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‎Project.toml

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‎README.md

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‎tutorials/01-gaussian-mixture-model/Manifest.toml

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[[deps.NNlib]]
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deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Pkg", "Random", "Requires", "Statistics"]
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git-tree-sha1 = "e0cea7ec219ada9ac80ec2e82e374ab2f154ae05"
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git-tree-sha1 = "3d4617f943afe6410206a5294a95948c8d1b35bd"
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uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
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version = "0.9.16"
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version = "0.9.17"
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[deps.NNlib.extensions]
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NNlibAMDGPUExt = "AMDGPU"
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[[deps.NamedArrays]]
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deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
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git-tree-sha1 = "0ae91efac93c3859f5c812a24c9468bb9e50b028"
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git-tree-sha1 = "c7aab3836df3f31591a2b4167fcd87b741dacfc9"
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uuid = "86f7a689-2022-50b4-a561-43c23ac3c673"
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version = "0.10.1"
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version = "0.10.2"
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[[deps.NaturalSort]]
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git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"

‎tutorials/01-gaussian-mixture-model/index.qmd

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```
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```{julia}
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#| output: false
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sampler = Gibbs(PG(100, :k), HMC(0.05, 10, :μ, :w))
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nsamples = 100
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nchains = 3
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chains = sample(model, sampler, MCMCThreads(), nsamples, nchains);
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```
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::: {.callout-warning collapse="true"}
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## Sampling With Multiple Threads
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The `sample()` call above assumes that you have at least `nchains` threads available in your Julia instance. If you do not, the multiple chains
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will run sequentially, and you may notice a warning. For more information, see [the Turing documentation on sampling multiple chains.](https://turinglang.org/dev/docs/using-turing/guide/#sampling-multiple-chains)
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:::
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```{julia}
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#| echo: false
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let

‎tutorials/05-linear-regression/Manifest.toml

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[[deps.LLVM]]
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deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"]
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git-tree-sha1 = "839c82932db86740ae729779e610f07a1640be9a"
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git-tree-sha1 = "065c36f95709dd4a676dc6839a35d6fa6f192f24"
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uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
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version = "6.6.3"
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version = "7.1.0"
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[deps.LLVM.extensions]
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BFloat16sExt = "BFloat16s"
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[[deps.NNlib]]
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deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Pkg", "Random", "Requires", "Statistics"]
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git-tree-sha1 = "e0cea7ec219ada9ac80ec2e82e374ab2f154ae05"
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git-tree-sha1 = "3d4617f943afe6410206a5294a95948c8d1b35bd"
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uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
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version = "0.9.16"
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version = "0.9.17"
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[deps.NNlib.extensions]
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NNlibAMDGPUExt = "AMDGPU"
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[[deps.NamedArrays]]
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deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
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git-tree-sha1 = "0ae91efac93c3859f5c812a24c9468bb9e50b028"
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git-tree-sha1 = "c7aab3836df3f31591a2b4167fcd87b741dacfc9"
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uuid = "86f7a689-2022-50b4-a561-43c23ac3c673"
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version = "0.10.1"
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version = "0.10.2"
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[[deps.NaturalSort]]
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git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"
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[[deps.SentinelArrays]]
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deps = ["Dates", "Random"]
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uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
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version = "1.4.2"
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version = "1.4.3"
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[[deps.Serialization]]
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uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
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deps = ["LLVM", "UnsafeAtomics"]
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git-tree-sha1 = "d9f5962fecd5ccece07db1ff006fb0b5271bdfdd"
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uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
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version = "0.1.3"
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version = "0.1.4"
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git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"

‎tutorials/05-linear-regression/index.qmd

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The next step is to get our data ready for testing. We'll split the `mtcars` dataset into two subsets, one for training our model and one for evaluating our model. Then, we separate the targets we want to learn (`MPG`, in this case) and standardize the datasets by subtracting each column's means and dividing by the standard deviation of that column. The resulting data is not very familiar looking, but this standardization process helps the sampler converge far easier.
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```{julia}
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# Remove the model column.
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select!(data, Not(:Model))
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With our model specified, we can call the sampler. We will use the No U-Turn Sampler ([NUTS](https://turinglang.org/stable/docs/library/#Turing.Inference.NUTS)) here.
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```{julia}
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model = linear_regression(train, train_target)
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chain = sample(model, NUTS(), 5_000)
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We can also check the densities and traces of the parameters visually using the `plot` functionality.
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```{julia}
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plot(chain)
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```
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It looks like all parameters have converged.
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```{julia}
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A satisfactory test of our model is to evaluate how well it predicts. Importantly, we want to compare our model to existing tools like OLS. The code below uses the [GLM.jl]() package to generate a traditional OLS multiple regression model on the same data as our probabilistic model.
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# Import the GLM package.
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using GLM
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The function below accepts a chain and an input matrix and calculates predictions. We use the samples of the model parameters in the chain starting with sample 200.
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where $y_i$ is the actual value (true MPG) and $\hat{y_i}$ is the predicted value using either OLS or Bayesian linear regression. A lower SSE indicates a closer fit to the data.
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"Training set:",
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"\n\tBayes loss: ",
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```
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‎tutorials/docs-16-using-turing-external-samplers/Manifest.toml

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git-tree-sha1 = "36c2a6c87b7fbb68b3be89d2ea07051aeb4f3690"
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git-tree-sha1 = "e05f95a8256fdf83632f4ea3742f7fb43038a100"
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uuid = "234d2aa0-2291-45f7-9047-6fa6f316b0a8"
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git-tree-sha1 = "e0cea7ec219ada9ac80ec2e82e374ab2f154ae05"
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git-tree-sha1 = "3d4617f943afe6410206a5294a95948c8d1b35bd"
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git-tree-sha1 = "0ae91efac93c3859f5c812a24c9468bb9e50b028"
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git-tree-sha1 = "c7aab3836df3f31591a2b4167fcd87b741dacfc9"
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‎tutorials/docs-16-using-turing-external-samplers/index.qmd

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Using this as well as other inference methods outside the Turing ecosystem is as simple as executing the code shown below:
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```{julia}
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# Create MCHMC sampler
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n_adapts = 1_000 # adaptation steps

‎weave_tutorials.jl

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