def METHOD_NAME(
    adata: AnnData,
    *,
    theta: float = 100,
    clip: Optional[float] = None,
    n_top_genes: int = 1000,
    batch_key: Optional[str] = None,
    chunksize: int = 1000,
    n_comps: Optional[int] = 50,
    random_state: Optional[float] = 0,
    kwargs_pca: dict = {},
    check_values: bool = True,
    inplace: bool = True,
) -> Optional[Tuple[AnnData, pd.DataFrame]]:
    """\
    Full pipeline for HVG selection and normalization by analytic Pearson residuals ([Lause21]_).
    Applies gene selection based on Pearson residuals. On the resulting subset,
    Pearson residual normalization and PCA are performed.
    Expects raw count input.
    Params
    ------
    {adata}
    {dist_params}
    {genes_batch_chunk}
    {pca_chunk}
    {check_values}
    {inplace}
    Returns
    -------
    If `inplace=False`, separately returns the gene selection results (as
    :class:`~pandas.DataFrame`) and Pearson residual-based PCA results (as
    :class:`~anndata.AnnData`). If `inplace=True`, updates `adata` with the
    following fields for gene selection results:
    `.var['highly_variable']` : bool
        boolean indicator of highly-variable genes.
    `.var['means']` : float
        means per gene.
    `.var['variances']` : float
        variances per gene.
    `.var['residual_variances']` : float
        Pearson residual variance per gene. Averaged in the case of multiple
        batches.
    `.var['highly_variable_rank']` : float
        Rank of the gene according to residual variance, median rank in the
        case of multiple batches.
    `.var['highly_variable_nbatches']` : int
        If batch_key is given, this denotes in how many batches genes are
        detected as HVG.
    `.var['highly_variable_intersection']` : bool
        If batch_key is given, this denotes the genes that are highly variable
        in all batches.
    The following fields contain Pearson residual-based PCA results and
    normalization settings:
    `.uns['pearson_residuals_normalization']['pearson_residuals_df']`
         The subset of highly variable genes, normalized by Pearson residuals.
    `.uns['pearson_residuals_normalization']['theta']`
         The used value of the overdisperion parameter theta.
    `.uns['pearson_residuals_normalization']['clip']`
         The used value of the clipping parameter.
    `.obsm['X_pca']`
        PCA representation of data after gene selection and Pearson residual
        normalization.
    `.varm['PCs']`
         The principal components containing the loadings. When `inplace=True` this
         will contain empty rows for the genes not selected during HVG selection.
    `.uns['pca']['variance_ratio']`
         Ratio of explained variance.
    `.uns['pca']['variance']`
         Explained variance, equivalent to the eigenvalues of the covariance matrix.
    """
    hvg_args = dict(
        flavor='pearson_residuals',
        n_top_genes=n_top_genes,
        batch_key=batch_key,
        theta=theta,
        clip=clip,
        chunksize=chunksize,
        check_values=check_values,
    )
    if inplace:
        experimental.pp.highly_variable_genes(adata, **hvg_args, inplace=True)
        # TODO: are these copies needed?
        adata_pca = adata[:, adata.var['highly_variable']].copy()
    else:
        hvg = experimental.pp.highly_variable_genes(adata, **hvg_args, inplace=False)
        # TODO: are these copies needed?
        adata_pca = adata[:, hvg['highly_variable']].copy()
    experimental.pp.normalize_pearson_residuals(
        adata_pca, theta=theta, clip=clip, check_values=check_values
    )
    pca(adata_pca, n_comps=n_comps, random_state=random_state, **kwargs_pca)
    if inplace:
        normalization_param = adata_pca.uns['pearson_residuals_normalization']
        normalization_dict = dict(
            **normalization_param, pearson_residuals_df=adata_pca.to_df()
        )
        adata.uns['pca'] = adata_pca.uns['pca']
        adata.varm['PCs'] = np.zeros(shape=(adata.n_vars, n_comps))
        adata.varm['PCs'][adata.var['highly_variable']] = adata_pca.varm['PCs']
        adata.uns['pearson_residuals_normalization'] = normalization_dict
        adata.obsm['X_pca'] = adata_pca.obsm['X_pca']
        return None
    else:
        return adata_pca, hvg