Add optional inclusion of MLE point as initial internal point for sim…

…ultaneous method

src/bivariate_methods/bivariate_profile_likelihood.jl

@@ -178,7 +178,8 @@ function bivariate_confidenceprofile(bivariate_optimiser::Function,
                                     bivariate_optimiser, model, 
                                     num_points, consistent, ind1, ind2,
                                     mle_targetll, save_internal_points, channel,
-                                    min_proportion_unique=method.min_proportion_unique)
+                                    min_proportion_unique=method.min_proportion_unique,
+                                    use_MLE_point=method.use_MLE_point)
 
         elseif method isa RadialRandomMethod
             boundary, internal = bivariate_confidenceprofile_vectorsearch(

src/bivariate_methods/vectorsearch.jl

@@ -17,7 +17,8 @@ function findNpointpairs_simultaneous!(p::NamedTuple,
                                         mle_targetll::Float64,
                                         save_internal_points::Bool,
                                         biv_opt_is_ellipse_analytical::Bool,
-                                        min_proportion_unique::Real)
+                                        min_proportion_unique::Real,
+                                        use_MLE_point::Bool)
 
     internal  = zeros(2,num_points)
     internal_all = zeros(model.core.num_pars, save_internal_points ? num_points : 0)
@@ -28,6 +29,12 @@ function findNpointpairs_simultaneous!(p::NamedTuple,
 
     Ninside=0; Noutside=0
     iters=0
+
+    if use_MLE_point
+        Ninside +=1
+        internal[:,Ninside] = model.core.θmle[[ind1, ind2]]
+    end
+
     while Noutside<num_points && Ninside<num_points
 
         x, y = generatepoint(model, ind1, ind2)
@@ -104,6 +111,11 @@ function findNpointpairs_simultaneous!(p::NamedTuple,
         end
     end
 
+    if use_MLE_point
+        ll_values = ll_values[2:end]
+        internal_all = internal_all[:, 2:end]
+    end
+
     if save_internal_points && biv_opt_is_ellipse_analytical
         get_ωs_bivariate_ellipse_analytical!(internal_all, num_points,
                                                     p.consistent, ind1, ind2, 
@@ -288,6 +300,7 @@ function bivariate_confidenceprofile_vectorsearch(bivariate_optimiser::Function,
                                                     channel::RemoteChannel;
                                                     num_radial_directions::Int=0,
                                                     min_proportion_unique::Real=1.0,
+                                                    use_MLE_point::Bool=false,
                                                     ellipse_confidence_level::Float64=-1.0,
                                                     ellipse_start_point_shift::Float64=0.0,
                                                     ellipse_sqrt_distortion::Float64=0.0)
@@ -318,7 +331,7 @@ function bivariate_confidenceprofile_vectorsearch(bivariate_optimiser::Function,
             internal, internal_all, ll_values, external = 
                 findNpointpairs_simultaneous!(p, bivariate_optimiser, model, num_points, ind1, ind2,
                                                 mle_targetll, save_internal_points, biv_opt_is_ellipse_analytical,
-                                                min_proportion_unique)
+                                                min_proportion_unique, use_MLE_point)
         else
             internal, internal_all, ll_values, external = 
                 findNpointpairs_radialrandom!(p, bivariate_optimiser, model, num_points, 

src/types/bivariate_methods.jl

@@ -233,13 +233,14 @@ struct RadialRandomMethod <: AbstractBivariateVectorMethod
 end
 
 """
-    SimultaneousMethod(min_proportion_unique::Real=0.5)
+    SimultaneousMethod(min_proportion_unique::Real=0.5, include_MLE_point::Bool=true)
 
 Method for finding the bivariate boundary of a confidence profile by finding internal and external boundary points using a uniform random distribution on provided bounds, pairing these points in the order they're found and bracketing between each pair (see [`PlaceholderLikelihood.findNpointpairs_simultaneous!`](@ref) and [`PlaceholderLikelihood.bivariate_confidenceprofile_vectorsearch`](@ref)). Values of `min_proportion_unique` lower than zero may improve performance if finding either internal points or external points is difficult given the specified bounds on interest parameters.
     
 
 # Arguments
-- `min_proportion_unique`: a proportion ∈ (0.0, 1.0] for the minimum allowed proportion of unique points in one of the internal or external point vectors. One of these vectors will be fully unique. Whichever vector is not unique, will have at least `min_proportion_unique` unique points. Default is 0.5
+- `min_proportion_unique`: a proportion ∈ (0.0, 1.0] for the minimum allowed proportion of unique points in one of the internal or external point vectors. One of these vectors will be fully unique. Whichever vector is not unique, will have at least `min_proportion_unique` unique points. Default is 0.5.
+- `use_MLE_point`: whether to use the MLE point as the first internal point found or not. Default is true (use).
 
 # Details
 
@@ -277,9 +278,10 @@ Finds at least `ceil(min_proportion_unique * num_points)` internal points.
 """
 struct SimultaneousMethod <: AbstractBivariateVectorMethod 
     min_proportion_unique::Real
-    function SimultaneousMethod(min_proportion_unique::Real=0.5)
+    use_MLE_point::Bool
+    function SimultaneousMethod(min_proportion_unique::Real=0.5, use_MLE_point::Bool=true)
         (0.0 < min_proportion_unique && min_proportion_unique <= 1.0) || throw(DomainError("min_proportion_unique must be in the interval (0.0,1.0]"))
-        return new(min_proportion_unique)
+        return new(min_proportion_unique, use_MLE_point)
     end
 end