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Unifying stat method desc and linking to math summary #3005

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Unifying stat method descriptions and linking to math equation summar…
gregorgorjanc Sep 28, 2024
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gregorgorjanc Oct 5, 2024
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133 changes: 86 additions & 47 deletions python/tskit/trees.py
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Original file line number Diff line number Diff line change
Expand Up @@ -7515,7 +7515,6 @@ def sample_count_stat(
as sample sets will give ``f`` an argument of length two, giving the number
of samples in ``A`` and ``B`` below the node in question. So, if we define


.. code-block:: python

def f(x):
Expand Down Expand Up @@ -7892,13 +7891,15 @@ def diversity(
):
"""
Computes mean genetic diversity (also known as "pi") in each of the
sets of nodes from ``sample_sets``. The statistic is also known as
sets of nodes from ``sample_sets``. The statistic is also known as
"sample heterozygosity"; a common citation for the definition is
`Nei and Li (1979) <https://doi.org/10.1073/pnas.76.10.5269>`_
(equation 22), so it is sometimes called called "Nei's pi"
(but also sometimes "Tajima's pi").
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Please see the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
See the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
section for details on how the ``sample_sets`` argument is interpreted
and how it interacts with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
Expand Down Expand Up @@ -7960,8 +7961,10 @@ def divergence(
:math:`\pi_{XY}`. Note that the mean pairwise nucleotide diversity of a
sample set to itself (computed by passing an index of the form (j,j))
is its :meth:`diversity <.TreeSequence.diversity>` (see the note below).
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 2`` sample sets at a time; please see the
Operates on ``k = 2`` sample sets at a time; see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
interpreted and how they interact with the dimensions of the output array.
Expand Down Expand Up @@ -8246,6 +8249,9 @@ def genetic_relatedness(
"""
Computes genetic relatedness between (and within) pairs of
sets of nodes from ``sample_sets``.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
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Suggested change
Please see the :ref:`summary functions <sec_stats_summary_functions>`
See the :ref:`summary functions <sec_stats_summary_functions>`

For consistency.

section on the exact definition of the calculated statistic.

Operates on ``k = 2`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
Expand Down Expand Up @@ -8478,8 +8484,12 @@ def genetic_relatedness_weighted(
centre=True,
):
r"""
Computes weighted genetic relatedness. If the :math:`k` th pair of indices
is (i, j) then the :math:`k` th column of output will be
Computes weighted genetic relatedness.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.
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I don't actually think the "summary function" is a good place to refer people to here. That is a definition, but it only makes sense if someone understands How It All Works. The approach we've taken in other statistics is to provide a more plain (but equivalent) definition. I think here the thing to do is to just refer to the docs for genetic_relatedness, because this function's notion of genetic relatedness is the same as that one.


If the :math:`k` th pair of indices is (i, j),
then the :math:`k` th column of output will be
:math:`\sum_{a,b} W_{ai} W_{bj} C_{ab}`,
where :math:`W` is the matrix of weights, and :math:`C_{ab}` is the
:meth:`genetic_relatedness <.TreeSequence.genetic_relatedness>` between sample
Expand Down Expand Up @@ -8589,19 +8599,21 @@ def trait_covariance(self, W, windows=None, mode="site", span_normalise=True):
"""
Computes the mean squared covariances between each of the columns of ``W``
(the "phenotypes") and inheritance along the tree sequence.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.
Operates on all samples in the tree sequence.

Concretely, if `g` is a binary vector that indicates inheritance from an allele,
branch, or node and `w` is a column of W, normalised to have mean zero,
then the covariance of `g` and `w` is :math:`\\sum_i g_i w_i`, the sum of the
weights corresponding to entries of `g` that are `1`. Since weights sum to
zero, this is also equal to the sum of weights whose entries of `g` are 0.
So, :math:`cov(g,w)^2 = ((\\sum_i g_i w_i)^2 + (\\sum_i (1-g_i) w_i)^2)/2`.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on all samples in the tree sequence.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.

What is computed depends on ``mode``:

Expand Down Expand Up @@ -8653,17 +8665,19 @@ def trait_correlation(self, W, windows=None, mode="site", span_normalise=True):
"""
Computes the mean squared correlations between each of the columns of ``W``
(the "phenotypes") and inheritance along the tree sequence.
This is computed as squared covariance in
:meth:`trait_covariance <.TreeSequence.trait_covariance>`,
but divided by :math:`p (1-p)`, where `p` is the proportion of samples
inheriting from the allele, branch, or node in question.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on all samples in the tree sequence.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.
Operates on all samples in the tree sequence.

This is computed as squared covariance in
:meth:`trait_covariance <.TreeSequence.trait_covariance>`,
but divided by :math:`p (1-p)`, where `p` is the proportion of samples
inheriting from the allele, branch, or node in question.

What is computed depends on ``mode``:

Expand Down Expand Up @@ -8737,17 +8751,11 @@ def trait_linear_model(
):
"""
Finds the relationship between trait and genotype after accounting for
covariates. Concretely, for each trait w (i.e., each column of W),
covariates. Concretely, for each trait w (i.e., each column of W),
this does a least-squares fit of the linear model :math:`w \\sim g + Z`,
where :math:`g` is inheritance in the tree sequence (e.g., genotype)
and the columns of :math:`Z` are covariates, and returns the squared
coefficient of :math:`g` in this linear model.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.
Operates on all samples in the tree sequence.

