d6e5db1e8640c3c5e3fe7d564"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
-version = "2.8.1"
+version = "2.9.0"
 
 [[FixedPointNumbers]]
 deps = ["Statistics"]
@@ -231,10 +243,10 @@ uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
 [[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "ef3fec65f9db26fa2cf8f4133c697c5b7ce63c1d"
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "2b72a5624e289ee18256111657663721d59c143e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.22"
+version = "0.10.24"
 
 [[FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
@@ -260,22 +272,22 @@ uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
 version = "3.3.5+1"
 
 [[GPLikelihoods]]
-deps = ["Distributions", "Functors", "LinearAlgebra", "Random", "StatsFuns"]
-git-tree-sha1 = "bdfe8a65b3ca3aa92812d74138264570f33aa66e"
+deps = ["Distributions", "Functors", "InverseFunctions", "LinearAlgebra", "Random", "StatsFuns", "Test"]
+git-tree-sha1 = "ca3cc4ca49bf8dcf3f6e92f2e2fec8bdd8e8359c"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
-version = "0.2.4"
+version = "0.2.6"
 
 [[GR]]
 deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
-git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
+git-tree-sha1 = "b9a93bcdf34618031891ee56aad94cfff0843753"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
-version = "0.62.1"
+version = "0.63.0"
 
 [[GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
-git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
+git-tree-sha1 = "f97acd98255568c3c9b416c5a3cf246c1315771b"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
-version = "0.62.0+0"
+version = "0.63.0+0"
 
 [[GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
@@ -308,9 +320,9 @@ version = "1.0.2"
 
 [[HTTP]]
 deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
-git-tree-sha1 = "14eece7a3308b4d8be910e265c724a6ba51a9798"
+git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "0.9.16"
+version = "0.9.17"
 
 [[HarfBuzz_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
@@ -326,9 +338,9 @@ version = "0.2.2"
 
 [[IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
+git-tree-sha1 = "006127162a51f0effbdfaab5ac0c83f8eb7ea8f3"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.3"
+version = "0.4.4"
 
 [[IfElse]]
 git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
@@ -347,9 +359,9 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "f0c6489b12d28fb4c2103073ec7452f3423bd308"
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.1"
+version = "0.1.2"
 
 [[IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
@@ -357,9 +369,9 @@ uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.1.1"
 
 [[IterTools]]
-git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
-version = "1.3.0"
+version = "1.4.0"
 
 [[IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -503,10 +515,10 @@ uuid = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
 version = "2.9.4"
 
 [[LogExpFunctions]]
-deps = ["ChainRulesCore", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "6193c3815f13ba1b78a51ce391db8be016ae9214"
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.4"
+version = "0.3.6"
 
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -555,18 +567,18 @@ uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
 version = "7.8.2"
 
 [[NaNMath]]
-git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+git-tree-sha1 = "f755f36b19a5116bb580de457cda0c140153f283"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.5"
+version = "0.3.6"
 
 [[NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
 [[Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
-version = "1.3.5+0"
+version = "1.3.5+1"
 
 [[OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -574,9 +586,9 @@ uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
 [[OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
+git-tree-sha1 = "648107615c15d4e09f7eca16307bc821c1f718d8"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
-version = "1.1.10+0"
+version = "1.1.13+0"
 
 [[OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
@@ -586,9 +598,9 @@ version = "0.5.5+0"
 
 [[Optim]]
 deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
-git-tree-sha1 = "35d435b512fbab1d1a29138b5229279925eba369"
+git-tree-sha1 = "916077e0f0f8966eb0dc98a5c39921fdb8f49eb4"
 uuid = "429524aa-4258-5aef-a3af-852621145aeb"
-version = "1.5.0"
+version = "1.6.0"
 
 [[Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -609,9 +621,9 @@ version = "8.44.0+0"
 
