>htn .SrSSKrSSKJr /SQrSrSSSS S S S S SSSS. r/SQSS/SS/SS/SS/SS//SQ/SQSS //S!QS"// r0r \H"r \ S\ \ S'\ S#SH r \ S\ \ 'M M$ S*S$jr S+S%jr S,S&jrS-S'jr"S(S)5rg).zQMultiple Testing and P-Value Correction Author: Josef Perktold License: BSD-3 N) RegressionFDR) fdrcorrectionfdrcorrection_twostage local_fdr multipletestsNullDistributionrcd[U5n[R"SUS-5[U5- $)z2no frills empirical cdf used in fdrcorrection )lennparangefloat)xnobss nC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/stats/multitest.py_ecdfrs+ q6D 99QtAv uT{ ** BonferroniSidakHolmz Holm-SidakzSimes-HochbergHommelzFDR Benjamini-HochbergzFDR Benjamini-YekutielizFDR 2-stage Benjamini-Hochbergz'FDR 2-stage Benjamini-Krieger-Yekutieliz&FDR adaptive Gavrilov-Benjamini-Sarkar) bshhsshhofdr_bhfdr_byfdr_tsbh fdr_tsbkyfdr_gbsrbonf bonferronirsidakrholmr holm-sidakrsimes-hochbergrhommelrfdr_ifdr_pfdrifdrprfdr_nfdr_cfdrnfdrcorrr fdr_2sbhr! fdr_2sbky fdr_twostager"r c  SSKn[R"U5nUnU(d,[R"U5n[R"X5n[ U5n S[R "SU- SU - 5- n U[U 5- n UR5S;aX :*n U[U 5-n GOUR5S;a5X :*n [R"U [R"U*5-5*n GOUR5S;aS[R "SU- S[R"U SS5- 5- nX:nA[R"U5SnURS:Xa [ U5nO[R"U5nS UUS&U)n A[R"[R"U SS5[R"U*5-5*n[RR!U5n AGOUR5S ;aX[R"U SS5- :n[R"U5SnURS:Xa [ U5nO[R"U5nS UUS&U)n U[R"U SS5-n[RR!U5n AUR#5 GOUR5S ;aU[R"U SS5- nUU:*n [R"U 5nUSRS:a/[R$"[R"U 55nS U SU&[R"U SS5U-n[R&R!USSS25SSS2n AGOUR5S ;aUR)5n[+U SS5Hn[R"UUU*S-[R"SUS-5- 5n[R"UU*SU5UU*S&[R"USU*[R&"UUSU*-U55USU*&M Un UU:*n GO.UR5S ;a[-XSS S9upGO UR5S;a[-XSS S9upOUR5S;a[/XSUS S9SSupOUR5S;a[/XSUS S9SSupOUR5S;a~[R"SU S-5nU S-U- U- U-SU- - n[RR!U5n[R&R!USSS25SSS2n AX:*n O [1S5eU bSXS:'U(dU(aXX4$[R2"U 5nU UW'A [R2"U 5nU UU'UUX4$)a= Test results and p-value correction for multiple tests Parameters ---------- pvals : array_like, 1-d uncorrected p-values. Must be 1-dimensional. alpha : float FWER, family-wise error rate, e.g. 0.1 method : str Method used for testing and adjustment of pvalues. Can be either the full name or initial letters. Available methods are: - `bonferroni` : one-step correction - `sidak` : one-step correction - `holm-sidak` : step down method using Sidak adjustments - `holm` : step-down method using Bonferroni adjustments - `simes-hochberg` : step-up method (independent) - `hommel` : closed method based on Simes tests (non-negative) - `fdr_bh` : Benjamini/Hochberg (non-negative) - `fdr_by` : Benjamini/Yekutieli (negative) - `fdr_tsbh` : two stage fdr correction (non-negative) - `fdr_tsbky` : two stage fdr correction (non-negative) maxiter : int or bool Maximum number of iterations for two-stage fdr, `fdr_tsbh` and `fdr_tsbky`. It is ignored by all other methods. maxiter=1 (default) corresponds to the two stage method. maxiter=-1 corresponds to full iterations which is maxiter=len(pvals). maxiter=0 uses only a single stage fdr correction using a 'bh' or 'bky' prior fraction of assumed true hypotheses. is_sorted : bool If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. returnsorted : bool not tested, return sorted p-values instead of original sequence Returns ------- reject : ndarray, boolean true for hypothesis that can be rejected for given alpha pvals_corrected : ndarray p-values corrected for multiple tests alphacSidak : float corrected alpha for Sidak method alphacBonf : float corrected alpha for Bonferroni method Notes ----- There may be API changes for this function in the future. Except for 'fdr_twostage', the p-value correction is independent of the alpha specified as argument. In these cases the corrected p-values can also be compared with a different alpha. In the case of 'fdr_twostage', the corrected p-values are specific to the given alpha, see ``fdrcorrection_twostage``. The 