Add brief example on main doc page to give a "feel" of the package

docs/src/index.md

@@ -1,9 +1,9 @@
 # SequentialSamplingModels.jl
 
-Documentation is under construction.
+**Documentation is under construction.**
 
-This package is a collection of sequential sampling models and is based on the Distributions.jl API.
-Sequential sampling models, also known as an evidence accumulation models, are a broad class of dynamic models of human decision making in which evidence for each option accumulates until the evidence for one option reaches a decision threshold. Models within this class make different assumptions about the nature of the evidence accumulation process. See the references below for a broad overview of sequential sampling models. An example of the evidence accumulation process is illustrated below for the leaking competing accumulator. 
+This package is a collection of sequential sampling models in Julia and is based on the Distributions.jl API.
+Sequential sampling models, also known as an evidence accumulation models, are a broad class of dynamic models of human decision making in which evidence for each option accumulates until the evidence for one option reaches a decision threshold. Models within this class make different assumptions about the nature of the evidence accumulation process. See the references below for a broad overview of sequential sampling models. An example of the evidence accumulation process is illustrated below for the leaking competing accumulator.
 
 ```@setup accumulation
 using Plots
@@ -14,7 +14,7 @@ using SequentialSamplingModels: increment!
 Random.seed!(8437)
 
 function sim(model)
-    
+
     n = length(model.ν)
     x = fill(0.0, n)
     μΔ = fill(0.0, n)
@@ -26,21 +26,21 @@ function sim(model)
         t += Δt
         increment!(model, x, μΔ, ϵ)
         push!(evidence, copy(x))
-    end  
+    end
     return t,evidence
 end
-parms = (α = 1.5, 
+parms = (α = 1.5,
             β=0.20,
-             λ=0.10, 
-             ν=[2.5,2.0], 
-             Δt=.001, 
-             τ=.30, 
+             λ=0.10,
+             ν=[2.5,2.0],
+             Δt=.001,
+             τ=.30,
              σ=1.0)
 model = LCA(; parms...)
 t,evidence = sim(model)
 n_steps = length(evidence)
 time_steps = range(0, t, length=n_steps)
-lca_plot = plot(time_steps, hcat(evidence...)', xlabel="Time (seconds)", ylabel="Evidence", 
+lca_plot = plot(time_steps, hcat(evidence...)', xlabel="Time (seconds)", ylabel="Evidence",
     label=["option1" "option2"], ylims=(0, 2.0), grid=false, linewidth = 2,
     color =[RGB(148/255, 90/255, 147/255) RGB(90/255, 112/255, 148/255)])
 hline!(lca_plot, [model.α], color=:black, linestyle=:dash, label="threshold", linewidth = 2)
@@ -50,7 +50,7 @@ savefig("lca_plot.png")
 ![](lca_plot.png)
 # Installation
 
-You can install a stable version of SequentialSamplingModels by running the following in the Julia REPL:
+You can install a stable version of *SequentialSamplingModels* by running the following in the Julia REPL:
 
 ```julia
 ] add SequentialSamplingModels
@@ -62,6 +62,26 @@ The package can then be loaded with:
 using SequentialSamplingModels
 ```
 
+# Quick Example
+
+The package implements sequential sampling models as distributions, that we can use you estimate the likelihood, or generate data from. In the example below, we instantiate a Linear Ballistic Accumulator (LBA) model, and generate data from it.
+
+```julia
+using StatsPlots
+
+# Create LBA distribution with known parameters
+dist = LBA(; ν=[0, 0.5], A=0.2, k=0.8, τ=0.3)
+# Sample 1000 random data points from this distribution
+choice, rt = rand(dist, 1000)
+
+# Plot the RT distribution for each choice
+histogram(layout=(2, 1), xlabel="Reaction Time", ylabel="Density", xlims = (0,5))
+histogram!(rt[choice.==1], subplot=1, color=:green)
+histogram!(rt[choice.==2], subplot=2, color=:red)
+```
+
+*SequentialSamplingModels* provides such unified interface to a variety of models.
+
 # References
 Evans, N. J. & Wagenmakers, E.-J. Evidence accumulation models: Current limitations and future directions. Quantitative Methods for Psychololgy 16, 73–90 (2020).