diff --git a/src/KDE01.jl b/src/KDE01.jl
index f43c59f..a7af13d 100644
--- a/src/KDE01.jl
+++ b/src/KDE01.jl
@@ -140,7 +140,7 @@ end
 
 Extract the marginal distribution from the given higher dimensional kernel density estimate object.
 """
-function marginal(bd::BallTreeDensity, ind::Array{Int,1})
+function marginal(bd::BallTreeDensity, ind::AbstractVector{<:Integer})
   pts = getPoints(bd)
   if size(bd.bandwidth,2) > 2*bd.bt.num_points
     sig = getBW(bd)
@@ -152,12 +152,12 @@ function marginal(bd::BallTreeDensity, ind::Array{Int,1})
   p = kde!(pts[ind,:],sig[ind], wts)
 end
 
-function randKernel(N::Int, M::Int, ::Type{KernelDensityEstimate.GaussianKer}) #t::Int)
+function randKernel(N::Int, M::Int, ::Type{<:KernelDensityEstimate.GaussianKer}) #t::Int)
   return randn(N,M)
 end
 
 """
-   $(SIGNATURES)
+    $(SIGNATURES)
 
 Randomly sample points from the KernelDensityEstimate object.
 """
diff --git a/src/StringSerialization.jl b/src/StringSerialization.jl
index 5c208dd..1b86dcd 100644
--- a/src/StringSerialization.jl
+++ b/src/StringSerialization.jl
@@ -1,16 +1,16 @@
-function string(d::KernelDensityEstimate.BallTreeDensity)
+function Base.string(d::KernelDensityEstimate.BallTreeDensity)
   # TODO only supports single bandwidth per dimension at this point
   pts = getPoints(d)
   return "KDE:$(size(pts,2)):$(getBW(d)[:,1]):$(pts)"
 end
 
-function parsestringvector(str::AS; dlim=',') where {AS <: AbstractString}
+function parsestringvector(str::AbstractString; dlim=',')
   sstr = split(split(strip(str),'[')[end],']')[1]
   ssstr = strip.(split(sstr,dlim))
   parse.(Float64, ssstr)
 end
 
-function convert(::Type{BallTreeDensity}, str::AS) where {AS <: AbstractString}
+function convert(::Type{<:BallTreeDensity}, str::AbstractString)
   @assert occursin(r"KDE:", str) # ismatch
   sstr = strip.(split(str, ':'))
   N = parse(Int, sstr[2])