diff --git a/.github/workflows/linting.yml b/.github/workflows/linting.yml
index bef121c02..308840f10 100644
--- a/.github/workflows/linting.yml
+++ b/.github/workflows/linting.yml
@@ -36,13 +36,3 @@ jobs:
         run: pip install tox
       - name: Run pylint through tox
         run: tox -e pylint
-
-  pylint-tox-config-check:
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v2
-      - uses: actions/setup-python@v2
-        with:
-          python-version: 3.8
-      - name: Check if the list of disabled messages in the local and global linting passes in ./tox.ini are correctly synchronized
-        run: python .github/workflows/pylint_check.py
diff --git a/.github/workflows/pylint_check.py b/.github/workflows/pylint_check.py
deleted file mode 100644
index 2e4879670..000000000
--- a/.github/workflows/pylint_check.py
+++ /dev/null
@@ -1,48 +0,0 @@
-from pathlib import Path
-
-TOXINI_FILE = Path("tox.ini")
-GLOBAL_DISABLES = {}
-
-
-# Parse ./tox.ini
-tox_lines = TOXINI_FILE.read_text().splitlines()
-tox_pylint_lines = [
-    l for l in tox_lines if l.strip().startswith("pylint src") and "--disable" in l
-]
-tox_global_disables = {m for m in tox_pylint_lines[0].split('"')[1].split(",")}
-tox_per_package_disables = {
-    m for l in tox_pylint_lines[1:] for m in l.split('"')[1].split(",")
-}
-
-
-# Check correctness and raise errors
-try:
-    global_but_not_per_package = tox_global_disables.difference(
-        tox_per_package_disables
-    ).difference(GLOBAL_DISABLES)
-    assert not global_but_not_per_package
-except AssertionError:
-    raise Exception(
-        f"""
-    The following pylint messages seem to be disabled in the global linting pass, but
-    not in the per-package linting passes in `./tox.ini`: {global_but_not_per_package}.
-    This could have two reasons with different solutions:
-    1. You fixed one or many pylint errors in one of the packages and there is no
-       package left that needs this specific message disabled. Then, please also remove
-       it from the global linting pass in `tox.ini` such that pylint runs in the
-       strictest configuration possible.
-    2. You decided to disable a message in the global linting pass in `./tox.ini`..
-       In this case either add it to the list of messages that should be disabled in the
-       long term (`pyproject.toml`) or add it to the `GLOBAL_DISABLES` variable in this
-       python script (`./github/workflows/pylint_check.py`) if the message should only
-       be disabled in the short term.
-    If you are not sure what exactly you are supposed to do, or if you think that this
-    message is wrong please feel free to open an issue on GitHub.
-    """
-    )
-
-
-print(
-    "The disabled pylint messages of the global and per-package linting passes in "
-    "`./tox.ini` seem to be correctly synchronized."
-)
diff --git a/linting-requirements.txt b/linting-requirements.txt
index 5cdbc3277..551d2831e 100644
--- a/linting-requirements.txt
+++ b/linting-requirements.txt
@@ -1,4 +1,4 @@
 # Dependencies for code linting
 
-pylint == 2.9.*
+pylint~=2.16.2
 # mypy
diff --git a/pyproject.toml b/pyproject.toml
index 3b05cbd90..fc24751ec 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -163,18 +163,17 @@ load-plugins = [
     "pylint.extensions.docstyle",
     "pylint.extensions.overlapping_exceptions",
     "pylint.extensions.mccabe",
+    "pylint.extensions.no_self_use",
 ]
 
 [tool.pylint.messages_control]
 disable = [
-    # Exceptions suggested by Black:
-    # https://github.com/psf/black/blob/7f75fe3669ebf0627b1b0476a6d02047e909b959/docs/compatible_configs.md#black-compatible-configurations
-    "bad-continuation",
-    "bad-whitespace",
     # We allow TODO comments in the following format: `# TODO (#[ISSUE NUMBER]): This needs to be done.`
     "fixme",
     # We want to use "mathematical notation" to name some of our variables, e.g. `A` for matrices
     "invalid-name",
+    # Assigning lambda expressions to a variable is sometimes useful, e.g. for defining `LambdaLinearOperator`s
+    "unnecessary-lambda-assignment",
     # Temporary ignore, see https://github.com/probabilistic-numerics/probnum/discussions/470#discussioncomment-1998097 for an explanation
     "missing-return-doc",
     "missing-yield-doc",
@@ -183,13 +182,23 @@ disable = [
 [tool.pylint.format]
 max-line-length = "88"
 
