Add vectorized HMC docs

docs/make.jl

@@ -16,6 +16,7 @@ makedocs(;
     pages=[
         "AdvancedHMC.jl" => "index.md",
         "Get Started" => "get_started.md",
+        "Vectorized HMC" => "vectorized.md",
         "Automatic Differentiation Backends" => "autodiff.md",
         "Detailed API" => "api.md",
         "Interfaces" => "interfaces.md",

docs/src/get_started.md

@@ -1,4 +1,4 @@
-# Sampling from a multivariate Gaussian using NUTS
+# [Sampling from a multivariate Gaussian using NUTS](@id get_started)
 
 In this section, we demonstrate a minimal example of sampling from a multivariate Gaussian (10-dimensional) using the No U-Turn Sampler (NUTS). Below we describe the major components of the Hamiltonian system which are essential to sample using this approach:
 

docs/src/vectorized.md

@@ -0,0 +1,28 @@
+# Vectorized HMC Sampling
+
+In this section, we explain how to easily employ vectorized Hamiltonian Monte Carlo with AdvancedHMC.jl. Let's continue with the previous example in [getting-started](@ref get_started), we want to sample a multivariate Gaussian (10-dimensional) with multiple chains, we can simply specify the number of chains in initial parameters, leapfrog integrator, and metric to tell AdvanceHMC.jl how many chains we want to sample. Here, the vectorized multivariate Gaussian log density problem come from [MCMCLogDensityProblems.jl](https://github.com/chalk-lab/MCMCLogDensityProblems.jl) which is a library of common log density target distributions designed for vectorized sampling.
+
+```julia
+using AdvancedHMC
+using MCMCLogDensityProblems
+
+D = 10
+target = HighDimGaussian(D)
+ℓπ(x) = logpdf(target, x)
+∂ℓπ∂θ(x) = logpdf_grad(target, x)
+
+n_chains = 5
+θ_init = rand(D, n_chains)
+ϵ = 0.1
+lfi = Leapfrog(fill(ϵ, n_chains))
+n_steps = 10
+n_samples = 20_000
+metric = DiagEuclideanMetric((D, n_chains))
+τ = Trajectory{EndPointTS}(lfi, FixedNSteps(n_steps))
+h = Hamiltonian(metric, ℓπ, ∂ℓπ∂θ)
+samples, stats = sample(h, HMCKernel(τ), θ_init, n_samples; verbose=false)
+```
+
+!!! note
+
+    Vectorized sampling only support static HMC, which means samplers like `NUTS` should not be used for vectorized sampling for now.