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@@ -583,7 +583,7 @@
     "href": "tutorials/16-contexts/index.html#contexts-within-contexts",
     "title": "A Mini Turing Implementation II: Contexts",
     "section": "Contexts within contexts",
-    "text": "Contexts within contexts\nLet’s use the above two contexts to provide a slightly more general definition of the SamplingContext and the Metropolis-Hastings sampler we wrote in the mini Turing tutorial.\n\nstruct SamplingContext{S<:AbstractMCMC.AbstractSampler,R<:Random.AbstractRNG}\n    rng::R\n    sampler::S\n    subcontext::Union{PriorContext, JointContext}\nend\n\nThe new aspect here is the subcontext field. Note that this is a context within a context! The idea is that we don’t need to hard code how the MCMC sampler evaluates the log probability, but rather can pass that work onto the subcontext. This way the same sampler can be used to sample from either the joint or the prior distribution.\nThe methods for SamplingContext are largely as in the our earlier mini Turing case, except they now pass some of the work onto the subcontext:\n\nfunction observe(context::SamplingContext, args...)\n    # Sampling doesn't affect the observed values, so nothing to do here other than pass to\n    # the subcontext.\n    return observe(context.subcontext, args...)\nend\n\nstruct PriorSampler <: AbstractMCMC.AbstractSampler end\n\nfunction assume(context::SamplingContext{PriorSampler}, varinfo, dist, var_id)\n    sample = Random.rand(context.rng, dist)\n    varinfo[var_id] = (sample, NaN)\n    # Once the value has been sampled, let the subcontext handle evaluating the log\n    # probability.\n    return assume(context.subcontext, varinfo, dist, var_id)\nend;\n\n# The subcontext field of the MHSampler determines which distribution this sampler\n# samples from.\nstruct MHSampler{D, T<:Real} <: AbstractMCMC.AbstractSampler\n    sigma::T\n    subcontext::D\nend\n\nMHSampler(subcontext) = MHSampler(1, subcontext)\n\nfunction assume(context::SamplingContext{<:MHSampler}, varinfo, dist, var_id)\n    sampler = context.sampler\n    old_value = varinfo.values[var_id]\n\n    # propose a random-walk step, i.e, add the current value to a random \n    # value sampled from a Normal distribution centered at 0\n    value = rand(context.rng, Normal(old_value, sampler.sigma))\n    varinfo[var_id] = (value, NaN)\n    # Once the value has been sampled, let the subcontext handle evaluating the log\n    # probability.\n    return assume(context.subcontext, varinfo, dist, var_id)\nend;\n\n# The following three methods are identical to before, except for passing\n# `sampler.subcontext` to the context SamplingContext.\nfunction AbstractMCMC.step(\n    rng::Random.AbstractRNG, model::MiniModel, sampler::MHSampler; kwargs...\n)\n    vi = VarInfo()\n    ctx = SamplingContext(rng, PriorSampler(), sampler.subcontext)\n    model.f(vi, ctx, values(model.data)...)\n    return vi, vi\nend\n\nfunction AbstractMCMC.step(\n    rng::Random.AbstractRNG,\n    model::MiniModel,\n    sampler::MHSampler,\n    prev_state::VarInfo; # is just the old trace\n    kwargs...,\n)\n    vi = prev_state\n    new_vi = deepcopy(vi)\n    ctx = SamplingContext(rng, sampler, sampler.subcontext)\n    model.f(new_vi, ctx, values(model.data)...)\n\n    # Compute log acceptance probability\n    # Since the proposal is symmetric the computation can be simplified\n    logα = sum(values(new_vi.logps)) - sum(values(vi.logps))\n\n    # Accept proposal with computed acceptance probability\n    if -Random.randexp(rng) < logα\n        return new_vi, new_vi\n    else\n        return prev_state, prev_state\n    end\nend;\n\nfunction AbstractMCMC.bundle_samples(\n    samples, model::MiniModel, ::MHSampler, ::Any, ::Type{Chains}; kwargs...