diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index e9eb196d..433182ab 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -25,6 +25,12 @@ jobs:
         with:
           python-version: ${{ matrix.python-version }}
 
+        # Clean python cache files
+      - name: Clean cache files
+        run: |
+          find . -type f -name "*.pyc" -delete
+          find . -type d -name "__pycache__" -delete
+          rm -f .coverage* coverage.xml
       # Cache Poetry dependencies
       # - name: Cache dependencies
       #   uses: actions/cache@v2
@@ -56,10 +62,15 @@ jobs:
         run: |
           poetry run python -c "import torch; print(torch.__version__); print('CUDA available:', torch.cuda.is_available())"
       
+      - name: Debug Coverage Config
+        run: |
+          cat pyproject.toml
+          poetry run coverage debug config
+
       - name: Run Tests with Coverage
         run: |
-          poetry run coverage run -m pytest
-          poetry run coverage xml -o coverage.xml
+          poetry run coverage run --source=. -m pytest
+          poetry run coverage xml -i -o coverage.xml
         env: 
           COVERAGE_FILE: ".coverage.${{ matrix.python-version }}"
 
diff --git a/.gitignore b/.gitignore
index 87b71f6b..25755c20 100644
--- a/.gitignore
+++ b/.gitignore
@@ -27,4 +27,8 @@ Thumbs.db
 *.DS_Store
 
 # VScode settings
-.vscode/
\ No newline at end of file
+.vscode/
+
+# Quarto
+README.html
+README_files/
\ No newline at end of file
diff --git a/README.md b/README.md
index e9e6e192..37d10f89 100644
--- a/README.md
+++ b/README.md
@@ -22,7 +22,7 @@ There's currently a lot of development, so we recommend installing the most curr
 pip install git+https://github.com/alan-turing-institute/autoemulate.git
 ```
 
-There's also a release available on PyPI (will not contain the most recent features and models)
+There's also a release available on PyPI (note: currently and older version and out of date with the documentation)
 ```bash
 pip install autoemulate
 ```
@@ -47,19 +47,27 @@ from autoemulate.simulations.projectile import simulate_projectile
 lhd = LatinHypercube([(-5., 1.), (0., 1000.)])
 X = lhd.sample(100)
 y = np.array([simulate_projectile(x) for x in X])
+
 # compare emulator models
 ae = AutoEmulate()
 ae.setup(X, y)
-best_model = ae.compare() 
+best_emulator = ae.compare() 
+
 # training set cross-validation results
 ae.summarise_cv() 
 ae.plot_cv()
+
 # test set results for the best model
-ae.evaluate(best_model) 
-ae.plot_eval(best_model)
+ae.evaluate(best_emulator) 
+ae.plot_eval(best_emulator)
+
 # refit on full data and emulate!
-best_model = ae.refit(best_model) 
-best_model.predict(X)
+emulator = ae.refit(best_emulator) 
+emulator.predict(X)
+
+# global sensitivity analysis
+si = ae.sensitivity_analysis(emulator)
+ae.plot_sensitivity_analysis(si)
 ```
 
 ## documentation
diff --git a/autoemulate/compare.py b/autoemulate/compare.py
index 7307ef03..f4b596e9 100644
--- a/autoemulate/compare.py
+++ b/autoemulate/compare.py
@@ -20,6 +20,9 @@
 from autoemulate.plotting import _plot_model
 from autoemulate.printing import _print_setup
 from autoemulate.save import ModelSerialiser
+from autoemulate.sensitivity_analysis import plot_sensitivity_analysis
+from autoemulate.sensitivity_analysis import sensitivity_analysis
+from autoemulate.utils import _ensure_2d
 from autoemulate.utils import _get_full_model_name
 from autoemulate.utils import _redirect_warnings
 from autoemulate.utils import get_model_name
@@ -522,3 +525,64 @@ def plot_eval(
         )
 
