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diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
diff --git a/.doctrees/examples/howto_custom_gradients.doctree b/.doctrees/examples/howto_custom_gradients.doctree
diff --git a/.doctrees/examples/howto_metropolis_within_gibbs.doctree b/.doctrees/examples/howto_metropolis_within_gibbs.doctree
diff --git a/.doctrees/examples/howto_sample_multiple_chains.doctree b/.doctrees/examples/howto_sample_multiple_chains.doctree
diff --git a/.doctrees/examples/howto_use_aesara.doctree b/.doctrees/examples/howto_use_aesara.doctree
diff --git a/.doctrees/examples/howto_use_numpyro.doctree b/.doctrees/examples/howto_use_numpyro.doctree
diff --git a/.doctrees/examples/howto_use_oryx.doctree b/.doctrees/examples/howto_use_oryx.doctree
diff --git a/.doctrees/examples/howto_use_pymc.doctree b/.doctrees/examples/howto_use_pymc.doctree
diff --git a/.doctrees/examples/howto_use_tfp.doctree b/.doctrees/examples/howto_use_tfp.doctree
diff --git a/.doctrees/examples/quickstart.doctree b/.doctrees/examples/quickstart.doctree
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diff --git a/_images/f0b15e37a33fda013d1cca4dda59efc1ce03c69565e6e53cb12602288e3b42cd.png b/_images/f0b15e37a33fda013d1cca4dda59efc1ce03c69565e6e53cb12602288e3b42cd.png
diff --git a/_images/f80189138a6f6471d4ac3aa9f0b9889f12d88b64611c022cf77914ce654b8ca8.png b/_images/f80189138a6f6471d4ac3aa9f0b9889f12d88b64611c022cf77914ce654b8ca8.png
diff --git a/_modules/blackjax/_version.html b/_modules/blackjax/_version.html
@@ -392,8 +392,8 @@ <h1>Source code for blackjax._version</h1><div class="highlight"><pre>
 <span class="n">version_tuple</span><span class="p">:</span> <span class="n">VERSION_TUPLE</span></div>
 
 
-<span class="n">__version__</span> <span class="o">=</span> <span class="n">version</span> <span class="o">=</span> <span class="s1">&#39;0.1.dev1+g2e25624&#39;</span>
-<span class="n">__version_tuple__</span> <span class="o">=</span> <span class="n">version_tuple</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;dev1&#39;</span><span class="p">,</span> <span class="s1">&#39;g2e25624&#39;</span><span class="p">)</span>
+<span class="n">__version__</span> <span class="o">=</span> <span class="n">version</span> <span class="o">=</span> <span class="s1">&#39;0.1.dev1+gf77297f&#39;</span>
+<span class="n">__version_tuple__</span> <span class="o">=</span> <span class="n">version_tuple</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;dev1&#39;</span><span class="p">,</span> <span class="s1">&#39;gf77297f&#39;</span><span class="p">)</span>
 </pre></div>
 
                 </article>

diff --git a/_modules/blackjax/mcmc/mala.html b/_modules/blackjax/mcmc/mala.html
@@ -474,14 +474,14 @@ <h1>Source code for blackjax.mcmc.mala</h1><div class="highlight"><pre>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;Transition energy to go from `state` to `new_state`&quot;&quot;&quot;</span>
         <span class="n">theta</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">tree_util</span><span class="o">.</span><span class="n">tree_map</span><span class="p">(</span>
             <span class="k">lambda</span> <span class="n">new_x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">g</span><span class="p">:</span> <span class="n">new_x</span> <span class="o">-</span> <span class="n">x</span> <span class="o">-</span> <span class="n">step_size</span> <span class="o">*</span> <span class="n">g</span><span class="p">,</span>
-            <span class="n">new_state</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
             <span class="n">state</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
-            <span class="n">state</span><span class="o">.</span><span class="n">logdensity_grad</span><span class="p">,</span>
+            <span class="n">new_state</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+            <span class="n">new_state</span><span class="o">.</span><span class="n">logdensity_grad</span><span class="p">,</span>
         <span class="p">)</span>
         <span class="n">theta_dot</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">tree_util</span><span class="o">.</span><span class="n">tree_reduce</span><span class="p">(</span>
             <span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="n">jax</span><span class="o">.</span><span class="n">tree_util</span><span class="o">.</span><span class="n">tree_map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span> <span class="o">*</span> <span class="n">x</span><span class="p">),</span> <span class="n">theta</span><span class="p">)</span>
         <span class="p">)</span>
-        <span class="k">return</span> <span class="o">-</span><span class="n">state</span><span class="o">.</span><span class="n">logdensity</span> <span class="o">+</span> <span class="mf">0.25</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="n">step_size</span><span class="p">)</span> <span class="o">*</span> <span class="n">theta_dot</span>
+        <span class="k">return</span> <span class="o">-</span><span class="n">new_state</span><span class="o">.</span><span class="n">logdensity</span> <span class="o">+</span> <span class="mf">0.25</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="n">step_size</span><span class="p">)</span> <span class="o">*</span> <span class="n">theta_dot</span>
 
