small update to the VI tutorial

tutorials/variational-inference/01_variational-inference.jmd

@@ -31,8 +31,8 @@ Random.seed!(42);
 The Normal-(Inverse)Gamma conjugate model is defined by the following generative process
 
 \begin{align}
-    s &\sim \mathrm{InverseGamma}(2, 3) \\\\
-    m &\sim \mathcal{N}(0, s) \\\\
+    s &\sim \mathrm{InverseGamma}(2, 3) \\
+    m &\sim \mathcal{N}(0, s) \\
     x_i &\overset{\text{i.i.d.}}{=} \mathcal{N}(m, s), \quad i = 1, \dots, n
 \end{align}
 
@@ -154,19 +154,18 @@ samples = rand(q, 10000);
 ```julia
 # setup for plotting
 using Plots, LaTeXStrings, StatsPlots
-pyplot()
 ```
 
 ```julia
 p1 = histogram(samples[1, :], bins=100, normed=true, alpha=0.2, color = :blue, label = "")
 density!(samples[1, :], label = "s (ADVI)", color = :blue, linewidth = 2)
-density!(collect(skipmissing(samples_nuts[:s].data)), label = "s (NUTS)", color = :green, linewidth = 2)
+density!(samples_nuts, :s; label = "s (NUTS)", color = :green, linewidth = 2)
 vline!([var(x)], label = "s (data)", color = :black)
 vline!([mean(samples[1, :])], color = :blue, label ="")
 
 p2 = histogram(samples[2, :], bins=100, normed=true, alpha=0.2, color = :blue, label = "")
 density!(samples[2, :], label = "m (ADVI)", color = :blue, linewidth = 2)
-density!(collect(skipmissing(samples_nuts[:m].data)), label = "m (NUTS)", color = :green, linewidth = 2)
+density!(samples_nuts, :m; label = "m (NUTS)", color = :green, linewidth = 2)
 vline!([mean(x)], color = :black, label = "m (data)")
 vline!([mean(samples[2, :])], color = :blue, label="")
 
@@ -219,7 +218,7 @@ p_μ_pdf = z -> exp(logpdf(p_μ, (z - μₙ) * exp(- 0.5 * log(βₙ) + 0.5 * lo
 p1 = plot();
 histogram!(samples[1, :], bins=100, normed=true, alpha=0.2, color = :blue, label = "")
 density!(samples[1, :], label = "s (ADVI)", color = :blue)
-density!(vec(samples_nuts[:s].data), label = "s (NUTS)", color = :green)
+density!(samples_nuts, :s; label = "s (NUTS)", color = :green)
 vline!([mean(samples[1, :])], linewidth = 1.5, color = :blue, label ="")
 
 # normalize using Riemann approx. because of (almost certainly) numerical issues
@@ -233,7 +232,7 @@ xlims!(0.75, 1.35);
 p2 = plot();
 histogram!(samples[2, :], bins=100, normed=true, alpha=0.2, color = :blue, label = "")
 density!(samples[2, :], label = "m (ADVI)", color = :blue)
-density!(vec(samples_nuts[:m].data), label = "m (NUTS)", color = :green)
+density!(samples_nuts, :m; label = "m (NUTS)", color = :green)
 vline!([mean(samples[2, :])], linewidth = 1.5, color = :blue, label="")
 
 
@@ -252,13 +251,13 @@ p = plot(p1, p2; layout=(2, 1), size=(900, 500))
 
 # Bayesian linear regression example using `ADVI`
 
-This is simply a duplication of the tutorial [5. Linear regression](../../tutorials/5-linearregression) but now with the addition of an approximate posterior obtained using `ADVI`.
+This is simply a duplication of the tutorial [5. Linear regression](../regression/02_linear-regression) but now with the addition of an approximate posterior obtained using `ADVI`.
 
 As we'll see, there is really no additional work required to apply variational inference to a more complex `Model`.
 
-## Copy-paste from [5. Linear regression](../../tutorials/5-linearregression)
+## Copy-paste from [5. Linear regression](../regression/02_linear-regression)
 
-This section is basically copy-pasting the code from the [linear regression tutorial](../../tutorials/5-linearregression).
+This section is basically copy-pasting the code from the [linear regression tutorial](../regression/02_linear-regression).
 
 
 ```julia