         return fig
+
+    def sensitivity_analysis(
+        self, model=None, problem=None, N=1024, conf_level=0.95, as_df=True
+    ):
+        """Perform Sobol sensitivity analysis on a fitted emulator.
+
+        Parameters
+        ----------
+        model : object, optional
+            Fitted model. If None, uses the best model from cross-validation.
+        problem : dict, optional
+            The problem definition, including 'num_vars', 'names', and 'bounds', optional 'output_names'.
+            If None, the problem is generated from X using minimum and maximum values of the features as bounds.
+
+            Example:
+                ```python
+                problem = {
+                    "num_vars": 2,
+                    "names": ["x1", "x2"],
+                    "bounds": [[0, 1], [0, 1]],
+                }
+                ```
+        N : int, optional
+            Number of samples to generate. Default is 1024.
+        conf_level : float, optional
+            Confidence level for the confidence intervals. Default is 0.95.
+        as_df : bool, optional
+            If True, return a long-format pandas DataFrame (default is True).
+        """
+        if model is None:
+            if not hasattr(self, "best_model"):
+                raise RuntimeError("Must run compare() before sensitivity_analysis()")
+            model = self.refit(self.best_model)
+            self.logger.info(
+                f"No model provided, using {get_model_name(model)}, which had the highest average cross-validation score, refitted on full data."
+            )
+
+        Si = sensitivity_analysis(model, problem, self.X, N, conf_level, as_df)
+        return Si
+
+    def plot_sensitivity_analysis(self, results, index="S1", n_cols=None, figsize=None):
+        """
+        Plot the sensitivity analysis results.
+
+        Parameters:
+        -----------
+        results : pd.DataFrame
+            The results from sobol_results_to_df.
+        index : str, default "S1"
+            The type of sensitivity index to plot.
+            - "S1": first-order indices
+            - "S2": second-order/interaction indices
+            - "ST": total-order indices
+        n_cols : int, optional
+            The number of columns in the plot. Defaults to 3 if there are 3 or more outputs,
+            otherwise the number of outputs.
+        figsize : tuple, optional
+            Figure size as (width, height) in inches.If None, automatically calculated.
+
+        """
+        return plot_sensitivity_analysis(results, index, n_cols, figsize)
diff --git a/autoemulate/sensitivity_analysis.py b/autoemulate/sensitivity_analysis.py
new file mode 100644
index 00000000..846d0e31
--- /dev/null
+++ b/autoemulate/sensitivity_analysis.py
@@ -0,0 +1,304 @@
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from SALib.analyze.sobol import analyze
+from SALib.sample.sobol import sample
+
+from autoemulate.utils import _ensure_2d
+
+
+def sensitivity_analysis(
+    model, problem=None, X=None, N=1024, conf_level=0.95, as_df=True
+):
+    """Perform Sobol sensitivity analysis on a fitted emulator.
+
+    Parameters:
+    -----------
+    model : fitted emulator model
+        The emulator model to analyze.
+    problem : dict
+        The problem definition, including 'num_vars', 'names', and 'bounds', optional 'output_names'.
+        Example:
+        ```python
+        problem = {
+            "num_vars": 2,
+            "names": ["x1", "x2"],
+            "bounds": [[0, 1], [0, 1]],
+        }
+        ```
+    N : int, optional
+        The number of samples to generate (default is 1024).
+    conf_level : float, optional
+        The confidence level for the confidence intervals (default is 0.95).
+    as_df : bool, optional
+        If True, return a pandas DataFrame (default is True).
+
+    Returns:
+    --------
+    pd.DataFrame or dict
+        If as_df is True, returns a long-format DataFrame with the sensitivity indices.
+        Otherwise, returns a dictionary where each key is the name of an output variable and each value is a dictionary
+        containing the Sobol indices keys ‘S1’, ‘S1_conf’, ‘ST’, and ‘ST_conf’, where each entry