 [[PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "c8b8775b2f242c80ea85c83714c64ecfa3c53355"
+git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.3"
+version = "0.11.5"
 
 [[Parameters]]
 deps = ["OrderedCollections", "UnPack"]
@@ -621,9 +633,9 @@ version = "0.12.3"
 
 [[Parsers]]
 deps = ["Dates"]
-git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
+git-tree-sha1 = "d7fa6237da8004be601e19bd6666083056649918"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
-version = "2.1.2"
+version = "2.1.3"
 
 [[Pixman_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -643,15 +655,15 @@ version = "2.0.1"
 
 [[PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
-git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
+git-tree-sha1 = "68604313ed59f0408313228ba09e79252e4b2da8"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
-version = "1.0.15"
+version = "1.1.2"
 
 [[Plots]]
-deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
-git-tree-sha1 = "7dc03c2b145168f5854085a16d054429d612b637"
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "Unzip"]
+git-tree-sha1 = "68e602f447344154f3b80f7d14bfb459a0f4dadf"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.23.5"
+version = "1.25.5"
 
 [[PositiveFactorizations]]
 deps = ["LinearAlgebra"]
@@ -661,9 +673,9 @@ version = "0.2.4"
 
 [[Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.2"
+version = "1.2.3"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -696,9 +708,9 @@ uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 version = "0.1.0"
 
 [[RecipesBase]]
-git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.2"
+version = "1.2.1"
 
 [[RecipesPipeline]]
 deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
@@ -713,9 +725,9 @@ version = "1.2.2"
 
 [[Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+git-tree-sha1 = "8f82019e525f4d5c669692772a6f4b0a58b06a6a"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.1.3"
+version = "1.2.0"
 
 [[Rmath]]
 deps = ["Random", "Rmath_jll"]
@@ -772,36 +784,36 @@ version = "1.8.1"
 
 [[Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
+git-tree-sha1 = "b4912cd034cdf968e06ca5f943bb54b17b97793a"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.4.0"
+version = "0.5.1"
 
 [[StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
-git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
+git-tree-sha1 = "88a559da57529581472320892576a486fa2377b9"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.2.13"
+version = "1.3.1"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.2.0"
 
 [[StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
+git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.12"
+version = "0.33.14"
 
 [[StatsFuns]]
-deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.12"
+version = "0.9.14"
 
 [[StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
@@ -825,9 +837,9 @@ version = "1.0.1"
 
 [[Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
+git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.6.0"
+version = "1.6.1"
 
 [[Tar]]
 deps = ["ArgTools", "SHA"]
@@ -866,6 +878,11 @@ git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"
 
+[[Unzip]]
+git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.1.2"
+
 [[Wayland_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
@@ -873,10 +890,10 @@ uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.19.0+0"
 
 [[Wayland_protocols_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
-git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.18.0+4"
+version = "1.23.0+0"
 
 [[XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
@@ -1028,9 +1045,9 @@ version = "1.5.0+0"
 
 [[Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "0fc9959bcabc4668c403810b4e851f6b8962eac9"
+git-tree-sha1 = "78da1a0a69bcc86b33f7cb07bc1566c926412de3"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.29"
+version = "0.6.33"
 
 [[ZygoteRules]]
 deps = ["MacroTools"]
diff --git a/src/ApproximateGPs.jl b/src/ApproximateGPs.jl
index ce26b625..20f46acf 100644
--- a/src/ApproximateGPs.jl
+++ b/src/ApproximateGPs.jl
@@ -12,6 +12,7 @@ using SpecialFunctions
 using ChainRulesCore
 using FillArrays
 using PDMats: chol_lower
+using IrrationalConstants: sqrt2, invsqrtπ
 
 using AbstractGPs: AbstractGP, FiniteGP, LatentFiniteGP, ApproxPosteriorGP, At_A, diag_At_A
 
diff --git a/src/expected_loglik.jl b/src/expected_loglik.jl
index c29ff3bb..cdc9f443 100644
--- a/src/expected_loglik.jl
+++ b/src/expected_loglik.jl
@@ -65,6 +65,7 @@ function expected_loglik(
     return sum(lls) / mc.n_samples
 end
 