\n)\n    # We get a vector of traces\n    values = [sample.values for sample in samples]\n    params = [key for key in keys(values[1]) if key ∉ keys(model.data)]\n    vals = reduce(hcat, [value[p] for value in values] for p in params)\n    # Composing the `Chains` data-structure, of which analyzing infrastructure is provided\n    chains = Chains(vals, params)\n    return chains\nend;\n\nWe can use this to sample from the joint distribution just like before:\n\nsample(MiniModel(m, (x=3.0,)), MHSampler(JointContext()), 1_000_000; chain_type=Chains, progress=false)\n\nChains MCMC chain (1000000×2×1 Array{Float64, 3}):\n\nIterations        = 1:1:1000000\nNumber of chains  = 1\nSamples per chain = 1000000\nparameters        = a, b\n\nSummary Statistics\n  parameters      mean       std      mcse      ess_bulk      ess_tail      rh ⋯\n      Symbol   Float64   Float64   Float64       Float64       Float64   Float ⋯\n\n           a    0.9756    0.9002    0.0031    81938.3955   120104.0916    1.00 ⋯\n           b    2.8807    0.4872    0.0012   170261.0295   212854.8961    1.00 ⋯\n                                                               2 columns omitted\n\nQuantiles\n  parameters      2.5%     25.0%     50.0%     75.0%     97.5%\n      Symbol   Float64   Float64   Float64   Float64   Float64\n\n           a   -0.7930    0.3689    0.9760    1.5845    2.7403\n           b    1.9278    2.5519    2.8801    3.2088    3.8362\n\n\nor we can choose to sample from the prior instead\n\nsample(MiniModel(m, (x=3.0,)), MHSampler(PriorContext()), 1_000_000; chain_type=Chains, progress=false)\n\nChains MCMC chain (1000000×2×1 Array{Float64, 3}):\n\nIterations        = 1:1:1000000\nNumber of chains  = 1\nSamples per chain = 1000000\nparameters        = a, b\n\nSummary Statistics\n  parameters      mean       std      mcse     ess_bulk      ess_tail      rha ⋯\n      Symbol   Float64   Float64   Float64      Float64       Float64   Float6 ⋯\n\n           a    0.4968    0.9976    0.0040   63599.5342   127012.8951    1.000 ⋯\n           b    0.4965    2.2315    0.0137   26513.8959    50948.6364    1.000 ⋯\n                                                               2 columns omitted\n\nQuantiles\n  parameters      2.5%     25.0%     50.0%     75.0%     97.5%\n      Symbol   Float64   Float64   Float64   Float64   Float64\n\n           a   -1.4610   -0.1750    0.4960    1.1698    2.4493\n           b   -3.8737   -1.0094    0.4960    2.0009    4.8792\n\n\nOf course, using an MCMC algorithm to sample from the prior is unnecessary and silly (PriorSampler exists, after all), but the point is to illustrate the flexibility of the context system. We could, for instance, use the same setup to implement an Approximate Bayesian Computation (ABC) algorithm.\nThe use of contexts also goes far beyond just evaluating log probabilities and sampling. Some examples from Turing are\n\nFixedContext, which fixes some variables to given values and removes them completely from the evaluation of any log probabilities. They power the Turing.fix and Turing.unfix functions.\nConditionContext conditions the model on fixed values for some parameters. They are used by Turing.condition and Turing.uncondition, i.e. the model | (parameter=value,) syntax. The difference between fix and condition is whether the log probability for the corresponding variable is included in the overall log density.\nPriorExtractorContext collects information about what the prior distribution of each variable is.\nPrefixContext adds prefixes to variable names, allowing models to be used within other models without variable name collisions.\nPointwiseLikelihoodContext records the log likelihood of each individual variable.\nDebugContext collects useful debugging information while executing the model.\n\nAll of the above are what Turing calls parent contexts, which is to say that they all keep a subcontext just like our above SamplingContext did. Their implementations of assume and observe call the implementation of the subcontext once they are done doing their own work of fixing/conditioning/prefixing/etc. Contexts are often chained, so that e.g. a DebugContext may wrap within it a PrefixContext, which may in turn wrap a ConditionContext, etc. The only contexts that don’t have a subcontext in the Turing are the ones for evaluating the prior, likelihood, and joint distributions. These are called leaf contexts.\nThe above version of mini Turing is still much simpler than the full Turing language, but the principles of how contexts are used are the same.",