+        is a list of length corresponding to the number of parameters.
+    """
+    Si = sobol_analysis(model, problem, X, N, conf_level)
+
+    if as_df:
+        return sobol_results_to_df(Si)
+    else:
+        return Si
+
+
+def _check_problem(problem):
+    """
+    Check that the problem definition is valid.
+    """
+    if not isinstance(problem, dict):
+        raise ValueError("problem must be a dictionary.")
+
+    if "num_vars" not in problem:
+        raise ValueError("problem must contain 'num_vars'.")
+    if "names" not in problem:
+        raise ValueError("problem must contain 'names'.")
+    if "bounds" not in problem:
+        raise ValueError("problem must contain 'bounds'.")
+
+    if len(problem["names"]) != problem["num_vars"]:
+        raise ValueError("Length of 'names' must match 'num_vars'.")
+    if len(problem["bounds"]) != problem["num_vars"]:
+        raise ValueError("Length of 'bounds' must match 'num_vars'.")
+
+    return problem
+
+
+def _get_output_names(problem, num_outputs):
+    """
+    Get the output names from the problem definition or generate default names.
+    """
+    # check if output_names is given
+    if "output_names" not in problem:
+        output_names = [f"y{i+1}" for i in range(num_outputs)]
+    else:
+        if isinstance(problem["output_names"], list):
+            output_names = problem["output_names"]
+        else:
+            raise ValueError("'output_names' must be a list of strings.")
+
+    return output_names
+
+
+def _generate_problem(X):
+    """
+    Generate a problem definition from a design matrix.
+    """
+    if X.ndim == 1:
+        raise ValueError("X must be a 2D array.")
+
+    return {
+        "num_vars": X.shape[1],
+        "names": [f"x{i+1}" for i in range(X.shape[1])],
+        "bounds": [[X[:, i].min(), X[:, i].max()] for i in range(X.shape[1])],
+    }
+
+
+def sobol_analysis(model, problem=None, X=None, N=1024, conf_level=0.95):
+    """
+    Perform Sobol sensitivity analysis on a fitted emulator.
+
+    Parameters:
+    -----------
+    model : fitted emulator model
+        The emulator model to analyze.
+    problem : dict
+        The problem definition, including 'num_vars', 'names', and 'bounds'.
+    N : int, optional
+        The number of samples to generate (default is 1000).
+
+    Returns:
+    --------
+    dict
+        A dictionary where each key is the name of an output variable and each value is a dictionary
+        containing the Sobol indices keys ‘S1’, ‘S1_conf’, ‘ST’, and ‘ST_conf’, where each entry
+        is a list of length corresponding to the number of parameters.
+    """
+    # get problem
+    if problem is not None:
+        problem = _check_problem(problem)
+    elif X is not None:
+        problem = _generate_problem(X)
+    else:
+        raise ValueError("Either problem or X must be provided.")
+
+    # saltelli sampling
+    param_values = sample(problem, N)
+
+    # evaluate
+    Y = model.predict(param_values)
+    Y = _ensure_2d(Y)
+
+    num_outputs = Y.shape[1]
+    output_names = _get_output_names(problem, num_outputs)
+
+    # single or multiple output sobol analysis
+    results = {}
+    for i in range(num_outputs):
+        Si = analyze(problem, Y[:, i], conf_level=conf_level)
+        results[output_names[i]] = Si
+
+    return results
+
+
+def sobol_results_to_df(results):
+    """
+    Convert Sobol results to a (long-format)pandas DataFrame.
+
+    Parameters:
+    -----------
+    results : dict
+        The Sobol indices returned by sobol_analysis.
+
+    Returns:
+    --------
+    pd.DataFrame
+        A DataFrame with columns: 'output', 'parameter', 'index', 'value', 'confidence'.
+    """
+    rows = []
+    for output, indices in results.items():
+        for index_type in ["S1", "ST", "S2"]:
+            values = indices.get(index_type)
+            conf_values = indices.get(f"{index_type}_conf")
+            if values is None or conf_values is None:
+                continue
+
+            if index_type in ["S1", "ST"]:
+                rows.extend(
+                    {
+                        "output": output,
+                        "parameter": f"X{i+1}",
+                        "index": index_type,
+                        "value": value,