+[tool.pylint.parameter_documentation]
+accept-no-param-doc = false
+accept-no-raise-doc = false
+accept-no-return-doc = false
+accept-no-yields-doc = false
+
 [tool.pylint.design]
 max-args = 10
 max-complexity = 14
 max-locals = 20
 
 [tool.pylint.similarities]
-ignore-imports = "yes"
+ignore-comments = true
+ignore-docstrings = true
+ignore-imports = true
+ignore-signatures = true
+min-similarity-lines = 4
 
 ################################################################################
 # Formatting Configuration                                                     #
diff --git a/src/probnum/_config.py b/src/probnum/_config.py
index 8cc6f98e9..098ab9fed 100644
--- a/src/probnum/_config.py
+++ b/src/probnum/_config.py
@@ -1,3 +1,5 @@
+"""ProbNum library configuration"""
+
 import contextlib
 import dataclasses
 from typing import Any
@@ -35,6 +37,9 @@ class Configuration:
 
     @dataclasses.dataclass
     class Option:
+        """Representation of a single configuration option as a key-value pair with a
+        default value and a description string for documentation purposes."""
+
         name: str
         default_value: Any
         description: str
@@ -49,7 +54,7 @@ def __init__(self) -> None:
         # This is the equivalent of `self._options_registry = dict()`.
         # After rewriting the `__setattr__` method, we have to fall back on the
         # `__setattr__` method of the super class.
-        object.__setattr__(self, "_options_registry", dict())
+        object.__setattr__(self, "_options_registry", {})
 
     def __getattr__(self, key: str) -> Any:
         if key not in self._options_registry:
@@ -68,7 +73,7 @@ def __repr__(self) -> str:
     @contextlib.contextmanager
     def __call__(self, **kwargs) -> None:
         """Context manager used to set values of registered config options."""
-        old_options = dict()
+        old_options = {}
 
         for key, value in kwargs.items():
             if key not in self._options_registry:
@@ -96,6 +101,11 @@ def register(self, key: str, default_value: Any, description: str) -> None:
             The default value of the configuration option.
         description:
             A short description of the configuration option and what it controls.
+
+        Raises
+        ------
+        KeyError
+            If the configuration option already exists.
         """
         if key in self._options_registry:
             raise KeyError(
@@ -156,5 +166,9 @@ def register(self, key: str, default_value: Any, description: str) -> None:
 ]
 
 # ... and register the default configuration options.
-for key, default_value, descr in _DEFAULT_CONFIG_OPTIONS:
-    _GLOBAL_CONFIG_SINGLETON.register(key, default_value, descr)
+def _register_defaults():
+    for key, default_value, descr in _DEFAULT_CONFIG_OPTIONS:
+        _GLOBAL_CONFIG_SINGLETON.register(key, default_value, descr)
+
+
+_register_defaults()
diff --git a/src/probnum/conftest.py b/src/probnum/conftest.py
index 7a2faa201..68c279ef7 100644
--- a/src/probnum/conftest.py
+++ b/src/probnum/conftest.py
@@ -7,7 +7,7 @@
 
 
 @pytest.fixture(autouse=True)
-def autoimport_packages(doctest_namespace):
+def autoimport_packages(doctest_namespace):  # pylint: disable=missing-any-param-doc
     """This fixture 'imports' standard packages automatically in order to avoid
     boilerplate code in doctests"""
 
diff --git a/src/probnum/functions/_function.py b/src/probnum/functions/_function.py
index 12573c6ec..27fcf5c80 100644
--- a/src/probnum/functions/_function.py
+++ b/src/probnum/functions/_function.py
@@ -129,9 +129,8 @@ def __sub__(self, other):
     @functools.singledispatchmethod
     def __mul__(self, other):
         if np.ndim(other) == 0:
-            from ._algebra_fallbacks import (  # pylint: disable=import-outside-toplevel
-                ScaledFunction,
-            )
+            # pylint: disable=import-outside-toplevel,cyclic-import
+            from ._algebra_fallbacks import ScaledFunction
 
             return ScaledFunction(function=self, scalar=other)
 
