From d410a729cc1f7a33adc2caa7d12306b651ac09fa Mon Sep 17 00:00:00 2001
From: waldie11 <86674066+waldie11@users.noreply.github.com>
Date: Mon, 5 Sep 2022 10:55:59 +0200
Subject: [PATCH] feature sequential application of RAM_sample

---
 README.md                              | 1 +
 src/RobustAdaptiveMetropolisSampler.jl | 5 ++++-
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index a0db79f..dc2578e 100644
--- a/README.md
+++ b/README.md
@@ -27,6 +27,7 @@ RAM_sample(logtarget, x0, M0, n; opt_α=0.234, γ=2/3, q=Normal(), show_progress
 * `γ`: a parameter for the computation of the step size sequence.
 * `q`: the proposal distribution.
 * `show_progress`: a flag that controls whether a progress bar is shown.
+* `nsampled`: in sequential application of `RAM_sample`, provide the number of global steps so far to yield consistent updates on the covariance matrix.
 * `output_log_probability_x`: a flag that controls whether to include output for the log-posterior scores from each Markov chain iteration.
 
 The function returns a `NamedTuple` with three (or optionally four) elements:
diff --git a/src/RobustAdaptiveMetropolisSampler.jl b/src/RobustAdaptiveMetropolisSampler.jl
index 19fb749..3afd3b6 100644
--- a/src/RobustAdaptiveMetropolisSampler.jl
+++ b/src/RobustAdaptiveMetropolisSampler.jl
@@ -32,6 +32,7 @@ function RAM_sample(
         γ=2 / 3,
         q=Normal(),
         show_progress::Bool=true,
+        nsampled::Int=0,
         output_log_probability_x::Bool=false
     )
 
@@ -85,7 +86,9 @@ function RAM_sample(
         # Step R3
 
         # This is taken from the second paragraph of section 5
-        η = min(1, d * i^-γ)
+        # A sequential application of RAM_Sample requires knowledge on the number of already
+        # processed steps.
+        η = min(1, d * (nsampled + i)^-γ)
 
         # Compute the new covariance matrix
         M = s.L * (I + η * (α - opt_α) * (u * u') / norm(u)^2 ) * s.L'