+                        "confidence": conf,
+                    }
+                    for i, (value, conf) in enumerate(zip(values, conf_values))
+                )
+
+            elif index_type == "S2":
+                n = values.shape[0]
+                rows.extend(
+                    {
+                        "output": output,
+                        "parameter": f"X{i+1}-X{j+1}",
+                        "index": index_type,
+                        "value": values[i, j],
+                        "confidence": conf_values[i, j],
+                    }
+                    for i in range(n)
+                    for j in range(i + 1, n)
+                    if not np.isnan(values[i, j])
+                )
+
+    return pd.DataFrame(rows)
+
+
+# plotting --------------------------------------------------------------------
+
+
+def _validate_input(results, index):
+    if not isinstance(results, pd.DataFrame):
+        results = sobol_results_to_df(results)
+        # we only want to plot one index type at a time
+    valid_indices = ["S1", "S2", "ST"]
+    if index not in valid_indices:
+        raise ValueError(
+            f"Invalid index type: {index}. Must be one of {valid_indices}."
+        )
+    return results[results["index"].isin([index])]
+
+
+def _calculate_layout(n_outputs, n_cols=None):
+    if n_cols is None:
+        n_cols = 3 if n_outputs >= 3 else n_outputs
+    n_rows = int(np.ceil(n_outputs / n_cols))
+    return n_rows, n_cols
+
+
+def _create_bar_plot(ax, output_data, output_name):
+    """Create a bar plot for a single output."""
+    bar_color = "#4C4B63"
+    x_pos = np.arange(len(output_data))
+
+    bars = ax.bar(
+        x_pos,
+        output_data["value"],
+        color=bar_color,
+        yerr=output_data["confidence"].values / 2,
+        capsize=3,
+    )
+
+    ax.set_xticks(x_pos)
+    ax.set_xticklabels(output_data["parameter"], rotation=45, ha="right")
+    ax.set_ylabel("Sobol Index")
+    ax.set_title(f"Output: {output_name}")
+
+
+def plot_sensitivity_analysis(results, index="S1", n_cols=None, figsize=None):
+    """
+    Plot the sensitivity analysis results.
+
+    Parameters:
+    -----------
+    results : pd.DataFrame
+        The results from sobol_results_to_df.
+    index : str, default "S1"
+        The type of sensitivity index to plot.
+        - "S1": first-order indices
+        - "S2": second-order/interaction indices
+        - "ST": total-order indices
+    n_cols : int, optional
+        The number of columns in the plot. Defaults to 3 if there are 3 or more outputs,
+        otherwise the number of outputs.
+    figsize : tuple, optional
+        Figure size as (width, height) in inches.If None, automatically calculated.
+
+    """
+    with plt.style.context("fast"):
+        # prepare data
+        results = _validate_input(results, index)
+        unique_outputs = results["output"].unique()
+        n_outputs = len(unique_outputs)
+
+        # layout
+        n_rows, n_cols = _calculate_layout(n_outputs, n_cols)
+        figsize = figsize or (4.5 * n_cols, 4 * n_rows)
+
+        fig, axes = plt.subplots(n_rows, n_cols, figsize=figsize)
+        if isinstance(axes, np.ndarray):
+            axes = axes.flatten()
+        elif n_outputs == 1:
+            axes = [axes]
+
+        for ax, output in zip(axes, unique_outputs):
+            output_data = results[results["output"] == output]
+            _create_bar_plot(ax, output_data, output)
+
+        # remove any empty subplots
+        for idx in range(len(unique_outputs), len(axes)):
+            fig.delaxes(axes[idx])
+
+        index_names = {
+            "S1": "First-Order",
+            "S2": "Second-order/Interaction",
+            "ST": "Total-Order",
+        }
+
+        # title
+        fig.suptitle(
+            f"{index_names[index]} indices and 95% CI",
+            fontsize=14,
+        )
+
+        plt.tight_layout()
+        # prevent double plotting in notebooks
+        plt.close(fig)
+
+    return fig
diff --git a/poetry.lock b/poetry.lock
index 56e95794..34dd0522 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -446,63 +446,73 @@ test-no-images = ["pytest", "pytest-cov", "pytest-xdist", "wurlitzer"]
 