+    "text": "Contexts within contexts\nLet’s use the above two contexts to provide a slightly more general definition of the SamplingContext and the Metropolis-Hastings sampler we wrote in the mini Turing tutorial.\n\nstruct SamplingContext{S<:AbstractMCMC.AbstractSampler,R<:Random.AbstractRNG}\n    rng::R\n    sampler::S\n    subcontext::Union{PriorContext, JointContext}\nend\n\nThe new aspect here is the subcontext field. Note that this is a context within a context! The idea is that we don’t need to hard code how the MCMC sampler evaluates the log probability, but rather can pass that work onto the subcontext. This way the same sampler can be used to sample from either the joint or the prior distribution.\nThe methods for SamplingContext are largely as in the our earlier mini Turing case, except they now pass some of the work onto the subcontext:\n\nfunction observe(context::SamplingContext, args...)\n    # Sampling doesn't affect the observed values, so nothing to do here other than pass to\n    # the subcontext.\n    return observe(context.subcontext, args...)\nend\n\nstruct PriorSampler <: AbstractMCMC.AbstractSampler end\n\nfunction assume(context::SamplingContext{PriorSampler}, varinfo, dist, var_id)\n    sample = Random.rand(context.rng, dist)\n    varinfo[var_id] = (sample, NaN)\n    # Once the value has been sampled, let the subcontext handle evaluating the log\n    # probability.\n    return assume(context.subcontext, varinfo, dist, var_id)\nend;\n\n# The subcontext field of the MHSampler determines which distribution this sampler\n# samples from.\nstruct MHSampler{D, T<:Real} <: AbstractMCMC.AbstractSampler\n    sigma::T\n    subcontext::D\nend\n\nMHSampler(subcontext) = MHSampler(1, subcontext)\n\nfunction assume(context::SamplingContext{<:MHSampler}, varinfo, dist, var_id)\n    sampler = context.sampler\n    old_value = varinfo.values[var_id]\n\n    # propose a random-walk step, i.e, add the current value to a random \n    # value sampled from a Normal distribution centered at 0\n    value = rand(context.rng, Normal(old_value, sampler.sigma))\n    varinfo[var_id] = (value, NaN)\n    # Once the value has been sampled, let the subcontext handle evaluating the log\n    # probability.\n    return assume(context.subcontext, varinfo, dist, var_id)\nend;\n\n# The following three methods are identical to before, except for passing\n# `sampler.subcontext` to the context SamplingContext.\nfunction AbstractMCMC.step(\n    rng::Random.AbstractRNG, model::MiniModel, sampler::MHSampler; kwargs...\n)\n    vi = VarInfo()\n    ctx = SamplingContext(rng, PriorSampler(), sampler.subcontext)\n    model.f(vi, ctx, values(model.data)...)\n    return vi, vi\nend\n\nfunction AbstractMCMC.step(\n    rng::Random.AbstractRNG,\n    model::MiniModel,\n    sampler::MHSampler,\n    prev_state::VarInfo; # is just the old trace\n    kwargs...,\n)\n    vi = prev_state\n    new_vi = deepcopy(vi)\n    ctx = SamplingContext(rng, sampler, sampler.subcontext)\n    model.f(new_vi, ctx, values(model.data)...)\n\n    # Compute log acceptance probability\n    # Since the proposal is symmetric the computation can be simplified\n    logα = sum(values(new_vi.logps)) - sum(values(vi.logps))\n\n    # Accept proposal with computed acceptance probability\n    if -Random.randexp(rng) < logα\n        return new_vi, new_vi\n    else\n        return prev_state, prev_state\n    end\nend;\n\nfunction AbstractMCMC.bundle_samples(\n    samples, model::MiniModel, ::MHSampler, ::Any, ::Type{Chains}; kwargs...