     <span class="n">compute_acceptance_ratio</span> <span class="o">=</span> <span class="n">proposal</span><span class="o">.</span><span class="n">compute_asymmetric_acceptance_ratio</span><span class="p">(</span>
         <span class="n">transition_energy</span>

diff --git a/examples/howto_custom_gradients.html b/examples/howto_custom_gradients.html
@@ -599,7 +599,7 @@ <h3>Using the function with Blackjax<a class="headerlink" href="#using-the-funct
 </div>
 <div class="cell_output docutils container">
 <div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(HMCState(position=1.0, logdensity=Array(-2.5600991, dtype=float32), logdensity_grad=Array(-1.6666666, dtype=float32, weak_type=True)),
- HMCState(position=Array(0.9531961, dtype=float32, weak_type=True), logdensity=Array(-2.4846258, dtype=float32), logdensity_grad=Array(-1.5589187, dtype=float32, weak_type=True)))
+ HMCState(position=Array(1.1598474, dtype=float32, weak_type=True), logdensity=Array(-2.8572288, dtype=float32), logdensity_grad=Array(-2.056678, dtype=float32, weak_type=True)))
 </pre></div>
 </div>
 </div>

diff --git a/examples/howto_metropolis_within_gibbs.html b/examples/howto_metropolis_within_gibbs.html
@@ -604,8 +604,8 @@ <h3>Sampling<a class="headerlink" href="#sampling" title="Link to this heading">
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 1.02 s, sys: 42.3 ms, total: 1.07 s
-Wall time: 1.06 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 989 ms, sys: 56.6 ms, total: 1.05 s
+Wall time: 1.04 s
 </pre></div>
 </div>
 </div>
@@ -622,7 +622,7 @@ <h3>Sampling<a class="headerlink" href="#sampling" title="Link to this heading">
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/cc20028e15ba133a86e7140835df37f6b059d7f05048f317caaa3681b7907115.png" src="../_images/cc20028e15ba133a86e7140835df37f6b059d7f05048f317caaa3681b7907115.png" />
+<img alt="../_images/13d5c13f6cec000a8193e6e8445f38dcb5d83ee4133dce93c5358f01bb9630ef.png" src="../_images/13d5c13f6cec000a8193e6e8445f38dcb5d83ee4133dce93c5358f01bb9630ef.png" />
 </div>
 </div>
 </section>
@@ -743,7 +743,7 @@ <h3>Sampling<a class="headerlink" href="#id2" title="Link to this heading">#</a>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 683 ms, sys: 45 ms, total: 728 ms
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 684 ms, sys: 45.4 ms, total: 729 ms
 Wall time: 719 ms
 </pre></div>
 </div>

diff --git a/examples/howto_sample_multiple_chains.html b/examples/howto_sample_multiple_chains.html
@@ -524,8 +524,8 @@ <h3>Using <code class="docutils literal notranslate"><span class="pre">jax.vmap<
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 15.2 s, sys: 455 ms, total: 15.7 s
-Wall time: 15.7 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16 s, sys: 400 ms, total: 16.4 s
+Wall time: 16.4 s
 </pre></div>
 </div>
 </div>
@@ -629,8 +629,8 @@ <h3>Back to our example<a class="headerlink" href="#back-to-our-example" title="
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17.6 s, sys: 76 ms, total: 17.7 s
-Wall time: 5.56 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17.7 s, sys: 72.2 ms, total: 17.8 s
+Wall time: 5.52 s
 </pre></div>
 </div>
 </div>

diff --git a/examples/howto_use_aesara.html b/examples/howto_use_aesara.html
@@ -655,7 +655,7 @@ <h1>Use with Aesara models<a class="headerlink" href="#use-with-aesara-models" t
                |Elemwise{sigmoid,no_inplace} [id FD]
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;ipykernel.iostream.OutStream at 0x7f74aded2a10&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;ipykernel.iostream.OutStream at 0x7fee00c16a10&gt;
 </pre></div>
 </div>
 </div>
@@ -757,7 +757,7 @@ <h1>Use with Aesara models<a class="headerlink" href="#use-with-aesara-models" t
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/0b146ca8344f773ba53810750be12a0ee25d27b9abe196471c24ff1b06797211.png" src="../_images/0b146ca8344f773ba53810750be12a0ee25d27b9abe196471c24ff1b06797211.png" />
+<img alt="../_images/d19226a9b8f4bd051db6626e278ec5aa66eede0999094b857213dbb28b9fc3d6.png" src="../_images/d19226a9b8f4bd051db6626e278ec5aa66eede0999094b857213dbb28b9fc3d6.png" />
 </div>
 </div>
 </section>