@@ -140,9 +139,8 @@ def __mul__(self, other):
     @functools.singledispatchmethod
     def __rmul__(self, other):
         if np.ndim(other) == 0:
-            from ._algebra_fallbacks import (  # pylint: disable=import-outside-toplevel
-                ScaledFunction,
-            )
+            # pylint: disable=import-outside-toplevel,cyclic-import
+            from ._algebra_fallbacks import ScaledFunction
 
             return ScaledFunction(function=self, scalar=other)
 
diff --git a/src/probnum/linops/_arithmetic_fallbacks.py b/src/probnum/linops/_arithmetic_fallbacks.py
index cf9a1106b..52f7c73ec 100644
--- a/src/probnum/linops/_arithmetic_fallbacks.py
+++ b/src/probnum/linops/_arithmetic_fallbacks.py
@@ -137,10 +137,10 @@ def __neg__(self):
         return SumLinearOperator(*(-summand for summand in self._summands))
 
     def __repr__(self):
-        res = "SumLinearOperator [\n"
-        for s in self._summands:
-            res += f"\t{s}, \n"
-        return res + "]"
+        res = "SumLinearOperator [\n\t"
+        res += ",\n\t".join(repr(summand) for summand in self._summands)
+        res += "\n]"
+        return res
 
     @staticmethod
     def _expand_sum_ops(*summands: LinearOperator) -> Tuple[LinearOperator, ...]:
@@ -230,10 +230,10 @@ def _expand_prod_ops(*factors: LinearOperator) -> Tuple[LinearOperator, ...]:
         return tuple(expanded_factors)
 
     def __repr__(self):
-        res = "ProductLinearOperator [\n"
-        for s in self._factors:
-            res += f"\t{s}, \n"
-        return res + "]"
+        res = "ProductLinearOperator [\n\t"
+        res += ",\n\t".join(repr(factor) for factor in self._factors)
+        res += "\n]"
+        return res
 
     def _solve(self, B: np.ndarray) -> np.ndarray:
         return functools.reduce(lambda b, op: op.solve(b), self._factors, B)
diff --git a/src/probnum/linops/_linear_operator.py b/src/probnum/linops/_linear_operator.py
index b1b8662cc..8bf5e642c 100644
--- a/src/probnum/linops/_linear_operator.py
+++ b/src/probnum/linops/_linear_operator.py
@@ -10,7 +10,7 @@
 import scipy.linalg
 import scipy.sparse
 
-from probnum import config
+from probnum import config  # pylint: disable=cyclic-import
 from probnum.typing import ArrayLike, DTypeLike, ScalarLike, ShapeLike
 import probnum.utils
 
@@ -384,6 +384,13 @@ def todense(self, cache: bool = True) -> np.ndarray:
         This method can be computationally very costly depending on the shape of the
         linear operator. Use with caution.
 
+        Parameters
+        ----------
+        cache
+            If this is set to :data:`True`, then the dense matrix representation will
+            be cached and subsequent calls will return the cached value (even if
+            :code:`dense` is set to :data:`False` in these subsequent calls).
+
         Returns
         -------
         matrix : np.ndarray
@@ -413,7 +420,14 @@ def is_symmetric(self) -> Optional[bool]:
         """Whether the ``LinearOperator`` :math:`L` is symmetric, i.e. :math:`L = L^T`.
 
         If this is ``None``, it is unknown whether the operator is symmetric or not.
-        Only square operators can be symmetric."""
+        Only square operators can be symmetric.
+
+        Raises
+        ------
+        ValueError
+            When setting :attr:`is_symmetric` to :data:`True` on a non-square
+            :class:`LinearOperator`.
+        """
         return self._is_symmetric
 
     @is_symmetric.setter
@@ -458,6 +472,12 @@ def is_positive_definite(self) -> Optional[bool]:
 
         If this is ``None``, it is unknown whether the matrix is positive-definite or
         not. Only symmetric operators can be positive-definite.
+
+        Raises
+        ------
+        ValueError
+            When setting :attr:`is_positive_definite` to :data:`True` while
+            :attr:`is_symmetric` is :data:`False`.
         """
         return self._is_positive_definite
 
@@ -520,7 +540,13 @@ def _eigvals(self) -> np.ndarray:
         return np.linalg.eigvals(self.todense(cache=False))
 
     def eigvals(self) -> np.ndarray:
-        """Eigenvalue spectrum of the linear operator."""
+        """Eigenvalue spectrum of the linear operator.
+
+        Raises
+        ------
+        numpy.linalg.LinAlgError
+            If :meth:`eigvals` is called on a non-square operator.
+        """
         if self._eigvals_cache is None:
             if not self.is_square:
                 raise np.linalg.LinAlgError(
@@ -871,9 +897,8 @@ def _lu_factor(self):
     ####################################################################################
 
     def __neg__(self) -> "LinearOperator":
-        from ._arithmetic import (  # pylint: disable=import-outside-toplevel
-            NegatedLinearOperator,
-        )
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import NegatedLinearOperator
 
         return NegatedLinearOperator(self)
 
@@ -912,6 +937,18 @@ def transpose(self, *axes: Union[int, Tuple[int]]) -> "LinearOperator":
         """Transpose this linear operator.
 
