diff --git a/man/outstandR-package.Rd b/man/outstandR-package.Rd
index 1888188..a645b08 100644
--- a/man/outstandR-package.Rd
+++ b/man/outstandR-package.Rd
@@ -18,7 +18,7 @@ Useful links:
 
 }
 \author{
-\strong{Maintainer}: Nathan Green \email{n.green@ucl.ac.uk} (\href{https://orcid.org/0000-0003-2745-1736}{ORCID}) (02jx3x895) [copyright holder]
+\strong{Maintainer}: Nathan Green \email{n.green@ucl.ac.uk} (\href{https://orcid.org/0000-0003-2745-1736}{ORCID}) (\href{https://ror.org/02jx3x895}{ROR}) [copyright holder]
 
 Authors:
 \itemize{
diff --git a/scripts/exercises2.html b/scripts/exercises2.html
index 9e84347..85b25dd 100644
--- a/scripts/exercises2.html
+++ b/scripts/exercises2.html
@@ -315,8 +315,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 0.000114 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.14 seconds.
+Chain 1: Gradient evaluation took 5.3e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.53 seconds.
 Chain 1: Adjust your expectations accordingly!
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@@ -327,15 +327,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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+Chain 1:  Elapsed Time: 0.223 seconds (Warm-up)
+Chain 1:                0.208 seconds (Sampling)
+Chain 1:                0.431 seconds (Total)
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 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 2.1e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.
+Chain 2: Gradient evaluation took 1.8e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
 Chain 2: Adjust your expectations accordingly!
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+Chain 2:  Elapsed Time: 0.216 seconds (Warm-up)
+Chain 2:                0.204 seconds (Sampling)
+Chain 2:                0.42 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -369,8 +369,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 2.6e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
+Chain 1: Gradient evaluation took 2.4e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
 Chain 1: Adjust your expectations accordingly!
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@@ -387,15 +387,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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+Chain 1:  Elapsed Time: 0.229 seconds (Warm-up)
+Chain 1:                0.21 seconds (Sampling)
+Chain 1:                0.439 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 2e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
+Chain 2: Gradient evaluation took 1.6e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
 Chain 2: Adjust your expectations accordingly!
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-Chain 2:                0.258 seconds (Sampling)
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+Chain 2:  Elapsed Time: 0.211 seconds (Warm-up)
+Chain 2:                0.216 seconds (Sampling)
+Chain 2:                0.427 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -570,8 +570,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 2.8e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.28 seconds.
+Chain 1: Gradient evaluation took 2.5e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
 Chain 1: Adjust your expectations accordingly!
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@@ -582,15 +582,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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+Chain 1:  Elapsed Time: 0.225 seconds (Warm-up)
+Chain 1:                0.205 seconds (Sampling)
+Chain 1:                0.43 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 2.2e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
+Chain 2: Gradient evaluation took 1.7e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
 Chain 2: Adjust your expectations accordingly!
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@@ -601,9 +601,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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-Chain 2:                0.259 seconds (Sampling)
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+Chain 2:  Elapsed Time: 0.215 seconds (Warm-up)
+Chain 2:                0.204 seconds (Sampling)
+Chain 2:                0.419 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -659,8 +659,8 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
 <pre><code>
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 2.6e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
+Chain 1: Gradient evaluation took 3.2e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.
 Chain 1: Adjust your expectations accordingly!
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@@ -677,15 +677,15 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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+Chain 1:  Elapsed Time: 0.227 seconds (Warm-up)
+Chain 1:                0.209 seconds (Sampling)
+Chain 1:                0.436 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
 Chain 2: 
-Chain 2: Gradient evaluation took 2.2e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.
+Chain 2: Gradient evaluation took 1.7e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
 Chain 2: Adjust your expectations accordingly!
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@@ -702,9 +702,9 @@ <h2 class="anchored" data-anchor-id="function-arguments">Function Arguments</h2>
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-Chain 2:  Elapsed Time: 0.259 seconds (Warm-up)
-Chain 2:                0.264 seconds (Sampling)
-Chain 2:                0.523 seconds (Total)
+Chain 2:  Elapsed Time: 0.21 seconds (Warm-up)
+Chain 2:                0.224 seconds (Sampling)
+Chain 2:                0.434 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -1029,8 +1029,8 @@ <h4 class="anchored" data-anchor-id="exercises-1">Exercises</h4>
 <pre><code>
 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
 Chain 1: 
-Chain 1: Gradient evaluation took 4.8e-05 seconds
-Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.48 seconds.
+Chain 1: Gradient evaluation took 6.8e-05 seconds
+Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.68 seconds.
 Chain 1: Adjust your expectations accordingly!
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+Chain 1:  Elapsed Time: 0.121 seconds (Warm-up)
+Chain 1:                0.14 seconds (Sampling)
+Chain 1:                0.261 seconds (Total)
 Chain 1: 
 
