Allow running findmap from a given starting point

src/optimization.jl

@@ -10,39 +10,49 @@ single row.
 Returning a Chains object is a bit weird, but this way 
 it can be handled the same as our posteriors, plotted, etc.
 """
-function findmap(model::LogDensityModel,N=100_000;verbosity=0)
-    θ′ = _findmap(model,N;verbosity)
-    logpost = model.ℓπcallback(model.link(θ′))
-    nt = (; logpost, model.arr2nt(θ′)...)
+function findmap(model::LogDensityModel;starting_position=nothing,N=100_000,verbosity=0)
+    if isnothing(starting_position)
+        starting_position, _ = guess_starting_position(model.system,N)
+    end
+
+    logpost = model.ℓπcallback(model.link(starting_position))
+
+    θ_t′ = _findmap(model,model.link(starting_position);verbosity)
+    θ′ = model.invlink(θ_t′)
+    # Evaluate log post and log like
+    logpost = model.ℓπcallback(θ_t′)
+    resolved_namedtuple = model.arr2nt(θ′)
+    # Add log posterior, tree depth, and numerical error reported by
+    # the sampler.
+    # Also recompute the log-likelihood and add that too.
+    ln_like = make_ln_like(model.system, resolved_namedtuple)
+    loglike = ln_like(model.system, resolved_namedtuple)
+    nt = (; logpost, loglike, model.arr2nt(θ′)...)
     return result2mcmcchain(
         [nt], 
-        Dict(:internals => [:logpost])
+        Dict(:internals => [:logpost, :loglike])
     )
 end
 
 # Returns the raw parameter vector
-function _findmap(model::LogDensityModel,N=100_000;verbosity=0)
+function _findmap(model::LogDensityModel,initial_θ_t;verbosity=0)
     func = OptimizationFunction(
         (θ,model)->-model.ℓπcallback(θ),
         grad=(G,θ,model)->G.=.-model.∇ℓπcallback(θ)[2],
     )
     verbosity > 1 && @info "Guessing starting position" N
-    θ0, _ = guess_starting_position(model.system,N)
-
-    # Start with Simulated Annealing
-    prob = OptimizationProblem(func, θ0, model)
+    # # Start with Simulated Annealing
+    prob = OptimizationProblem(func, initial_θ_t, model)
     verbosity > 1 && @info "Simualted annealing optimization" N
     sol = solve(prob, SimulatedAnnealing(), iterations=1_00_000, x_tol=0)
-    θ0 = sol.u
 
     # Then iterate with qusi-Newton
     prob = OptimizationProblem(func, sol.u, model)
     verbosity > 1 && @info "LBFGS optimization" N
-    sol = solve(prob, LBFGS(), g_tol=1e-12, iterations=10000, allow_f_increases=true)
-    θ0 = sol.u
+    sol = solve(prob, LBFGS(), g_tol=1e-12, iterations=100000, allow_f_increases=true)
+    θ_map2 = sol.u
 
-    θ′ = model.invlink(θ0)
-    return θ′
+    return θ_map2
 
     #     logpost = model.ℓπcallback(model.link(θ′))
     #     if sol.retcode == ReturnCode.Success && isfinite(logpost)