         Can be abbreviated self.T instead of self.transpose().
+
+        Parameters
+        ----------
+        *axes
+            Permutation of the axes of the :class:`LinearOperator`.
+
+        Raises
+        ------
+        ValueError
+            If the given axis indices do not constitute a valid permutation of the axes.
+        numpy.AxisError
+            If the axis indices are out of bounds.
         """
         if len(axes) > 0:
             if len(axes) == 1 and isinstance(axes[0], tuple):
@@ -1167,7 +1204,8 @@ def __matmul__(
 
             return y
 
-        from ._arithmetic import matmul  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import matmul
 
         return matmul(self, other)
 
@@ -1193,7 +1231,8 @@ def __rmatmul__(
 
             return y
 
-        from ._arithmetic import matmul  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import matmul
 
         return matmul(other, self)
 
@@ -1731,7 +1770,7 @@ def __init__(self, indices, shape, dtype=np.double):
         )
 
     @property
-    def indices(self):
+    def indices(self) -> Tuple[int]:
         """Indices which will be selected when applying the linear operator to a
         vector."""
         return self._indices
diff --git a/src/probnum/linops/_vectorize.py b/src/probnum/linops/_vectorize.py
index bc40d1e5d..bdf88e815 100644
--- a/src/probnum/linops/_vectorize.py
+++ b/src/probnum/linops/_vectorize.py
@@ -1,20 +1,32 @@
 """Vectorization utilities for matrix-{vector, matrix} products."""
 
 import functools
-from typing import Callable, Optional
+from typing import Callable, Optional, Union
 
 import numpy as np
 
+_VectorizationDecoratorReturnType = Union[
+    Callable[[np.ndarray], np.ndarray],
+    Callable[[Callable[[np.ndarray], np.ndarray]], Callable[[np.ndarray], np.ndarray]],
+]
+
 
 def vectorize_matmat(
     matmat: Optional[Callable[[np.ndarray], np.ndarray]] = None,
     method: bool = False,
-):
+) -> _VectorizationDecoratorReturnType:
     """Broadcasting for a (implicitly defined) matrix-matrix product.
 
     Convenience function / decorator to broadcast the definition of a matrix-matrix
     product to stacks of matrices. This can be used to easily construct a new linear
     operator only from a matrix-matrix product.
+
+    Parameters
+    ----------
+    matmat
+        Function computing a matrix-matrix product.
+    method
+        Whether the decorator is being applied to a method or a function.
     """
 
     def _vectorize_matmat(
@@ -43,12 +55,19 @@ def vectorized_matmat(*args) -> np.ndarray:
 def vectorize_matvec(
     matvec: Optional[Callable[[np.ndarray], np.ndarray]] = None,
     method: bool = False,
-):
+) -> _VectorizationDecoratorReturnType:
     """Broadcasting for a (implicitly defined) matrix-vector product.
 
     Convenience function / decorator to broadcast the definition of a matrix-vector
     product. This can be used to easily construct a new linear operator only from a
     matrix-vector product.
+
+    Parameters
+    ----------
+    matvec
+        Function computing a matrix-vector product.
+    method
+        Whether the decorator is being applied to a method or a function.
     """
 
     def _vectorize_matvec(
diff --git a/src/probnum/randprocs/_random_process.py b/src/probnum/randprocs/_random_process.py
index 5fba2462b..061a1f8db 100644
--- a/src/probnum/randprocs/_random_process.py
+++ b/src/probnum/randprocs/_random_process.py
@@ -96,7 +96,7 @@ def __init__(
         if cov is not None:
             if not isinstance(cov, kernels.Kernel):
                 raise TypeError(
-                    "The covariance functions must be implemented as a " "`Kernel`."
+                    "The covariance functions must be implemented as a `Kernel`."
                 )
 
             if cov.input_shape != self._input_shape:
@@ -169,7 +169,7 @@ def __call__(self, args: InputType) -> randvars.RandomVariable[OutputType]:
             at the input(s).
         """
 
-    def marginal(self, args: InputType) -> randvars._RandomVariableList:
+    def marginal(self, args: InputType) -> "randvars._RandomVariableList":
         """Batch of random variables defining the marginal distributions at the inputs.
 
