Make MCSE for constant arrays always return a NaN

Project.toml

@@ -1,7 +1,7 @@
 name = "MCMCDiagnosticTools"
 uuid = "be115224-59cd-429b-ad48-344e309966f0"
 authors = ["David Widmann", "Seth Axen"]
-version = "0.3.11"
+version = "0.3.12"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/mcse.jl

@@ -94,7 +94,7 @@ function _mcse(
 end
 
 function _mcse_quantile(x, p, Seff)
-    Seff === missing && return missing
+    (Seff === missing || isnan(Seff)) && return Seff
     S = length(x)
     # quantile error distribution is asymptotically normal; estimate σ (mcse) with 2
     # quadrature points: xl and xu, chosen as quantiles so that xu - xl = 2σ
@@ -133,6 +133,10 @@ function _mcse_sbm(f, x, batch_size)
     any(x -> x === missing, x) && return missing
     n = length(x)
     i1 = firstindex(x)
+    if all(==(first(x)), x)
+        y1 = f(view(x, i1:(i1 + batch_size - 1)))
+        return oftype(y1, NaN)
+    end
     v = Statistics.var(
         f(view(x, i:(i + batch_size - 1))) for i in i1:(i1 + n - batch_size);
         corrected=false,

test/mcse.jl

@@ -83,6 +83,23 @@ using StatsBase
         end
     end
 
+    @testset "mcse for scalar array is always a NaN" begin
+        x = ones(100)
+        @testset for kind in [
+            mean,
+            median,
+            std,
+            mad,
+            # uses sbm
+            x -> mean(x),
+            x -> median(x),
+            x -> std(x),
+            x -> mad(x),
+        ]
+            @test isnan(mcse(x; kind))
+        end
+    end
+
     @testset "estimand is within interval defined by MCSE estimate" begin
         # we check the MCSE estimates by simulating uncorrelated, correlated, and
         # anticorrelated chains, mapping the draws to a target distribution, computing the