 [[package]]
 name = "coverage"
-version = "7.4.3"
+version = "7.6.4"
 description = "Code coverage measurement for Python"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
 files = [
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 [package.dependencies]
@@ -568,6 +578,21 @@ files = [
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 ]
 
+[[package]]
+name = "dill"
+version = "0.3.9"
+description = "serialize all of Python"
+optional = false
+python-versions = ">=3.8"
+files = [
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+]
+
+[package.extras]
+graph = ["objgraph (>=1.7.2)"]
+profile = ["gprof2dot (>=2022.7.29)"]
+
 [[package]]
 name = "distlib"
 version = "0.3.8"
@@ -1679,6 +1704,34 @@ docs = ["sphinx"]
 gmpy = ["gmpy2 (>=2.1.0a4)"]
 tests = ["pytest (>=4.6)"]
 
+[[package]]
+name = "multiprocess"
+version = "0.70.17"
+description = "better multiprocessing and multithreading in Python"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "multiprocess-0.70.17-pp310-pypy310_pp73-macosx_10_15_x86_64.whl", hash = "sha256:7ddb24e5bcdb64e90ec5543a1f05a39463068b6d3b804aa3f2a4e16ec28562d6"},
+    {file = "multiprocess-0.70.17-pp310-pypy310_pp73-macosx_11_0_arm64.whl", hash = "sha256:d729f55198a3579f6879766a6d9b72b42d4b320c0dcb7844afb774d75b573c62"},
+    {file = "multiprocess-0.70.17-pp310-pypy310_pp73-manylinux_2_28_x86_64.whl", hash = "sha256:c2c82d0375baed8d8dd0d8c38eb87c5ae9c471f8e384ad203a36f095ee860f67"},
+    {file = "multiprocess-0.70.17-pp38-pypy38_pp73-macosx_10_9_arm64.whl", hash = "sha256:a22a6b1a482b80eab53078418bb0f7025e4f7d93cc8e1f36481477a023884861"},
+    {file = "multiprocess-0.70.17-pp38-pypy38_pp73-macosx_10_9_x86_64.whl", hash = "sha256:349525099a0c9ac5936f0488b5ee73199098dac3ac899d81d326d238f9fd3ccd"},
+    {file = "multiprocess-0.70.17-pp38-pypy38_pp73-manylinux_2_28_x86_64.whl", hash = "sha256:27b8409c02b5dd89d336107c101dfbd1530a2cd4fd425fc27dcb7adb6e0b47bf"},
+    {file = "multiprocess-0.70.17-pp39-pypy39_pp73-macosx_10_13_arm64.whl", hash = "sha256:2ea0939b0f4760a16a548942c65c76ff5afd81fbf1083c56ae75e21faf92e426"},
+    {file = "multiprocess-0.70.17-pp39-pypy39_pp73-macosx_10_13_x86_64.whl", hash = "sha256:2b12e081df87ab755190e227341b2c3b17ee6587e9c82fecddcbe6aa812cd7f7"},
+    {file = "multiprocess-0.70.17-pp39-pypy39_pp73-manylinux_2_28_x86_64.whl", hash = "sha256:a0f01cd9d079af7a8296f521dc03859d1a414d14c1e2b6e676ef789333421c95"},
+    {file = "multiprocess-0.70.17-py310-none-any.whl", hash = "sha256:38357ca266b51a2e22841b755d9a91e4bb7b937979a54d411677111716c32744"},
+    {file = "multiprocess-0.70.17-py311-none-any.whl", hash = "sha256:2884701445d0177aec5bd5f6ee0df296773e4fb65b11903b94c613fb46cfb7d1"},
+    {file = "multiprocess-0.70.17-py312-none-any.whl", hash = "sha256:2818af14c52446b9617d1b0755fa70ca2f77c28b25ed97bdaa2c69a22c47b46c"},
+    {file = "multiprocess-0.70.17-py313-none-any.whl", hash = "sha256:20c28ca19079a6c879258103a6d60b94d4ffe2d9da07dda93fb1c8bc6243f522"},
+    {file = "multiprocess-0.70.17-py38-none-any.whl", hash = "sha256:1d52f068357acd1e5bbc670b273ef8f81d57863235d9fbf9314751886e141968"},
+    {file = "multiprocess-0.70.17-py39-none-any.whl", hash = "sha256:c3feb874ba574fbccfb335980020c1ac631fbf2a3f7bee4e2042ede62558a021"},
+    {file = "multiprocess-0.70.17.tar.gz", hash = "sha256:4ae2f11a3416809ebc9a48abfc8b14ecce0652a0944731a1493a3c1ba44ff57a"},
+]
+
+[package.dependencies]
+dill = ">=0.3.9"
+
 [[package]]
 name = "mypy-extensions"
 version = "1.0.0"
@@ -2901,6 +2954,30 @@ files = [
     {file = "rpds_py-0.18.0.tar.gz", hash = "sha256:42821446ee7a76f5d9f71f9e33a4fb2ffd724bb3e7f93386150b61a43115788d"},
 ]
 