         Parameters
@@ -183,7 +183,13 @@ def marginal(self, args: InputType) -> randvars._RandomVariableList:
 
     @property
     def mean(self) -> functions.Function:
-        r"""Mean function :math:`m(x) := \mathbb{E}[f(x)]` of the random process."""
+        r"""Mean function :math:`m(x) := \mathbb{E}[f(x)]` of the random process.
+
+        Raises
+        ------
+        NotImplementedError
+            If no mean function was assigned to the random process.
+        """
         if self._mean is None:
             raise NotImplementedError
 
@@ -202,6 +208,11 @@ def cov(self) -> kernels.Kernel:
                     (f(x_1) - \mathbb{E}[f(x_1)])^\top
                 \right]
             \end{equation}
+
+        Raises
+        ------
+        NotImplementedError
+            If no covariance function was assigned to the random process.
         """
         if self._cov is None:
             raise NotImplementedError
@@ -304,6 +315,11 @@ def sample(
             i.e. callables are returned.
         size
             Size of the sample.
+
+        Raises
+        ------
+        NotImplementedError
+            General path sampling is currently not supported.
         """
         if args is None:
             raise NotImplementedError
diff --git a/src/probnum/randprocs/kernels/_arithmetic.py b/src/probnum/randprocs/kernels/_arithmetic.py
index 0d7d460ae..51592d8ab 100644
--- a/src/probnum/randprocs/kernels/_arithmetic.py
+++ b/src/probnum/randprocs/kernels/_arithmetic.py
@@ -3,6 +3,7 @@
 from ._kernel import BinaryOperandType, Kernel
 
 
+# pylint: disable=missing-param-doc
 def add(op1: BinaryOperandType, op2: BinaryOperandType) -> Kernel:
     """Kernel summation."""
     return SumKernel(op1, op2)
@@ -11,3 +12,6 @@ def add(op1: BinaryOperandType, op2: BinaryOperandType) -> Kernel:
 def mul(op1: BinaryOperandType, op2: BinaryOperandType) -> Kernel:
     """Kernel multiplication."""
     return _mul_fallback(op1, op2)
+
+
+# pylint: enable=missing-param-doc
diff --git a/src/probnum/randprocs/kernels/_arithmetic_fallbacks.py b/src/probnum/randprocs/kernels/_arithmetic_fallbacks.py
index fda387ee9..c6db31dae 100644
--- a/src/probnum/randprocs/kernels/_arithmetic_fallbacks.py
+++ b/src/probnum/randprocs/kernels/_arithmetic_fallbacks.py
@@ -113,10 +113,10 @@ def _evaluate_linop(
         )
 
     def __repr__(self):
-        res = "SumKernel [\n"
-        for s in self._summands:
-            res += f"\t{s}, \n"
-        return res + "]"
+        res = "SumKernel [\n\t"
+        res += ",\n\t".join(repr(summand) for summand in self._summands)
+        res += "\n]"
+        return res
 
     @staticmethod
     def _expand_sum_kernels(*summands: Kernel) -> Tuple[Kernel, ...]:
@@ -173,10 +173,10 @@ def _evaluate(self, x0: np.ndarray, x1: Optional[np.ndarray]) -> np.ndarray:
         )
 
     def __repr__(self):
-        res = "ProductKernel [\n"
-        for s in self._factors:
-            res += f"\t{s}, \n"
-        return res + "]"
+        res = "ProductKernel [\n\t"
+        res += ",\n\t".join(repr(factor) for factor in self._factors)
+        res += "\n]"
+        return res
 
     @staticmethod
     def _expand_prod_kernels(*factors: Kernel) -> Tuple[Kernel, ...]:
diff --git a/src/probnum/randprocs/kernels/_exponentiated_quadratic.py b/src/probnum/randprocs/kernels/_exponentiated_quadratic.py
index 9b61f44f2..a42c0eb55 100644
--- a/src/probnum/randprocs/kernels/_exponentiated_quadratic.py
+++ b/src/probnum/randprocs/kernels/_exponentiated_quadratic.py
@@ -69,7 +69,7 @@ def lengthscales(self) -> np.ndarray:
         return self._lengthscales
 
     @property
-    def lengthscale(self) -> np.ndarray:
+    def lengthscale(self) -> np.ndarray:  # pylint: disable=missing-raises-doc
         """Deprecated."""
         if self._lengthscales.shape == ():
             return self._lengthscales
diff --git a/src/probnum/randprocs/kernels/_kernel.py b/src/probnum/randprocs/kernels/_kernel.py
index 3aecfcf8d..7ebf8db6b 100644
--- a/src/probnum/randprocs/kernels/_kernel.py
+++ b/src/probnum/randprocs/kernels/_kernel.py
@@ -195,7 +195,13 @@ def input_size_1(self) -> int:
     @property
     def input_shape(self) -> ShapeType:
         r"""Shorthand for the input shape of a covariance function with
-        :attr:`input_shape_0` ``==`` :attr:`input_shape_1`."""
+        :attr:`input_shape_0` ``==`` :attr:`input_shape_1`.
+
+        Raises
+        ------
+        ValueError
+            If the input shapes of the :class:`Kernel` are not equal.
+        """
         if self.input_shape_0 != self.input_shape_1:
             raise ValueError("The input shapes of the `Kernel` are not equal.")
 