 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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-Chain 2: Gradient evaluation took 3.4e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.34 seconds.
+Chain 2: Gradient evaluation took 2.1e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.
 Chain 2: Adjust your expectations accordingly!
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+Chain 2:  Elapsed Time: 0.099 seconds (Warm-up)
+Chain 2:                0.14 seconds (Sampling)
+Chain 2:                0.239 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -1102,15 +1102,15 @@ <h4 class="anchored" data-anchor-id="exercises-1">Exercises</h4>
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+Chain 1:  Elapsed Time: 0.115 seconds (Warm-up)
+Chain 1:                0.12 seconds (Sampling)
+Chain 1:                0.235 seconds (Total)
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 SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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-Chain 2: Gradient evaluation took 1.2e-05 seconds
-Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.
+Chain 2: Gradient evaluation took 3.8e-05 seconds
+Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds.
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+Chain 2:  Elapsed Time: 0.122 seconds (Warm-up)
+Chain 2:                0.141 seconds (Sampling)
+Chain 2:                0.263 seconds (Total)
 Chain 2: </code></pre>
 </div>
 </details>
@@ -1359,15 +1359,15 @@ <h4 class="anchored" data-anchor-id="exercises-3">Exercises</h4>
 </details>
 </div>
 <p>3.&nbsp;Calculate the unadjusted (naive) estimates for comparison.</p>
-<p>To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let <span class="math inline">\(p_A\)</span> and <span class="math inline">\(p_{C(AC)}\)</span> be the raw probabilities of the event in the IPD trial, and let <span class="math inline">\(p_B\)</span> and <span class="math inline">\(p_{C(BC)}\)</span> be the raw probabilities in the ALD trial.</p>
+<p>To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let <span class="math inline">\(p_{A(AC)}\)</span> and <span class="math inline">\(p_{C(AC)}\)</span> be the raw probabilities of the event in the IPD trial, and let <span class="math inline">\(p_{B(BC)}\)</span> and <span class="math inline">\(p_{C(BC)}\)</span> be the raw probabilities in the ALD trial.</p>
 <ul>
 <li><strong>Naive Anchored Risk Difference:</strong> This assumes the relative effect is transportable without adjustment (the classic Bucher indirect comparison).</li>
 </ul>
-<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_A - p_{C(AC)}) - (p_B - p_{C(BC)})\]</span></p>
+<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_{A(AC)} - p_{C(AC)}) - (p_{B(BC)} - p_{C(BC)})\]</span></p>
 <ul>
 <li><strong>Naive Unanchored Risk Difference:</strong> This drops the common comparator entirely and assumes absolute exchangeability between the two isolated active arms.</li>
 </ul>
-<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_A - p_B\]</span></p>
+<p><span class="math display">\[\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_{A(AC)} - p_{B(BC)}\]</span></p>
 <div class="callout callout-style-default callout-warning callout-titled">
 <div class="callout-header d-flex align-content-center">
 <div class="callout-icon-container">
diff --git a/scripts/exercises2.qmd b/scripts/exercises2.qmd
index ae3bad7..49dce62 100644
--- a/scripts/exercises2.qmd
+++ b/scripts/exercises2.qmd
@@ -605,16 +605,16 @@ cat("Unanchored Risk Difference (A vs B):", round(unanchored_rd, 3), "\n")
 
 3.\ Calculate the unadjusted (naive) estimates for comparison.
 
-To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let $p_A$ and $p_{C(AC)}$ be the raw probabilities of the event in the IPD trial, and let $p_B$ and $p_{C(BC)}$ be the raw probabilities in the ALD trial.
+To see exactly how much our PAIC methods moved the needle, we will calculate the naive estimators. Let $p_{A(AC)}$ and $p_{C(AC)}$ be the raw probabilities of the event in the IPD trial, and let $p_{B(BC)}$ and $p_{C(BC)}$ be the raw probabilities in the ALD trial.
 
 * **Naive Anchored Risk Difference:** This assumes the relative effect is transportable without adjustment (the classic Bucher indirect comparison).
 
-$$\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_A - p_{C(AC)}) - (p_B - p_{C(BC)})$$
+$$\hat{\Delta}_{AB}^{\text{naive\_anchored}} = (p_{A(AC)} - p_{C(AC)}) - (p_{B(BC)} - p_{C(BC)})$$
 
 
 * **Naive Unanchored Risk Difference:** This drops the common comparator entirely and assumes absolute exchangeability between the two isolated active arms.
 
-$$\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_A - p_B$$
+$$\hat{\Delta}_{AB}^{\text{naive\_unanchored}} = p_{A(AC)} - p_{B(BC)}$$
 
 
 ::: {.callout-warning}
diff --git a/scripts/practical_paic.pdf b/scripts/practical_paic.pdf
index 67aee73..d516d0f 100644
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