\n)\n    # We get a vector of traces\n    values = [sample.values for sample in samples]\n    params = [key for key in keys(values[1]) if key ∉ keys(model.data)]\n    vals = reduce(hcat, [value[p] for value in values] for p in params)\n    # Composing the `Chains` data-structure, of which analyzing infrastructure is provided\n    chains = Chains(vals, params)\n    return chains\nend;\n\nWe can use this to sample from the joint distribution just like before:\n\nsample(MiniModel(m, (x=3.0,)), MHSampler(JointContext()), 1_000_000; chain_type=Chains, progress=false)\n\nChains MCMC chain (1000000×2×1 Array{Float64, 3}):\n\nIterations        = 1:1:1000000\nNumber of chains  = 1\nSamples per chain = 1000000\nparameters        = a, b\n\nSummary Statistics\n  parameters      mean       std      mcse      ess_bulk      ess_tail      rh ⋯\n      Symbol   Float64   Float64   Float64       Float64       Float64   Float ⋯\n\n           a    0.9800    0.8998    0.0032    79854.8573   122024.0634    1.00 ⋯\n           b    2.8804    0.4874    0.0012   173435.9080   213392.1069    1.00 ⋯\n                                                               2 columns omitted\n\nQuantiles\n  parameters      2.5%     25.0%     50.0%     75.0%     97.5%\n      Symbol   Float64   Float64   Float64   Float64   Float64\n\n           a   -0.7817    0.3711    0.9787    1.5872    2.7449\n           b    1.9247    2.5521    2.8799    3.2079    3.8390\n\n\nor we can choose to sample from the prior instead\n\nsample(MiniModel(m, (x=3.0,)), MHSampler(PriorContext()), 1_000_000; chain_type=Chains, progress=false)\n\nChains MCMC chain (1000000×2×1 Array{Float64, 3}):\n\nIterations        = 1:1:1000000\nNumber of chains  = 1\nSamples per chain = 1000000\nparameters        = a, b\n\nSummary Statistics\n  parameters      mean       std      mcse     ess_bulk      ess_tail      rha ⋯\n      Symbol   Float64   Float64   Float64      Float64       Float64   Float6 ⋯\n\n           a    0.4928    0.9975    0.0039   64665.7870   126806.7300    1.000 ⋯\n           b    0.4622    2.2379    0.0135   27501.9212    52628.0032    1.000 ⋯\n                                                               2 columns omitted\n\nQuantiles\n  parameters      2.5%     25.0%     50.0%     75.0%     97.5%\n      Symbol   Float64   Float64   Float64   Float64   Float64\n\n           a   -1.4660   -0.1785    0.4930    1.1652    2.4435\n           b   -3.9475   -1.0457    0.4666    1.9788    4.8259\n\n\nOf course, using an MCMC algorithm to sample from the prior is unnecessary and silly (PriorSampler exists, after all), but the point is to illustrate the flexibility of the context system. We could, for instance, use the same setup to implement an Approximate Bayesian Computation (ABC) algorithm.\nThe use of contexts also goes far beyond just evaluating log probabilities and sampling. Some examples from Turing are\n\nFixedContext, which fixes some variables to given values and removes them completely from the evaluation of any log probabilities. They power the Turing.fix and Turing.unfix functions.\nConditionContext conditions the model on fixed values for some parameters. They are used by Turing.condition and Turing.uncondition, i.e. the model | (parameter=value,) syntax. The difference between fix and condition is whether the log probability for the corresponding variable is included in the overall log density.\nPriorExtractorContext collects information about what the prior distribution of each variable is.\nPrefixContext adds prefixes to variable names, allowing models to be used within other models without variable name collisions.\nPointwiseLikelihoodContext records the log likelihood of each individual variable.\nDebugContext collects useful debugging information while executing the model.\n\nAll of the above are what Turing calls parent contexts, which is to say that they all keep a subcontext just like our above SamplingContext did. Their implementations of assume and observe call the implementation of the subcontext once they are done doing their own work of fixing/conditioning/prefixing/etc. Contexts are often chained, so that e.g. a DebugContext may wrap within it a PrefixContext, which may in turn wrap a ConditionContext, etc. The only contexts that don’t have a subcontext in the Turing are the ones for evaluating the prior, likelihood, and joint distributions. These are called leaf contexts.\nThe above version of mini Turing is still much simpler than the full Turing language, but the principles of how contexts are used are the same.",
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