@@ -648,22 +654,26 @@ def _euclidean_inner_products(
     """
 
     def __add__(self, other: BinaryOperandType) -> Kernel:
-        from ._arithmetic import add  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import add
 
         return add(self, other)
 
     def __radd__(self, other: BinaryOperandType) -> Kernel:
-        from ._arithmetic import add  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import add
 
         return add(other, self)
 
     def __mul__(self, other: BinaryOperandType) -> Kernel:
-        from ._arithmetic import mul  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import mul
 
         return mul(self, other)
 
     def __rmul__(self, other: BinaryOperandType) -> Kernel:
-        from ._arithmetic import mul  # pylint: disable=import-outside-toplevel
+        # pylint: disable=import-outside-toplevel,cyclic-import
+        from ._arithmetic import mul
 
         return mul(other, self)
 
diff --git a/src/probnum/randprocs/kernels/_matern.py b/src/probnum/randprocs/kernels/_matern.py
index f7b5449d6..186a15848 100644
--- a/src/probnum/randprocs/kernels/_matern.py
+++ b/src/probnum/randprocs/kernels/_matern.py
@@ -152,7 +152,7 @@ def lengthscales(self) -> np.ndarray:
         return self._lengthscales
 
     @property
-    def lengthscale(self) -> np.ndarray:
+    def lengthscale(self) -> np.ndarray:  # pylint: disable=missing-raises-doc
         """Deprecated."""
         if self._lengthscales.shape == ():
             return self._lengthscales
diff --git a/src/probnum/randprocs/kernels/_product_matern.py b/src/probnum/randprocs/kernels/_product_matern.py
index 8b14ea26c..74fcc9cf6 100644
--- a/src/probnum/randprocs/kernels/_product_matern.py
+++ b/src/probnum/randprocs/kernels/_product_matern.py
@@ -71,21 +71,21 @@ def __init__(
         input_dim = 1 if input_shape == () else input_shape[0]
 
         # If only single scalar lengthcsale or nu is given, use this in every dimension
-        def expand_array(x, ndim):
+        def _expand_array(x, ndim):
             return np.full((ndim,), _utils.as_numpy_scalar(x))
 
         if isinstance(lengthscales, np.ndarray):
             if lengthscales.shape == ():
-                lengthscales = expand_array(lengthscales, input_dim)
+                lengthscales = _expand_array(lengthscales, input_dim)
         if isinstance(nus, np.ndarray):
             if nus.shape == ():
-                nus = expand_array(nus, input_dim)
+                nus = _expand_array(nus, input_dim)
 
         # also expand if scalars are given
         if np.isscalar(lengthscales):
-            lengthscales = expand_array(lengthscales, input_dim)
+            lengthscales = _expand_array(lengthscales, input_dim)
         if np.isscalar(nus):
-            nus = expand_array(nus, input_dim)
+            nus = _expand_array(nus, input_dim)
 
         univariate_materns = []
         for dim in range(input_dim):
diff --git a/src/probnum/utils/argutils.py b/src/probnum/utils/argutils.py
index 55754dba0..cde3f70bf 100644
--- a/src/probnum/utils/argutils.py
+++ b/src/probnum/utils/argutils.py
@@ -17,6 +17,15 @@ def as_shape(x: ShapeLike, ndim: Optional[numbers.Integral] = None) -> ShapeType
     ----------
     x
         Shape representation.
+    ndim
+        The required number of dimensions in the shape.
+
+    Raises
+    ------
+    TypeError
+        If ``x`` is not a valid :const:`ShapeLike`.
+    TypeError
+        If ``x`` does not feature the required number of dimensions.
     """
     if isinstance(x, (int, numbers.Integral, np.integer)):
         shape = (int(x),)
@@ -51,6 +60,11 @@ def as_numpy_scalar(x: ScalarLike, dtype: DTypeLike = None) -> np.ndarray:
         Scalar value.
     dtype
         Data type of the scalar.
+
+    Raises
+    ------
+    ValueError
+        If :code:`x` can not be interpreted as a scalar.
     """
 
     if np.ndim(x) != 0:
diff --git a/src/probnum/utils/arrayutils.py b/src/probnum/utils/arrayutils.py
index c18a9675a..279de4d56 100644
--- a/src/probnum/utils/arrayutils.py
+++ b/src/probnum/utils/arrayutils.py
@@ -1,14 +1,19 @@
 """Utility functions for arrays and the like."""
 