+[[package]]
+name = "salib"
+version = "1.5.1"
+description = "Tools for global sensitivity analysis. Contains Sobol', Morris, FAST, DGSM, PAWN, HDMR, Moment Independent and fractional factorial methods"
+optional = false
+python-versions = ">=3.9"
+files = [
+    {file = "salib-1.5.1-py3-none-any.whl", hash = "sha256:a978b619c5a93eb14dd8c527f12e22d354b02f1f7143aba3cb84c1c7bc1382e5"},
+    {file = "salib-1.5.1.tar.gz", hash = "sha256:e4a9c319b8dd02995a8dc983f57c452cb7e5b6dbd43e7b7856c90cb6a332bb5f"},
+]
+
+[package.dependencies]
+matplotlib = ">=3.5"
+multiprocess = "*"
+numpy = ">=1.20.3"
+pandas = ">=2.0"
+scipy = ">=1.9.3"
+
+[package.extras]
+dev = ["hatch", "myst-parser", "numpydoc", "pathos (>=0.3.2)", "pre-commit", "pydata-sphinx-theme (>=0.15.2)", "pytest", "pytest-cov", "sphinx"]
+distributed = ["pathos (>=0.3.2)"]
+doc = ["myst-parser", "numpydoc", "pydata-sphinx-theme (>=0.15.2)", "sphinx"]
+test = ["pathos (>=0.3.2)", "pytest", "pytest-cov"]
+
 [[package]]
 name = "scikit-learn"
 version = "1.4.1.post1"
@@ -3920,4 +3997,4 @@ docs = []
 [metadata]
 lock-version = "2.0"
 python-versions = ">=3.10,<3.13"
-content-hash = "4ca19f29dda8b99a25194547084293b75b74107e44e6b43663104cbf1ab18ba9"
+content-hash = "7a6830c251b5aef183659d85f7eae56e380f37fed39a2bd6aa370a249233a3f5"
diff --git a/pyproject.toml b/pyproject.toml
index adc351c5..652012a7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -27,6 +27,7 @@ iprogress = "^0.4"
 lightgbm = "^4.3.0"
 ipywidgets = "^8.1.2"
 gpytorch = "^1.12"
+salib = "^1.5.1"
 
 
 [tool.poetry.group.dev.dependencies]
@@ -41,7 +42,7 @@ black = "^23.10.1"
 pre-commit = "^3.5.0"
 jupyter-book = "^1.0.0"
 pytest-cov = "^4.1.0"
-coverage = "^7.3.1"
+coverage = "^7.6.4"
 plotnine = "^0.13.6"
 
 
@@ -55,4 +56,8 @@ requires = ["poetry-core"]
 build-backend = "poetry.core.masonry.api"
 
