Modeling

A collection of interfaces for modeling binding enrichments, and estimating significance.

phippery.modeling.gamma_poisson_model(ds, starting_alpha=0.8, starting_beta=0.1, trim_percentile=99.9, data_table='size_factors', inplace=True, new_table_name='gamma_poisson_mlxp')[source]

Fit a Gamma distribution to determine Poisson rates per peptide for the non-specific binding background and estimate the \(-\log_{10}(p)\) value, or mlxp, for each sample-peptide enrichment in the dataset provided. We use the following parameterization of the Gamma distribution:

\[f(x) = \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x}\]

The fit is performed on the distribution of peptide average counts to obtain \(\alpha\) and \(\beta\). If there are \(n\) samples involved in the fit, and for a given peptide with counts \(x_1, x_2, \ldots, x_n\), the background Poisson distribution is determined by the rate,

\[\lambda = \frac{\alpha + \sum^n_{k=1} x_k}{\beta + n}\]

Note

much of this source code is derived from https://github.com/lasersonlab/phip-stat and written by Uri Laserson.

Parameters:

  • ds (xarray.DataSet) – The dataset you would like to fit to.

  • starting_alpha (float) – Initial value for the shape parameter of the Gamma distribution.

  • starting_beta (float) – Initial value for the rate parameter of the Gamma distribution.

  • trim_percentile (float) – The percentile cutoff for removing peptides with very high counts. (e.g. a value of 98 means peptides in the highest 2% in counts would be removed from the fit) This parameter is used to remove potential signal peptides that would bias the fit.

  • data_table (str) – The name of the enrichment layer you would like to fit mlxp to.

  • new_table_name (str) – The name of the new layer you would like to append to the dataset.

  • inplace (bool) – If True, then this function appends a dataArray to ds which is indexed with the same coordinate dimensions as ‘data_table’. If False, a copy of ds is returned with the appended dataArray

Returns:

the alpha, and beta values of the fit. If inplace is false, a copy of the new dataset is returned first.

Return type:

tuple

phippery.modeling.zscore(ds, beads_ds, data_table='cpm', min_Npeptides_per_bin=300, lower_quantile_limit=0.05, upper_quantile_limit=0.95, inplace=True, new_table_name='zscore')[source]

Calculate a Z-score of empirical enrichment relative to expected background mean CPM (\(\mu\)) and stddev CPM (\(\sigma\)) from beads-only samples, for each sample-peptide enrichment in the dataset provided. For a peptide with CPM \(n\), the Z-score is,

\[z = \frac{n - \mu}{\sigma}\]

Note

This implementation follows the method described in the supplement to DOI:10.1126/science.aay6485.

Parameters:

  • ds (xarray.DataSet) – The dataset containing samples to estimate significance on.

  • beads_ds (xarray.DataSet) – The dataset containing beads only control samples to estimate background means and stddevs.

  • min_Npeptides_per_bin (int) – Minimum number of peptides per bin.

  • lower_quantile_limit (float) – Counts below this quantile are ignored for computing background mean and stddev.

  • upper_quantile_limit (float) – Counts above this quantile are ignored for computing background mean and stddev.

  • data_table (str) – The name of the enrichment layer from which you would like to compute Z-scores.

  • new_table_name (str) – The name of the new layer you would like to append to the dataset.

  • inplace (bool) – If True, then this function appends a dataArray to ds which is indexed with the same coordinate dimensions as ‘data_table’. If False, a copy of ds is returned with the appended dataArray

Returns:

If inplace is false, a copy of the new dataset is returned.

Return type:

None, xarray.DataSet