diff --git a/examples/19_bayesian_sindy/example.ipynb b/examples/19_bayesian_sindy/example.ipynb
index 83a153e4b..00ea8f3f4 100644
--- a/examples/19_bayesian_sindy/example.ipynb
+++ b/examples/19_bayesian_sindy/example.ipynb
@@ -180,8 +180,8 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "sample: 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2500/2500 [00:02<00:00, 991.89it/s, 63 steps of size 5.70e-02. acc. prob=0.84]\n",
-      "sample: 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2500/2500 [00:01<00:00, 2170.87it/s, 63 steps of size 7.15e-02. acc. prob=0.81]\n"
+      "sample: 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2500/2500 [00:02<00:00, 937.32it/s, 63 steps of size 5.70e-02. acc. prob=0.84]\n",
+      "sample: 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2500/2500 [00:01<00:00, 2029.96it/s, 63 steps of size 7.15e-02. acc. prob=0.81]\n"
      ]
     },
     {
@@ -189,14 +189,19 @@
       "text/html": [
        "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SINDy(differentiation_method=FiniteDifference(),\n",
        "      feature_library=PolynomialLibrary(), feature_names=[&#x27;P&#x27;, &#x27;Q&#x27;],\n",
-       "      optimizer=SBR())</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SINDy</label><div class=\"sk-toggleable__content\"><pre>SINDy(differentiation_method=FiniteDifference(),\n",
+       "      optimizer=SBR(mcmc_kwargs={&#x27;num_chains&#x27;: 2, &#x27;seed&#x27;: 123},\n",
+       "                    num_samples=2000, num_warmup=500))</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SINDy</label><div class=\"sk-toggleable__content\"><pre>SINDy(differentiation_method=FiniteDifference(),\n",
        "      feature_library=PolynomialLibrary(), feature_names=[&#x27;P&#x27;, &#x27;Q&#x27;],\n",
-       "      optimizer=SBR())</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">feature_library: PolynomialLibrary</label><div class=\"sk-toggleable__content\"><pre>PolynomialLibrary()</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PolynomialLibrary</label><div class=\"sk-toggleable__content\"><pre>PolynomialLibrary()</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">optimizer: SBR</label><div class=\"sk-toggleable__content\"><pre>SBR()</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SBR</label><div class=\"sk-toggleable__content\"><pre>SBR()</pre></div></div></div></div></div></div></div></div></div></div>"
+       "      optimizer=SBR(mcmc_kwargs={&#x27;num_chains&#x27;: 2, &#x27;seed&#x27;: 123},\n",
+       "                    num_samples=2000, num_warmup=500))</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">feature_library: PolynomialLibrary</label><div class=\"sk-toggleable__content\"><pre>PolynomialLibrary()</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PolynomialLibrary</label><div class=\"sk-toggleable__content\"><pre>PolynomialLibrary()</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">optimizer: SBR</label><div class=\"sk-toggleable__content\"><pre>SBR(mcmc_kwargs={&#x27;num_chains&#x27;: 2, &#x27;seed&#x27;: 123}, num_samples=2000,\n",
+       "    num_warmup=500)</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SBR</label><div class=\"sk-toggleable__content\"><pre>SBR(mcmc_kwargs={&#x27;num_chains&#x27;: 2, &#x27;seed&#x27;: 123}, num_samples=2000,\n",
+       "    num_warmup=500)</pre></div></div></div></div></div></div></div></div></div></div>"
       ],
       "text/plain": [
        "SINDy(differentiation_method=FiniteDifference(),\n",
        "      feature_library=PolynomialLibrary(), feature_names=['P', 'Q'],\n",
-       "      optimizer=SBR())"
+       "      optimizer=SBR(mcmc_kwargs={'num_chains': 2, 'seed': 123},\n",
+       "                    num_samples=2000, num_warmup=500))"
       ]
      },
      "execution_count": 8,
@@ -206,7 +211,10 @@
    ],
    "source": [
     "# initialise the Sparse bayesian Regression optimizer.\n",
-    "optimizer = ps.optimizers.SBR(seed=sampling_seed, num_warmup=num_warmup, num_samples=num_samples, num_chains=num_chains)\n",
+    "optimizer = ps.optimizers.SBR(num_warmup=num_warmup,\n",
+    "                              num_samples=num_samples,\n",
+    "                              mcmc_kwargs={\"seed\": sampling_seed,\n",
+    "                                           \"num_chains\": num_chains})\n",
     "\n",
     "# use the standard polynomial features.\n",
     "feature_library = ps.feature_library.polynomial_library.PolynomialLibrary(include_interaction=True)\n",