nicer docs

docs/src/emulate_sample.md

@@ -1,6 +1,55 @@
 # Emulate and Sample
 Once you have run a successful calibration, we can fit an emulator to the resulting input/output pairs.
 
+First, import the necessary packages:
+```julia
+using CalibrateEmulateSample.Emulators
+using CalibrateEmulateSample.MarkovChainMonteCarlo
+
+import EnsembleKalmanProcesses as EKP
+using EnsembleKalmanProcesses.ParameterDistributions
+using EnsembleKalmanProcesses.TOMLInterface
+
+import JLD2
+
+import CalibrateAtmos as CAL
+```
+
+Next, load in the data, EKP object, and prior distribution.
+```julia
+y_obs = [261.5493]
+y_noise_cov = [0.02619;;]
+ekp = JLD2.load_object(
+    joinpath(
+        pkgdir(CAL),
+        "docs",
+        "src",
+        "assets",
+        "eki_file_for_emulate_example.jld2",
+    ),
+)
+init_params = [EKP.get_u_final(ekp)[1]]
+
+prior_path = joinpath(
+    pkgdir(CAL),
+    "experiments",
+    "sphere_held_suarez_rhoe_equilmoist",
+    "parameters.toml",
+)
+
+prior = CAL.get_prior(prior_path)
+```
+Get the input-output pairs which will be used to train the emulator:
+```julia
+input_output_pairs = CAL.get_input_output_pairs(ekp)
+```
+Create the Gaussian Process-based emulator, obtain samples, and save the samples to a JLD2 file.
+```julia
+emulator = CAL.gp_emulator(input_output_pairs, y_noise_cov)
+(; mcmc, chain) = CAL.sample(emulator, y_obs, prior, init_params)
+constrained_posterior = CAL.save_samples(mcmc, chain, prior; filename = "samples.jld2")
+```
+
 ```@example
 include("emulate_sample_example.jl")
 ```

test/Project.toml

@@ -8,4 +8,5 @@ EnsembleKalmanProcesses = "aa8a2aa5-91d8-4396-bcef-d4f2ec43552d"
 JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"