+# Compute the expected_loglik over a collection of observations and marginal distributions
 function expected_loglik(
     gh::GaussHermite, y::AbstractVector, q_f::AbstractVector{<:Normal}, lik
 )
@@ -72,10 +73,27 @@ function expected_loglik(
     # using a reparameterisation by change of variable
     # (see e.g. en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature)
     xs, ws = gausshermite(gh.n_points)
-    # size(fs): (length(y), n_points)
-    fs = √2 * std.(q_f) .* xs' .+ mean.(q_f)
-    lls = loglikelihood.(lik.(fs), y)
-    return sum((1 / √π) * lls * ws)
+    return sum(Broadcast.instantiate(
+        Broadcast.broadcasted(y, q_f) do yᵢ, q_fᵢ  # Loop over every pair
+            # of marginal distribution q(fᵢ) and observation yᵢ
+            expected_loglik(gh, yᵢ, q_fᵢ, lik, (xs, ws))
+        end,
+    ))
+end
+
+# Compute the expected_loglik for one observation and a marginal distributions
+function expected_loglik(
+    gh::GaussHermite, y, q_f::Normal, lik, (xs, ws)=gausshermite(gh.n_points)
+)
+    μ = mean(q_f)
+    σ̃ = sqrt2 * std(q_f)
+    return invsqrtπ * sum(Broadcast.instantiate(
+        Broadcast.broadcasted(xs, ws) do x, w # Loop over every
+            # pair of Gauss-Hermite point x with weight w
+            f = σ̃ * x + μ
+            loglikelihood(lik(f), y) * w
+        end,
+    ))
 end
 
 ChainRulesCore.@non_differentiable gausshermite(n)
diff --git a/test/expected_loglik.jl b/test/expected_loglik.jl
index 715a595e..b8c34124 100644
--- a/test/expected_loglik.jl
+++ b/test/expected_loglik.jl
@@ -45,4 +45,43 @@
         GaussHermite(), zeros(10), q_f, GaussianLikelihood()
     ) isa Real
     @test ApproximateGPs._default_quadrature(θ -> Normal(0, θ)) isa GaussHermite
+
+    @testset "testing Zygote compatibility with GaussHermite" begin # see issue #82
+        N = 10
+        gh = GaussHermite(12)
+        μs = randn(rng, N)
+        σs = rand(rng, N)
+        # Test differentiation with variational parameters
+        for lik in likelihoods_to_test
+            y = rand.(rng, lik.(rand.(Normal.(μs, σs))))
+            gμ, glogσ = Zygote.gradient(μs, log.(σs)) do μ, logσ
+                ApproximateGPs.expected_loglik(gh, y, Normal.(μ, exp.(logσ)), lik)
+            end
+            @test all(isfinite, gμ)
+            @test all(isfinite, glogσ)
+        end
+        # Test differentiation with likelihood parameters
+        # Test GaussianLikelihood parameter
+        σ = 1.0
+        y = randn(rng, N)
+        glogσ = only(
+            Zygote.gradient(log(σ)) do x
+                ApproximateGPs.expected_loglik(
+                    gh, y, Normal.(μs, σs), GaussianLikelihood(exp(x))
+                )
+            end,
+        )
+        @test isfinite(glogσ)
+        # Test GammaLikelihood parameter
+        α = 2.0
+        y = rand.(rng, Gamma.(α, rand(N)))
+        glogα = only(
+            Zygote.gradient(log(α)) do x
+                ApproximateGPs.expected_loglik(
+                    gh, y, Normal.(μs, σs), GammaLikelihood(exp(x))
+                )
+            end,
+        )
+        @test isfinite(glogα)
+    end
 end