'fdr_gbs' procedure is not verified against another package, p-values are derived from scratch and are not derived in the reference. In Monte Carlo experiments the method worked correctly and maintained the false discovery rate. All procedures that are included, control FWER or FDR in the independent case, and most are robust in the positively correlated case. `fdr_gbs`: high power, fdr control for independent case and only small violation in positively correlated case **Timing**: Most of the time with large arrays is spent in `argsort`. When we want to calculate the p-value for several methods, then it is more efficient to presort the pvalues, and put the results back into the original order outside of the function. Method='hommel' is very slow for large arrays, since it requires the evaluation of n partitions, where n is the number of p-values. rNr ?r#)rr&)rr(T)rr')rr))rr*r+indepalphamethod is_sortedr0nr6bky)r>r?maxiterr@)r r5bh)r"zmethod not recognized)gcr asarrayargsorttaker powerrlowerexpm1log1pr nonzerosizeminmaximum accumulatecollectmaxminimumcopyrangerr ValueError empty_like)pvalsr>r?rCr@ returnsortedrFalphafsortindntests alphacSidak alphacBonfrejectpvals_correctedalphacSidak_all notrejectnr_index notrejectminpvals_corrected_rawalphashrejind rejectmaxamcimiiqpvals_corrected_reject_s rrr?sh JJu E F **U#' ZFbhhV bi88K%-'J ||~44$%-/ > )%88FRXXuf-=$=>> / /bhhV ')"))FAr*B'BDD+ ::i(+ ==A u:L66(+L#' ,-   "xx &!R(@(*%(8)9 ::**//0CD  = (RYYvq"%=== ::i(+ ==A u:L66(+L#' ,- #bii2&>>**//0CD  3 3299VQ33'!F# !9>>A rzz&12I!%F:I  ii26>**//0CDbD0IJ4R4P  + + JJLvq"%A&&UA23Z"))Aad*;;3(GHAcrF&f G G"/8?;?#A J J"/8;;?#A E E"8@EAHCG#IJL!#M 3 3"8@DAHCG#IJL!#M ; &YYq&1* % b[2 r !E )R%Z 8 jj33A6**//0CDbD0IJ4R4P  )011"-.)*L ??==9$3! --'!(+AArc [R"U5nURS:XdS5eU(d-[R"U5n[R"X5nOUnUS;a [ U5nOZUS;aI[R "S[R"S[U5S-5- 5n[ U5U- nO [S5eXVU-:*nUR5(a'[[R"U5S5n SUS U &XV- n [RRU S S S 25S S S 2n A SXS:'U(d8[R"U 5n XW'A [R"U5n XU'X4$X4$) a pvalue correction for false discovery rate. This covers Benjamini/Hochberg for independent or positively correlated and Benjamini/Yekutieli for general or negatively correlated tests. Parameters ---------- pvals : array_like, 1d Set of p-values of the individual tests. alpha : float, optional Family-wise error rate. Defaults to ``0.05``. method : {'i', 'indep', 'p', 'poscorr', 'n', 'negcorr'}, optional Which method to use for FDR correction. ``{'i', 'indep', 'p', 'poscorr'}`` all refer to ``fdr_bh`` (Benjamini/Hochberg for independent or positively correlated tests). ``{'n', 'negcorr'}`` both refer to ``fdr_by`` (Benjamini/Yekutieli for general or negatively correlated tests). Defaults to ``'indep'``. is_sorted : bool, optional If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. Returns ------- rejected : ndarray, bool True if a hypothesis is rejected, False if not pvalue-corrected : ndarray pvalues adjusted for multiple hypothesis testing to limit FDR Notes ----- If there is prior information on the fraction of true hypothesis, then alpha should be set to ``alpha * m/m_0`` where m is the number of tests, given by the p-values, and m_0 is an estimate of the true hypothesis. (see Benjamini, Krieger and Yekuteli) The two-step method of Benjamini, Krieger and Yekutiel that estimates the number of false hypotheses will be available (soon). Both methods exposed via this function (Benjamini/Hochberg, Benjamini/Yekutieli) are also available in the function ``multipletests``, as ``method="fdr_bh"`` and ``method="fdr_by"``, respectively. See also -------- multipletests r z2pvals must be 1-dimensional, that is of shape (n,))ir<pposcorr)rAnegcorrr:z"only indep