diff --git a/sklearn/decomposition/_pca.py b/sklearn/decomposition/_pca.py
index 80ac7e856dfd0..ac4a1d1d9816b 100644
--- a/sklearn/decomposition/_pca.py
+++ b/sklearn/decomposition/_pca.py
@@ -32,7 +32,8 @@ def _assess_dimension(spectrum, rank, n_samples):
     """Compute the log-likelihood of a rank ``rank`` dataset.
 
     The dataset is assumed to be embedded in gaussian noise of shape(n,
-    dimf) having spectrum ``spectrum``.
+    dimf) having spectrum ``spectrum``. This implements the method of
+    T. P. Minka.
 
     Parameters
     ----------
@@ -50,10 +51,11 @@ def _assess_dimension(spectrum, rank, n_samples):
     ll : float
         The log-likelihood.
 
-    Notes
-    -----
+    References
+    ----------
     This implements the method of `Thomas P. Minka:
-    Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604`
+    Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604
+    <https://proceedings.neurips.cc/paper/2000/file/7503cfacd12053d309b6bed5c89de212-Paper.pdf>`_
     """
 
     n_features = spectrum.shape[0]
@@ -271,26 +273,30 @@ class PCA(_BasePCA):
 
     References
     ----------
-    For n_components == 'mle', this class uses the method of *Minka, T. P.
-    "Automatic choice of dimensionality for PCA". In NIPS, pp. 598-604*
+    For n_components == 'mle', this class uses the method from:
+    `Minka, T. P.. "Automatic choice of dimensionality for PCA".
+    In NIPS, pp. 598-604 <https://tminka.github.io/papers/pca/minka-pca.pdf>`_
 
     Implements the probabilistic PCA model from:
-    Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
+    `Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
     component analysis". Journal of the Royal Statistical Society:
     Series B (Statistical Methodology), 61(3), 611-622.
+    <http://www.miketipping.com/papers/met-mppca.pdf>`_
     via the score and score_samples methods.
-    See http://www.miketipping.com/papers/met-mppca.pdf
 
     For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.
 
     For svd_solver == 'randomized', see:
-    *Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
+    `Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
     "Finding structure with randomness: Probabilistic algorithms for
     constructing approximate matrix decompositions".
-    SIAM review, 53(2), 217-288.* and also
-    *Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
+    SIAM review, 53(2), 217-288.
+    <https://doi.org/10.1137/090771806>`_
+    and also
+    `Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
     "A randomized algorithm for the decomposition of matrices".
-    Applied and Computational Harmonic Analysis, 30(1), 47-68.*
+    Applied and Computational Harmonic Analysis, 30(1), 47-68
+    <https://doi.org/10.1016/j.acha.2010.02.003>`_.
 
     Examples
     --------