Use keyword syntax for ess, ess_rhat, rhat, and mcse (#72)

* Create rhat.jl

* Add missing _expectand_proxy method

* Remove duplicate rhat_tail

* Update ESS methods

* Define estimator keyword for mcse

* Reduce exports

* Fix bug

* Run formatter

* Shortcut rank-normalizing a `Missing`

* Update ESS tests

* Use new mcse syntax

* Update documented methods

* Update text

* Fix test

* Use new mcse signature

* Update type kwarg to estimator

* Update mcse docstring

* Fix variable name

* Make tail-ESS work for typeunion with Missing

* Add rank for ESS

* Rearrange tests

* Test against ess

* Add consistency test

* Add inferrability tests for estimators

* Add more error tests

* Try to resolve type-instability

* Add Compat for `@constprop` macro

* Aggressively constprop

* Test type-inferrability with Vals

* Make work for typeunions with Missing on v1.6

* Avoid repeating split_chains docs

* Rename ess.jl to ess_rhat.jl

* Move rhat to same file as ess

* Update costring

* Run formatter

* Remove rhat.jl

* Better unify tests

* Add missing type annotations

* Apply suggestions from code review

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Avoid `@constprop`, rename `type` and `estimator` to `kind`

* Cleanup

* Rename `estimator` to `kind` for `mcse`

* Update tests

* Update kinds accepted for ESS

* Remove unused utility

* Constrain kind to Symbol when applicable

* Remove stray tick

* Apply suggestions from code review

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Apply suggestions from code review

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Add comment explaining kind checks

* Change vectors to tuples

---------

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

docs/src/index.md

@@ -6,16 +6,13 @@ CurrentModule = MCMCDiagnosticTools
 
 ## Effective sample size and $\widehat{R}$
 
-The effective sample size (ESS) and $\widehat{R}$ can be estimated with [`ess_rhat`](@ref).
-
 ```@docs
+ess
+rhat
 ess_rhat
-ess_rhat_bulk
-ess_tail
-rhat_tail
 ```
 
-The following methods are supported:
+The following `method`s are supported:
 
 ```@docs
 ESSMethod

src/MCMCDiagnosticTools.jl

@@ -16,7 +16,7 @@ using Statistics: Statistics
 
 export bfmi
 export discretediag
-export ess_rhat, ess_rhat_bulk, ess_tail, rhat_tail, ESSMethod, FFTESSMethod, BDAESSMethod
+export ess, ess_rhat, rhat, ESSMethod, FFTESSMethod, BDAESSMethod
 export gelmandiag, gelmandiag_multivariate
 export gewekediag
 export heideldiag
@@ -27,7 +27,7 @@ export rstar
 include("utils.jl")
 include("bfmi.jl")
 include("discretediag.jl")
-include("ess.jl")
+include("ess_rhat.jl")
 include("gelmandiag.jl")
 include("gewekediag.jl")
 include("heideldiag.jl")