add and test partial missing data in the getting started example

EpiAware/docs/src/examples/getting_started.jl

@@ -239,7 +239,24 @@ We do the inference by MCMC/NUTS using the `Turing` NUTS sampler with default wa
 # ╔═╡ c8ce0d46-a160-4c40-a055-69b3d10d1770
 truth_data = generated_obs
 
+# ╔═╡ 4a4c6e91-8d8f-4bbf-bb7e-a36dc281e312
+md"
+The observation model supports partially complete data. To test this we set some of the generated observations to be `missing`.
+"
+
+# ╔═╡ 259a7042-e74f-43c7-aeb4-97a3beeb7776
+let
+    truth_data = Union{Int, Missing}[truth_data...]
+    truth_data[vcat([3, 5], 10:20)] .= missing
+end
+
+# ╔═╡ 32638954-2c99-4d4e-8e03-52154030c657
+md"
+We now make the model but fixing the initial condition of the random walk to be 0.
+"
+
 # ╔═╡ b4033728-b321-4100-8194-1fd9fe2d268d
+
 inference_mdl = fix(
     make_epi_aware(truth_data, time_horizon; epi_model = epi_model,
         latent_model = rwp, observation_model = obs_model),
@@ -297,6 +314,8 @@ let
         size = (700, 400))
 end
 
+# ╔═╡ 2293b711-0bd0-44d5-8a30-94e56c5e4c65
+
 # ╔═╡ fd6321b1-4c3a-4123-b0dc-c45b951e0b80
 md"
 As well as checking the posterior predictions for latent infections, we can also check how well inference recovered unknown parameters, such as the random walk variance or the cluster factor of the negative binomial observations.
@@ -382,12 +401,16 @@ end
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+# ╠═b5bc8f05-b538-4abf-aa84-450bf2dff3d9
 # ╠═c8ce0d46-a160-4c40-a055-69b3d10d1770
+# ╟─4a4c6e91-8d8f-4bbf-bb7e-a36dc281e312
+# ╠═259a7042-e74f-43c7-aeb4-97a3beeb7776
+# ╟─32638954-2c99-4d4e-8e03-52154030c657
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