To do this, if `g` is a binary vector that indicates inheritance from an allele,
branch, or node and `w` is a column of W, there are :math:`k` columns of
Expand All @@ -8756,6 +8764,15 @@ def trait_linear_model(
then this returns the number :math:`b_1^2`. If :math:`g` lies in the linear span
of the columns of :math:`Z`, then :math:`b_1` is set to 0. To fit the
linear model without covariates (only the intercept), set `Z = None`.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on all samples in the tree sequence.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.

What is computed depends on ``mode``:

Expand Down Expand Up @@ -8823,7 +8840,10 @@ def segregating_sites(
"""
Computes the density of segregating sites for each of the sets of nodes
from ``sample_sets``, and related quantities.
Please see the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

See the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
section for details on how the ``sample_sets`` argument is interpreted
and how it interacts with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
Expand Down Expand Up @@ -8878,6 +8898,7 @@ def allele_frequency_spectrum(
"""
Computes the allele frequency spectrum (AFS) in windows across the genome for
with respect to the specified ``sample_sets``.

See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`sample sets <sec_stats_sample_sets>`,
:ref:`windows <sec_stats_windows>`,
Expand Down Expand Up @@ -8977,14 +8998,7 @@ def allele_frequency_spectrum(
def Tajimas_D(self, sample_sets=None, windows=None, mode="site"):
"""
Computes Tajima's D of sets of nodes from ``sample_sets`` in windows.
Please see the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
section for details on how the ``sample_sets`` argument is interpreted
and how it interacts with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`, :ref:`mode <sec_stats_mode>`,
and :ref:`return value <sec_stats_output_format>`.
Operates on ``k = 1`` sample sets at a
time. For a sample set ``X`` of ``n`` nodes, if and ``T`` is the mean
For a sample set ``X`` of ``n`` nodes, if ``T`` is the mean
number of pairwise differing sites in ``X`` and ``S`` is the number of
sites segregating in ``X`` (computed with :meth:`diversity
<.TreeSequence.diversity>` and :meth:`segregating sites
Expand All @@ -9000,6 +9014,14 @@ def Tajimas_D(self, sample_sets=None, windows=None, mode="site"):
b = 2 * (n**2 + n + 3) / (9 * n * (n - 1)) - (n + 2) / (h * n) + g / h**2
c = h**2 + g

Operates on ``k = 1`` sample sets at a time.
Please see the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
section for details on how the ``sample_sets`` argument is interpreted
and how it interacts with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`, :ref:`mode <sec_stats_mode>`,
and :ref:`return value <sec_stats_output_format>`.

What is computed for diversity and divergence depends on ``mode``;
see those functions for more details.

Expand Down Expand Up @@ -9040,16 +9062,6 @@ def Fst(
):
"""
Computes "windowed" Fst between pairs of sets of nodes from ``sample_sets``.
Operates on ``k = 2`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
interpreted and how they interact with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.

For sample sets ``X`` and ``Y``, if ``d(X, Y)`` is the
:meth:`divergence <.TreeSequence.divergence>`
between ``X`` and ``Y``, and ``d(X)`` is the
Expand All @@ -9060,6 +9072,16 @@ def Fst(

Fst = 1 - 2 * (d(X) + d(Y)) / (d(X) + 2 * d(X, Y) + d(Y))

Operates on ``k = 2`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
interpreted and how they interact with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`,
:ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.

What is computed for diversity and divergence depends on ``mode``;
see those functions for more details.

Expand Down Expand Up @@ -9149,6 +9171,9 @@ def Y3(
):
"""
Computes the 'Y' statistic between triples of sets of nodes from ``sample_sets``.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 3`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
Expand Down Expand Up @@ -9202,6 +9227,9 @@ def Y2(
):
"""
Computes the 'Y2' statistic between pairs of sets of nodes from ``sample_sets``.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 2`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
Expand Down Expand Up @@ -9245,14 +9273,17 @@ def Y1(self, sample_sets, windows=None, mode="site", span_normalise=True):
"""
Computes the 'Y1' statistic within each of the sets of nodes given by
``sample_sets``.
Please see the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 1`` sample set at a time.
See the :ref:`one-way statistics <sec_stats_sample_sets_one_way>`
section for details on how the ``sample_sets`` argument is interpreted
and how it interacts with the dimensions of the output array.
See the :ref:`statistics interface <sec_stats_interface>` section for details on
:ref:`windows <sec_stats_windows>`, :ref:`mode <sec_stats_mode>`,
:ref:`span normalise <sec_stats_span_normalise>`,
and :ref:`return value <sec_stats_output_format>`.
Operates on ``k = 1`` sample set at a time.

What is computed depends on ``mode``. Each is computed exactly as
``Y3``, except that the average is across every possible trio of samples
Expand Down Expand Up @@ -9284,6 +9315,9 @@ def f4(
"""
Computes Patterson's f4 statistic between four groups of nodes from
``sample_sets``.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 4`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
Expand Down Expand Up @@ -9351,6 +9385,8 @@ def f3(
is usually placed as population ``A`` (see
`Peter (2016) <https://doi.org/10.1534/genetics.115.183913>`_
for more discussion).
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 3`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
Expand Down Expand Up @@ -9396,6 +9432,9 @@ def f2(
"""
Computes Patterson's f2 statistic between two groups of nodes from
``sample_sets``.
Please see the :ref:`summary functions <sec_stats_summary_functions>`
section on the exact definition of the calculated statistic.

Operates on ``k = 2`` sample sets at a time; please see the
:ref:`multi-way statistics <sec_stats_sample_sets_multi_way>`
section for details on how the ``sample_sets`` and ``indexes`` arguments are
Expand Down
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