Updated homepage

docs/index.md

@@ -1,6 +1,18 @@
 # StochTree
 
-`stochtree` (short for "stochastic tree") unlocks flexible decision tree modeling in R or Python. 
+`stochtree` (short for "stochastic trees") unlocks flexible decision tree modeling in R or Python. 
+
+## Table of Contents
+
+* [Getting Started](getting-started.md): Details on how to install and use `stochtree`
+* [About](about.md): Overview of the models supported by stochtree and pointers to further reading
+* [R Package](R_docs/index.md): Complete documentation of the R package
+* [Python Package](python_docs/index.md): Complete documentation of the Python package
+* [C++ Core API and Architecture](cpp_docs/index.md): Overview and documentation of the C++ codebase that supports stochtree
+* [Development](development/index.md): Roadmap and how to contribute
+
+## What does the software do?
+
 Boosted decision tree models (like [xgboost](https://xgboost.readthedocs.io/en/stable/), 
 [LightGBM](https://lightgbm.readthedocs.io/en/latest/), or 
 [scikit-learn's HistGradientBoostingRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.HistGradientBoostingRegressor.html)) 
@@ -15,11 +27,26 @@ are great, but often require time-consuming hyperparameter tuning.
 The "core" of the software is written in C++, but it provides R and Python APIs. 
 The R package is [available on CRAN](https://cran.r-project.org/web/packages/stochtree/index.html) and the python package will soon be on PyPI.
 
-## Table of Contents
+## Why "stochastic" trees?
 
-* [Getting Started](getting-started.md): Details on how to install and use `stochtree`
-* [About](about.md): Overview of the models supported by stochtree and pointers to further reading
-* [R Package](R_docs/index.md): Complete documentation of the R package
-* [Python Package](python_docs/index.md): Complete documentation of the Python package
-* [C++ Core API and Architecture](cpp_docs/index.md): Overview and documentation of the C++ codebase that supports stochtree
-* [Development](development/index.md): Roadmap and how to contribute
+"Stochastic" loosely means the same thing as "random." This naturally raises the question: how is `stochtree` different from a random forest library?
+At a superficial level, both are decision tree ensembles that use randomness in training.
+
+The difference lies in how that "randomness" is deployed. 
+Random forests take random subsets of a training dataset, and then run a deterministic decision tree fitting algorithm ([recursive partitioning](https://en.wikipedia.org/wiki/Recursive_partitioning)).
+Stochastic tree algorithms use randomness to construct decision tree ensembles from a fixed training dataset.
+
+The original stochastic tree model, [Bayesian Additive Regression Trees (BART)](https://projecteuclid.org/journals/annals-of-applied-statistics/volume-4/issue-1/BART-Bayesian-additive-regression-trees/10.1214/09-AOAS285.full), used [Markov Chain Monte Carlo (MCMC)](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) to sample forests from their posterior distribution. 
+
+So why not call our project `bayesiantree`?
+
+Some algorithms implemented in `stochtree` are "quasi-Bayesian" in that they are inspired by a Bayesian model, but are sampled with fast algorithms that do not provide a valid Bayesian posterior distribution.
+
+Moreover, we think of stochastic forests as general-purpose modeling tools. 
+What makes them useful is that their strong empirical performance -- especially on small or noisy datasets -- not their adherence to any statistical framework.
+
+So why not just call our project `decisiontree`?
+
+Put simply, the sampling approach is part of what makes BART and other `stochtree` algorithms work so well -- we know because we have tested out versions that did not do stochastic sampling of the tree fits. 
+
+So we settled on the term "stochastic trees", or "stochtree" for short (pronounced "stoke-tree").