changing language about ess to refer to posterior expectations instea…

…d of means

README.md

@@ -69,7 +69,8 @@ python -m pip install -r requirements-dev.txt  # install dev requirements
 ### Install with conda
 
 ```bash
-conda create --name pyei --channel conda-forge python=3.8 --file requirements.txt --file requirements-dev.txt
+conda create --name pyei --channel conda-forge python=3.8 --file requirements.txt --file requirements-dev.txt # create conda environment and install requirements
+pip install -e . #install project locally
 ```
 
 ### Testing

paper/paper.md

@@ -74,7 +74,7 @@ In several of these cases, `PyEI` includes modifications to the models as origin
 Several R libraries implementing different ecological inference methods exist, such as `eiPack` [@eiPack], `RxCEcolInf` [@RxCEcolInf], `ei` [@ei], and `eiCompare` [@eiCompare]. In addition to presenting a Python-based option that researchers who primarily use Python may appreciate, `PyEI` 
 incorporates the following key features and characteristics.
 
-First, the Bayesian hierarchical methods implemented in `PyEI` rest on modern probabilistic programming tooling [@salvatier2016probabilistic] and gradient-based MCMC methods such as the No U-Turn Sampler (NUTS) [@hoffman2014no; @betancourt2018conceptual]. Using NUTS where possible should allow for faster convergence than existing implementations that rest primarily on Metropolis-Hastings and Gibbs sampling steps. Consider effective sample size, which is a measure of how the variance of the mean of drawn samples compare to the variance of independent samples from the posterior distribution (or, very roughly, how “effective” the samples are for computing the posterior mean, compared to independent samples) [@BDA3]. Under certain assumptions on the target posterior distribution, in Metropolis-Hastings the number of evaluations of the log-posterior required for a given effective sample size scales linearly with the dimensionality of the parameter space, while in Hamiltonian Monte Carlo approaches such as NUTS, the number of required evaluations of the gradient of the log-posterior scales only as the fourth root of the dimension [@neal2011mcmc]. Reasonable scaling with the dimensionality of the parameter space is important in ecological inference, as that dimensionality is large when there are many precincts.
+First, the Bayesian hierarchical methods implemented in `PyEI` rest on modern probabilistic programming tooling [@salvatier2016probabilistic] and gradient-based MCMC methods such as the No U-Turn Sampler (NUTS) [@hoffman2014no; @betancourt2018conceptual]. Using NUTS where possible should allow for faster convergence than existing implementations that rest primarily on Metropolis-Hastings and Gibbs sampling steps. Consider effective sample size, which is a measure of how the variance of a Monte Carlo estimate of a posterior expectation computed from dependent samples compares to the variance of the corresponding estimate computed from independent samples from the posterior distribution (or, very roughly, how “effective” the samples are for estimating a posterior expectation, compared to independent samples) [@BDA3]. Under certain assumptions on the target posterior distribution, in Metropolis-Hastings the number of evaluations of the log-posterior required for a given effective sample size scales linearly with the dimensionality of the parameter space, while in Hamiltonian Monte Carlo approaches such as NUTS, the number of required evaluations of the gradient of the log-posterior scales only as the fourth root of the dimension [@neal2011mcmc]. Reasonable scaling with the dimensionality of the parameter space is important in ecological inference, as that dimensionality is large when there are many precincts.
 
 Second, integration with the existing tools `PyMC3` [@salvatier2016probabilistic] and `ArviZ` [@arviz_2019] makes the results amenable to state of the art diagnostics (e.g. convergence diagnostics) and some reasonable checks are automatically performed.