Docs update

README.md

@@ -58,3 +58,8 @@ intensity = HawkesProcesses.intensity(ts, simevents, bg, kappa, kernel)
 
 * Likelihood with functional background
 * Generic Bayesian inference.
+
+## Blog Posts
+
+* [HawkesProcesses.jl: An Introduction](http://dm13450.github.io/2020/05/26/HawkesProcessesPackage.html)
+* [Hawkes Processes and DIC](http://dm13450.github.io/2020/08/26/Hawkes-and-DIC.html)

docs/src/inference.md

@@ -1,5 +1,5 @@
 
-This package was designed to provide an implementation of an efficient Bayesian sampling algorithm but using the availabel functions you can also use frequentist methods. 
+This package was designed to provide an implementation of an efficient Bayesian sampling algorithm but using the available functions you can also use frequentist methods. 
 
 ### Bayesian Inference
 
@@ -16,9 +16,26 @@ simEvents = HawkesProcesses.simulate(bg, kappa, kernF, maxT)
 bgSamples, kappaSamples, kernSamples = HawkesProcesses.fit(simEvents, maxT, 1000)
 ```
 
-Here we now have MCMC chains for the three different parameters.
+Here we now have MCMC chains for the three different parameters. 
+
+At the minute, only the exponential distribution for the kernel is implemented. 
+In future releases this will be changed to be generic for any kernel you specify. 
 
 
 ### Frequentist Inference
 
-TBC
+Another (and potentially quicker) method of infering the parameters is to maximise the likelihood function. 
+
+```@example
+using Optim
+
+opt = optimize(x-> -1*HawkesProcesses.likelihood(simEvents, 
+                                                 x[1],
+                                                 x[2],
+                                                 Distriubtions.Exponential(x[3]),
+                                                 maxT),
+                rand(3))
+Optim.minimizer(opt)
+```
+
+Simply passing the likelihood function through to the optimiser allows for a quick and easy estimate of the parameters. 

docs/src/modelchecking.md

@@ -14,6 +14,8 @@ Then by looking at what likelihood is larger can suggest which model is better s
 
 ## Residuals 
 
+TBC
 
+## Probability Calibration
 
-## Probability Calibration
+TBC

docs/src/simulating.md

@@ -1,7 +1,7 @@
 
 You can simulate a Hawkes process easily using the `simulate` function. Both constant and functional background rates are currently supported. 
 
-To simulate from a Hawkes process we first generate the background events from a Poisson process with the background rate. Then for each event generated from the background we simulate a inhomogenous Poisson process with rate kappa*g(t-t_parent), any further events that arise are then also used to simulate further events. 
+To simulate from a Hawkes process we first generate the background events from a Poisson process with the background rate. Then for each event generated from the background we simulate a inhomogeneous Poisson process with rate kappa*g(t-t_parent), any further events that arise are then also used to simulate further events. 
 
 ### Constant Background