 [tool.coverage.run]
-relative_files = true
\ No newline at end of file
+relative_files = true
+source = [
+    ".",
+    "/tmp"
+]
\ No newline at end of file
diff --git a/tests/test_sensitivity_analysis.py b/tests/test_sensitivity_analysis.py
new file mode 100644
index 00000000..db01adeb
--- /dev/null
+++ b/tests/test_sensitivity_analysis.py
@@ -0,0 +1,206 @@
+import numpy as np
+import pandas as pd
+import pytest
+from sklearn.datasets import make_regression
+
+from autoemulate.emulators import RandomForest
+from autoemulate.experimental_design import LatinHypercube
+from autoemulate.sensitivity_analysis import _calculate_layout
+from autoemulate.sensitivity_analysis import _check_problem
+from autoemulate.sensitivity_analysis import _generate_problem
+from autoemulate.sensitivity_analysis import _get_output_names
+from autoemulate.sensitivity_analysis import _validate_input
+from autoemulate.sensitivity_analysis import sobol_analysis
+from autoemulate.sensitivity_analysis import sobol_results_to_df
+from autoemulate.simulations.projectile import simulate_projectile
+from autoemulate.simulations.projectile import simulate_projectile_multioutput
+
+
+@pytest.fixture
+def Xy_1d():
+    lhd = LatinHypercube([(-5.0, 1.0), (0.0, 1000.0)])
+    X = lhd.sample(100)
+    y = np.array([simulate_projectile(x) for x in X])
+    return X, y
+
+
+@pytest.fixture
+def Xy_2d():
+    lhd = LatinHypercube([(-5.0, 1.0), (0.0, 1000.0)])
+    X = lhd.sample(100)
+    y = np.array([simulate_projectile_multioutput(x) for x in X])
+    return X, y
+
+
+@pytest.fixture
+def model_1d(Xy_1d):
+    X, y = Xy_1d
+    rf = RandomForest()
+    rf.fit(X, y)
+    return rf
+
+
+@pytest.fixture
+def model_2d(Xy_2d):
+    X, y = Xy_2d
+    rf = RandomForest()
+    rf.fit(X, y)
+    return rf
+
+
+# test problem checking ----------------------------------------------------------------
+def test_check_problem():
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+    }
+    problem = _check_problem(problem)
+    assert problem["num_vars"] == 2
+    assert problem["names"] == ["c", "v0"]
+    assert problem["bounds"] == [(-5.0, 1.0), (0.0, 1000.0)]
+
+
+def test_check_problem_invalid():
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+    }
+    with pytest.raises(ValueError):
+        _check_problem(problem)
+
+
+def test_check_problem_bounds():
+    problem = {"num_vars": 2, "names": ["c", "v0"], "bounds": [(-5.0, 1.0)]}
+    with pytest.raises(ValueError):
+        _check_problem(problem)
+
+
+# test output name retrieval --------------------------------------------------
+def test_get_output_names_default():
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+    }
+    output_names = _get_output_names(problem, 1)
+    assert output_names == ["y1"]
+
+
+def test_get_output_names_custom():
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+        "output_names": ["lol1", "lol2"],
+    }
+    output_names = _get_output_names(problem, 2)
+    assert output_names == ["lol1", "lol2"]
+
+
+def test_get_output_names_invalid():
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+        "output_names": "lol",
+    }
+    with pytest.raises(ValueError):
+        _get_output_names(problem, 1)
+
+
+# test Sobol analysis ------------------------------------------------------------
+def test_sobol_analysis(model_1d):
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+    }
+
+    Si = sobol_analysis(model_1d, problem)
+    assert isinstance(Si, dict)
+    assert "y1" in Si
+    assert all(
+        key in Si["y1"] for key in ["S1", "S1_conf", "S2", "S2_conf", "ST", "ST_conf"]
+    )
+
+
+def test_sobol_analysis_2d(model_2d):
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+    }
+    Si = sobol_analysis(model_2d, problem)
+    assert isinstance(Si, dict)
+    assert ["y1", "y2"] == list(Si.keys())
+
+
+@pytest.fixture
+def sobol_results_1d(model_1d):
+    problem = {
+        "num_vars": 2,
+        "names": ["c", "v0"],
+        "bounds": [(-5.0, 1.0), (0.0, 1000.0)],
+    }
+    return sobol_analysis(model_1d, problem)
+
+
+# test conversion to DataFrame --------------------------------------------------
+def test_sobol_results_to_df(sobol_results_1d):
+    df = sobol_results_to_df(sobol_results_1d)
+    assert isinstance(df, pd.DataFrame)
+    assert df.columns.tolist() == [
+        "output",
+        "parameter",
+        "index",
+        "value",
+        "confidence",
+    ]
+    assert ["X1", "X2", "X1-X2"] in df["parameter"].unique()
+    assert all(isinstance(x, float) for x in df["value"])
+    assert all(isinstance(x, float) for x in df["confidence"])
+
+
+# test plotting ----------------------------------------------------------------
+
+
+# test _validate_input ----------------------------------------------------------
+def test_validate_input(sobol_results_1d):
+    with pytest.raises(ValueError):
+        _validate_input(sobol_results_1d, "S3")
+
+
+def test_validate_input_valid(sobol_results_1d):
+    Si = _validate_input(sobol_results_1d, "S1")
+    assert isinstance(Si, pd.DataFrame)
+
+
+# test _calculate_layout ------------------------------------------------------
+def test_calculate_layout():
+    n_rows, n_cols = _calculate_layout(1)
+    assert n_rows == 1
+    assert n_cols == 1
+
+
+def test_calculate_layout_3_outputs():
+    n_rows, n_cols = _calculate_layout(3)
+    assert n_rows == 1
+    assert n_cols == 3
+
+
+def test_calculate_layout_custom():
+    n_rows, n_cols = _calculate_layout(3, 2)
+    assert n_rows == 2
+    assert n_cols == 2
+
+
+# test _generate_problem -----------------------------------------------------
+
+
+def test_generate_problem():
+    X = np.array([[0, 0], [1, 1], [2, 2]])
+    problem = _generate_problem(X)
+    assert problem["num_vars"] == 2
+    assert problem["names"] == ["x1", "x2"]
+    assert problem["bounds"] == [[0, 2], [0, 2]]