-from typing import Union
+from typing import Sequence, Union
 
 import numpy as np
-import scipy
+import scipy.sparse
 
 import probnum.randvars
+from probnum.typing import ArrayLike
 
 
-def atleast_1d(*rvs):
+def atleast_1d(  # pylint: disable=missing-raises-doc
+    *rvs: Union[ArrayLike, scipy.sparse.spmatrix, "probnum.randvars.RandomVariable"],
+) -> Sequence[
+    Union[np.ndarray, scipy.sparse.spmatrix, "probnum.randvars.RandomVariable"]
+]:
     """Convert arrays or random variables to arrays or random variables with at least
     one dimension.
 
diff --git a/src/probnum/utils/linalg/_cholesky_updates.py b/src/probnum/utils/linalg/_cholesky_updates.py
index a35c08105..cdca28c12 100644
--- a/src/probnum/utils/linalg/_cholesky_updates.py
+++ b/src/probnum/utils/linalg/_cholesky_updates.py
@@ -85,6 +85,11 @@ def tril_to_positive_tril(tril_mat: np.ndarray) -> np.ndarray:
     In other words, make it a valid lower Cholesky factor.
 
     The name of the function is based on `np.tril`.
+
+    Parameters
+    ----------
+    tril_mat:
+        A lower-triangular matrix.
     """
     d = np.sign(np.diag(tril_mat))
 
