diagnostics.R: a few minor doc edits

R/diagnostics.R

@@ -17,13 +17,13 @@
 #'   See **Details** for the motivation behind these defaults.
 #'
 #' @details
-#' 
+#'
 #' The reliability and approximate convergence rate of the PSIS-based
 #' estimates can be assessed using the estimates for the shape
 #' parameter \eqn{k} of the generalized Pareto distribution. The
 #' diagnostic threshold for Pareto \eqn{k} depends on sample size
 #' \eqn{S} (sample size dependent threshold was introduced by Vehtari
-#' et al., 2022, and before that fixed thresholds of 0.5 and 0.7 were
+#' et al. (2022), and before that fixed thresholds of 0.5 and 0.7 were
 #' recommended). For simplicity, `loo` package uses the nominal sample
 #' size \eqn{S} when computing the sample size specific
 #' threshold. This provides an optimistic threshold if the effective
@@ -35,7 +35,7 @@
 #'   sample size, the PSIS estimate and the corresponding Monte Carlo
 #'   standard error estimate are reliable.
 #'
-#' * If \eqn{1 - 1 / log10(S) <= k < 0.7}, PSIS estimate and the
+#' * If \eqn{1 - 1 / log10(S) <= k < 0.7}, the PSIS estimate and the
 #'   corresponding Monte Carlo standard error estimate are not
 #'   reliable, but increasing the (effective) sample size \eqn{S} above
 #'   2200 may help (this will increase the sample size specific
@@ -44,19 +44,19 @@
 #'
 #' * If \eqn{0.7 <= k < 1}, the PSIS estimate and the corresponding Monte
 #'   Carlo standard error have large bias and are not reliable. Increasing
-#'  the sample size may reduce the uncertainty in the \eqn{k} estimate.
+#'   the sample size may reduce the uncertainty in the \eqn{k} estimate.
 #'
-#' * If \eqn{0.7 <= k < 1}, PSIS estimate and the corresponding Monte
+#' * If \eqn{0.7 <= k < 1}, the PSIS estimate and the corresponding Monte
 #'   Carlo standard error have large bias and are not reliable. Increasing
-#'   sample size may reduce the variability in \eqn{k} estimate, which
+#'   the sample size may reduce the variability in \eqn{k} estimate, which
 #'   may result in lower \eqn{k} estimate, too.
 #'
 #' * If \eqn{k \geq 1}{k >= 1}, the target distribution is estimated to
-#'   have non-finite mean. The PSIS estimate and the corresponding Monte
+#'   have a non-finite mean. The PSIS estimate and the corresponding Monte
 #'   Carlo standard error are not well defined. Increasing the sample size
-#'   may reduce the variability in \eqn{k} estimate, which
-#'   may result in lower \eqn{k} estimate, too.
-#' 
+#'   may reduce the variability in the \eqn{k} estimate, which
+#'   may also result in a lower \eqn{k} estimate.
+#'
 #' \subsection{What if the estimated tail shape parameter \eqn{k}
 #' exceeds the diagnostic threshold?}{ Importance sampling is likely to
 #' work less well if the marginal posterior \eqn{p(\theta^s | y)} and
@@ -67,7 +67,7 @@
 #' warned. (Note: If \eqn{k} is greater than the diagnostic threshold
 #' then WAIC is also likely to fail, but WAIC lacks as accurate
 #' diagnostic.)  When using PSIS in the context of approximate LOO-CV,
-#' we recommend one of the following actions when \eqn{k > 0.7}:
+#' we recommend one of the following actions:
 #'
 #' * With some additional computations, it is possible to transform
 #'   the MCMC draws from the posterior distribution to obtain more
@@ -101,8 +101,8 @@
 #' sample size for importance sampling, which are more accurate for PSIS than
 #' for IS and TIS (see Vehtari et al (2022) for details). However, the PSIS
 #' effective sample size estimate will be
-#'  **over-optimistic when the estimate of \eqn{k} is greater than
-#'    \eqn{min(1-1/log10(S), 0.7)}**, where \eqn{S} is the sample size.
+#' **over-optimistic when the estimate of \eqn{k} is greater than**
+#' \eqn{min(1-1/log10(S), 0.7)}, where \eqn{S} is the sample size.
 #' }
 #'
 #' @seealso