update parameter estimation and monte carlo

docs/src/analysis/parameter_estimation.md

@@ -73,14 +73,18 @@ is a function which reduces the problem's solution. While this is very
 flexible, a two convenience routines is included for fitting to data:
 
 ```julia
-L2DistLoss(t,data)
-CostVData(t,data;loss_func = L2DistLoss)
+L2DistLoss(t,data;weight=nothing)
+CostVData(t,data;loss_func = L2DistLoss,weight=nothing)
 ```
 
 where `t` is the set of timepoints which the data is found at, and
 `data` which are the values that are known. `L2DistLoss` is an optimized version
 of the L2-distance. In `CostVData`, one can choose any loss function from
-LossFunctions.jl or use the default of an L2 loss.
+LossFunctions.jl or use the default of an L2 loss. The `weight` is a vector
+of weights for the loss function which must match the size of the data.
+
+Note that minimization of a weighted `L2DistLoss` is equivalent to maximum
+likelihood estimation of a heteroskedastic Normally distributed likelihood.
 
 #### Note About Loss Functions
 

docs/src/features/monte_carlo.md

@@ -32,7 +32,7 @@ One can specify a function `prob_func` which changes the problem. For example:
 
 ```julia
 function prob_func(prob,i,repeat)
-  prob.u0 = randn()*prob.u0
+  @. prob.u0 = randn()*prob.u0
   prob
 end
 ```
@@ -45,7 +45,7 @@ you can have the `i`th simulation use the `i`th initial condition via:
 
 ```julia
 function prob_func(prob,i,repeat)
-  prob.u0 = u0_arr[i]
+  @. prob.u0 = u0_arr[i]
   prob
 end
 ```
@@ -279,8 +279,7 @@ and use that for calculating the trajectory:
 
 ```julia
 function prob_func(prob,i,repeat)
-  prob.u0 = rand()*prob.u0
-  prob
+  ODEProblem(prob.f,rand()*prob.u0,prob.tspan)
 end
 ```
 
@@ -422,8 +421,7 @@ Our `prob_func` will simply randomize the initial condition:
 prob = ODEProblem((t,u)->1.01u,0.5,(0.0,1.0))
 
 function prob_func(prob,i,repeat)
-  prob.u0 = rand()*prob.u0
-  prob
+  ODEProblem(prob.f,rand()*prob.u0,prob.tspan)
 end
 ```