diff --git a/tox.ini b/tox.ini
index ac8ee1154..42938cdae 100644
--- a/tox.ini
+++ b/tox.ini
@@ -64,20 +64,20 @@ deps =
 ignore_errors = true
 commands =
     # Global Linting Pass
-    pylint src/probnum --disable="no-member,abstract-method,arguments-differ,arguments-renamed,redefined-builtin,redefined-outer-name,too-many-instance-attributes,too-many-arguments,too-many-locals,too-many-lines,too-many-statements,too-many-branches,too-complex,too-few-public-methods,protected-access,unnecessary-pass,unused-variable,unused-argument,attribute-defined-outside-init,no-else-return,no-else-raise,no-self-use,else-if-used,consider-using-from-import,duplicate-code,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,useless-param-doc,useless-type-doc,missing-return-type-doc" --jobs=0
+    pylint src/probnum \
+        --ignore-paths=src/probnum/_pnmethod,src/probnum/diffeq/,src/probnum/filtsmooth/,src/probnum/linalg/,src/probnum/problems/,src/probnum/quad/,src/probnum/randprocs/markov/,src/probnum/randvars/ \
+        --jobs=0
     # Per-package Linting Passes
-    pylint src/probnum/diffeq --disable="redefined-outer-name,too-many-instance-attributes,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unnecessary-pass,unused-variable,unused-argument,no-self-use,duplicate-code,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc" --jobs=0
-    pylint src/probnum/filtsmooth --disable="no-member,arguments-differ,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unused-variable,unused-argument,no-self-use,duplicate-code,useless-param-doc" --jobs=0
-    pylint src/probnum/linalg --disable="no-member,abstract-method,arguments-differ,else-if-used,redefined-builtin,too-many-instance-attributes,too-many-arguments,too-many-locals,too-many-lines,too-many-statements,too-many-branches,too-complex,too-few-public-methods,protected-access,unused-argument,attribute-defined-outside-init,no-else-return,no-else-raise,no-self-use,duplicate-code,missing-module-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc" --jobs=0
-    pylint src/probnum/linops --jobs=0
-    pylint src/probnum/problems --disable="too-many-arguments,too-many-locals,unused-variable,unused-argument,consider-using-from-import,duplicate-code,missing-module-docstring,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc" --jobs=0
-    pylint src/probnum/quad --disable="too-many-arguments,missing-module-docstring" --jobs=0
-    pylint src/probnum/randprocs --disable="arguments-differ,arguments-renamed,too-many-instance-attributes,too-many-arguments,too-many-locals,protected-access,unused-argument,no-else-return,duplicate-code,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-type-doc,missing-raises-doc,useless-param-doc,useless-type-doc,missing-return-type-doc" --jobs=0
-    pylint src/probnum/randprocs/kernels --disable="duplicate-code" --jobs=0
-    pylint src/probnum/randvars --disable="too-many-arguments,too-many-locals,too-many-branches,too-few-public-methods,protected-access,unused-argument,duplicate-code,missing-function-docstring,missing-raises-doc" --jobs=0
-    pylint src/probnum/utils --disable="missing-raises-doc,missing-return-type-doc" --jobs=0
+    pylint src/probnum/_pnmethod --disable="missing-param-doc,too-few-public-methods" --jobs=0
+    pylint src/probnum/diffeq --disable="redefined-outer-name,too-many-instance-attributes,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unnecessary-pass,unused-variable,unused-argument,used-before-assignment,no-self-use,duplicate-code,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc,missing-yield-type-doc,missing-any-param-doc" --jobs=0
+    pylint src/probnum/filtsmooth --disable="no-member,arguments-differ,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unused-variable,unused-argument,no-self-use,duplicate-code,useless-param-doc,missing-return-type-doc,missing-param-doc,missing-type-doc,missing-raises-doc,missing-yield-type-doc" --jobs=0
+    pylint src/probnum/linalg --disable="no-member,abstract-method,arguments-differ,else-if-used,redefined-builtin,too-many-instance-attributes,too-many-arguments,too-many-locals,too-many-lines,too-many-statements,too-many-branches,too-complex,too-few-public-methods,protected-access,unused-argument,attribute-defined-outside-init,no-else-return,no-else-raise,no-self-use,duplicate-code,missing-module-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc,consider-using-f-string,missing-any-param-doc" --jobs=0
+    pylint src/probnum/problems --disable="too-many-arguments,too-many-locals,unused-variable,unused-argument,consider-using-from-import,duplicate-code,missing-module-docstring,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc,missing-timeout,use-dict-literal,missing-any-param-doc" --jobs=0
+    pylint src/probnum/quad --disable="too-many-arguments,missing-module-docstring,use-dict-literal" --jobs=0
+    pylint src/probnum/randprocs/markov --disable="arguments-differ,arguments-renamed,too-many-instance-attributes,too-many-arguments,too-many-locals,protected-access,unused-argument,no-else-return,duplicate-code,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-type-doc,missing-raises-doc,useless-param-doc,useless-type-doc,missing-return-type-doc,missing-param-doc,missing-any-param-doc,method-cache-max-size-none" --jobs=0
+    pylint src/probnum/randvars --disable="too-many-arguments,too-many-locals,too-many-branches,too-few-public-methods,protected-access,unused-argument,duplicate-code,missing-function-docstring,missing-raises-doc,missing-return-type-doc,missing-param-doc,broad-exception-raised" --jobs=0
     # Benchmark and Test Code Linting Pass
     # pylint benchmarks --disable="unused-argument,attribute-defined-outside-init,missing-function-docstring" --jobs=0 # not a work in progress, but final
-    pylint benchmarks --disable="unused-argument,attribute-defined-outside-init,no-else-return,no-self-use,consider-using-from-import,missing-module-docstring,missing-class-docstring,missing-function-docstring" --jobs=0
+    pylint benchmarks --disable="unused-argument,attribute-defined-outside-init,no-else-return,no-self-use,consider-using-from-import,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-return-type-doc,missing-any-param-doc,missing-raises-doc,missing-param-doc,missing-type-doc" --jobs=0
     # pylint tests --disable="missing-function-docstring" --jobs=0 # not a work in progress, but final
-    pylint tests --disable="arguments-differ,redefined-outer-name,too-many-instance-attributes,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unnecessary-pass,unused-variable,unused-argument,unused-private-member,attribute-defined-outside-init,no-else-return,no-self-use,consider-using-from-import,duplicate-code,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc,redundant-returns-doc" --jobs=0
+    pylint tests --disable="arguments-differ,redefined-outer-name,too-many-instance-attributes,too-many-arguments,too-many-locals,too-few-public-methods,protected-access,unnecessary-pass,unused-variable,unused-argument,unused-private-member,attribute-defined-outside-init,no-else-return,no-self-use,consider-using-from-import,duplicate-code,missing-module-docstring,missing-class-docstring,missing-function-docstring,missing-param-doc,missing-type-doc,missing-raises-doc,missing-return-type-doc,redundant-returns-doc,missing-any-param-doc,unexpected-keyword-arg,no-member,use-dict-literal,import-error,superfluous-parens,used-before-assignment" --jobs=0