diff --git a/examples/howto_use_numpyro.html b/examples/howto_use_numpyro.html
@@ -551,7 +551,7 @@ <h1>Use with Numpyro models<a class="headerlink" href="#use-with-numpyro-models"
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/7f7087dd38e60bc0edd4a8410d4a550169bb9870915c11e9a38184155b87d5e3.png" src="../_images/7f7087dd38e60bc0edd4a8410d4a550169bb9870915c11e9a38184155b87d5e3.png" />
+<img alt="../_images/a02c81303d82dbd17a34f018fe934fca691597366aac63e76bc933ce50f28bd3.png" src="../_images/a02c81303d82dbd17a34f018fe934fca691597366aac63e76bc933ce50f28bd3.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -562,7 +562,7 @@ <h1>Use with Numpyro models<a class="headerlink" href="#use-with-numpyro-models"
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/318b778dd6384c8cf7e36c0d008ddb19bc87185747bc5fb556e414aad14c00b7.png" src="../_images/318b778dd6384c8cf7e36c0d008ddb19bc87185747bc5fb556e414aad14c00b7.png" />
+<img alt="../_images/c0de261caa00fa89da1ef84ef9a0ad6809d6c229290f7f37f7d128643cb637d4.png" src="../_images/c0de261caa00fa89da1ef84ef9a0ad6809d6c229290f7f37f7d128643cb637d4.png" />
 </div>
 </div>
 <div class="cell tag_hide-input docutils container">
@@ -581,14 +581,14 @@ <h1>Use with Numpyro models<a class="headerlink" href="#use-with-numpyro-models"
 </div>
 </details>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Relative treatment effect for school 0: 0.25
-Relative treatment effect for school 1: -0.19
-Relative treatment effect for school 2: -0.24
-Relative treatment effect for school 3: 0.11
-Relative treatment effect for school 4: -0.02
-Relative treatment effect for school 5: -0.07
-Relative treatment effect for school 6: 0.33
-Relative treatment effect for school 7: 0.04
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Relative treatment effect for school 0: 0.13
+Relative treatment effect for school 1: -0.17
+Relative treatment effect for school 2: 0.05
+Relative treatment effect for school 3: -0.59
+Relative treatment effect for school 4: 0.28
+Relative treatment effect for school 5: 0.61
+Relative treatment effect for school 6: 0.64
+Relative treatment effect for school 7: -0.08
 </pre></div>
 </div>
 </div>

diff --git a/examples/howto_use_oryx.html b/examples/howto_use_oryx.html
@@ -546,8 +546,8 @@ <h1>Use with Oryx models<a class="headerlink" href="#use-with-oryx-models" title
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17.3 s, sys: 451 ms, total: 17.7 s
-Wall time: 17.7 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17.6 s, sys: 487 ms, total: 18.1 s
+Wall time: 18 s
 </pre></div>
 </div>
 </div>
@@ -584,7 +584,7 @@ <h1>Use with Oryx models<a class="headerlink" href="#use-with-oryx-models" title
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16.6 s, sys: 191 ms, total: 16.8 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16.6 s, sys: 158 ms, total: 16.8 s
 Wall time: 16.7 s
 </pre></div>
 </div>
@@ -626,7 +626,7 @@ <h1>Use with Oryx models<a class="headerlink" href="#use-with-oryx-models" title
 </div>
 </details>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Average sample accuracy: 0.9798667
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Average sample accuracy: 0.97933334
 BMA accuracy: 0.9866667
 </pre></div>
 </div>

diff --git a/examples/howto_use_pymc.html b/examples/howto_use_pymc.html
@@ -511,7 +511,7 @@ <h1>Use with PyMC models<a class="headerlink" href="#use-with-pymc-models" title
 </div>
 </details>
 <div class="cell_output docutils container">
-<img alt="../_images/69b7297268b4a8493bfd9f7fe56ed57cd5b7dabbd5b8d05e65e01f7e24f8c533.png" src="../_images/69b7297268b4a8493bfd9f7fe56ed57cd5b7dabbd5b8d05e65e01f7e24f8c533.png" />
+<img alt="../_images/0eb870545e1f4aee1e26e67fafe332d5175667aba24cd68d30c2c5857a5b16a9.png" src="../_images/0eb870545e1f4aee1e26e67fafe332d5175667aba24cd68d30c2c5857a5b16a9.png" />
 </div>
 </div>
 </section>

diff --git a/examples/howto_use_tfp.html b/examples/howto_use_tfp.html
@@ -508,7 +508,7 @@ <h1>Use with TFP models<a class="headerlink" href="#use-with-tfp-models" title="
 </div>
 </details>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Average acceptance rate: 0.91
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Average acceptance rate: 0.93
 </pre></div>
 </div>
 </div>
@@ -544,7 +544,7 @@ <h1>Use with TFP models<a class="headerlink" href="#use-with-tfp-models" title="
 </div>
 </details>
 <div class="cell_output docutils container">
-<img alt="../_images/b6f5fe414d43168a59413a259250981abca237d5a43cfa9f63733de71269a9fa.png" src="../_images/b6f5fe414d43168a59413a259250981abca237d5a43cfa9f63733de71269a9fa.png" />
+<img alt="../_images/91458952ba9962c23aa243e3ede0008ebb1d18b485e759a5333b21273e702494.png" src="../_images/91458952ba9962c23aa243e3ede0008ebb1d18b485e759a5333b21273e702494.png" />
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