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@@ -754,9 +754,9 @@ of return statistics as expected by the user.
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Briefly, consider a pair of sites with {math}`n` alleles at the first locus and
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{math}`m` alleles at the second. (Whether this includes the ancestral allele
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depends on whether the statistic is polarised.) Write {math}`f_{i,j}` as the statistic
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computed for focal alleles {math}`A_i` and {math}`B_j`.
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Then the weighting schemes are defined as:
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depends on whether the statistic is polarised.) Write {math}`f_{i,j}` as the
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statistic computed for focal alleles {math}`A_i` and {math}`B_j`. Then the
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weighting schemes are defined as:
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- `hap_weighted`: {math}`\sum_{i=1}^{n}\sum_{j=1}^{m}p(A_{i}B_{j})f_{ij}`,
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where {math}`p(A_{i}B_{j})` is the frequency of haplotype {math}`A_{i}B_{j}`.
@@ -847,12 +847,12 @@ matrix for each list of samples.
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Some LD statistics can be computed between sample sets (two-way statistics are
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specified below), in which case `indexes` must be specified that reference the
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indexes of the `sample_sets`, which must be a list of lists of sample nodes.
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This results in an LD matrix computed for each list of indexes.
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The statistics are selected in the same way (with the `stat`
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argument), and these are limited to a handful of statistics (see
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This results in an LD matrix computed for each list of indexes. The statistics
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are selected in the same way (with the `stat` argument), and these are limited
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to a handful of statistics (see
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{ref}`sec_stats_two_locus_summary_functions_two_way`). The dimension-dropping
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rules for the result follow the rest of the tskit stats API in that a single list
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or tuple will produce a single two-dimensional matrix, while list of these
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rules for the result follow the rest of the tskit stats API in that a single
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list or tuple will produce a single two-dimensional matrix, while list of these
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will produce a three-dimensional array, with the first dimension of length
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equal to the length of the list.
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@@ -910,10 +910,10 @@ set.
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##### One-way Statistics
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One-way statistics are summaries of two loci in a single sample set, using a
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triple of haplotype counts {math}`\{w_{Ab}, w_{aB}, w_{AB}\}` and the size of
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the sample set {math}`n`, where the capitalized and lowercase letters in our notation
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represent alternate alleles.
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One-way statistics are summaries of two loci in a single sample set, using
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a triple of haplotype counts {math}`\{n_{Ab}, n_{aB}, n_{AB}\}` and the size of
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the sample set {math}`n`, where the capitalized and lowercase letters in our
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notation represent alternate alleles.
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(sec_stats_two_locus_sample_two_way_stats)=
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@@ -941,8 +941,8 @@ sets of samples (see also the note in {meth}`~TreeSequence.divergence`).
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##### One-way
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The two-locus summary functions all take haplotype counts and sample set size as
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input. Each of our summary functions has the signature
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The two-locus summary functions all take haplotype counts and sample set size
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as input. Each of our summary functions has the signature
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{math}`f(n_{Ab}, n_{aB}, n_{AB}, n)`, converting to haplotype frequencies
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{math}`\{p_{Ab}, p_{aB}, p_{AB}\}` where appropriate by dividing by {math}`n`.
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