and negcorr implementedrTNr;)r rGndimrHrIrsumr r rXanyrTrNrUrRrY)rZr>r?r@ pvals_sortind pvals_sorted ecdffactorcmrarjrgrbrprqs rrrsof JJu E ::?PPP?  5) wwu4   //<( # # VVBryyC $5a$788 9<(2- =>> - -F zz|| 6*1-. !z &3jj++,?",EFttLO)*OA%& ==9*9' --'!' ((&&rc[R"U5nUbSSKnSnURU[5 USLaSnOUSLdUS;a [ U5nU(d,[R "U5n[R"X5n[ U5n US:Xa S U-n X- n OUS :XaS n Un O [S 5eU /n [X S SS 9upU R5nUS:XdX:Xa U nX-nUnOU=nnU n[U5HenS U -U- nX-U- nU RU5 [UUS SS 9upU R5nUUS- :dUU:Xa OUU:a [S5eUnMg UUS -U - -nUS:XaUS U--nSXS:'U(d@[R"U5nUUW'A[R"U 5nU UU'UUU U- U 4$XU U- U 4$)a (iterated) two stage linear step-up procedure with estimation of number of true hypotheses Benjamini, Krieger and Yekuteli, procedure in Definition 6 Parameters ---------- pvals : array_like set of p-values of the individual tests. alpha : float error rate method : {'bky', 'bh') see Notes for details * 'bky' - implements the procedure in Definition 6 of Benjamini, Krieger and Yekuteli 2006 * 'bh' - the two stage method of Benjamini and Hochberg maxiter : int or bool Maximum number of iterations. maxiter=1 (default) corresponds to the two stage method. maxiter=-1 corresponds to full iterations which is maxiter=len(pvals). maxiter=0 uses only a single stage fdr correction using a 'bh' or 'bky' prior fraction of assumed true hypotheses. Boolean maxiter is allowed for backwards compatibility with the deprecated ``iter`` keyword. maxiter=False is two-stage fdr (maxiter=1) maxiter=True is full iteration (maxiter=-1 or maxiter=len(pvals)) .. versionadded:: 0.14 Replacement for ``iter`` with additional features. iter : bool ``iter`` is deprecated use ``maxiter`` instead. If iter is True, then only one iteration step is used, this is the two-step method. If iter is False, then iterations are stopped at convergence which occurs in a finite number of steps (at most len(pvals) steps). .. deprecated:: 0.14 Use ``maxiter`` instead of ``iter``. Returns ------- rejected : ndarray, bool True if a hypothesis is rejected, False if not pvalue-corrected : ndarray pvalues adjusted for multiple hypotheses testing to limit FDR m0 : int ntest - rej, estimated number of true (not rejected) hypotheses alpha_stages : list of floats A list of alphas that have been used at each stage Notes ----- The returned corrected p-values are specific to the given alpha, they cannot be used for a different alpha. The returned corrected p-values are from the last stage of the fdr_bh linear step-up procedure (fdrcorrection0 with method='indep') corrected for the estimated fraction of true hypotheses. This means that the rejection decision can be obtained with ``pval_corrected <= alpha``, where ``alpha`` is the original significance level. (Note: This has changed from earlier versions (<0.5.0) of statsmodels.) BKY described several other multi-stage methods, which would be easy to implement. However, in their simulation the simple two-stage method (with iter=False) was the most robust to the presence of positive correlation TODO: What should be returned? Nrz8iter keyword is deprecated, use maxiter keyword instead.Fr T)r;NrBr:rEz+only 'bky' and 'bh' are available as methodr<r=z oops - should not be here)r rGwarningswarn FutureWarningr rHrIrXrrxrWappend RuntimeErrorrY)rZr>r?rCiterr@rmsgrzr^fact alpha_prime alpha_stagesrej pvalscorrr1rariri_oldntests0it alpha_star pvalscorr_s rrrrs^ JJu E H c=) u} J.e*  5) - ZF 5l 4 FGG=L"5G-13NC B aR\ .BFlV+G$-7J    +*5 759;NCBgk!bFlf"#?@@F!" Ws]f,, U? "u* %IIk ]]9- $- =! s# #}z6B; <<v{L88rcSSKJn SSKJn SSKJn [ U5n [ U5n [R"XU5n [R"X 5Sn U SSU SS-S- n [R"XS-5nURS5nUS :nUSS2U4==UU-ss'U"[R"SU -5U5R5RnUS:a%U"XUR5S 9R!SUUS 9nO"U"XUR5S 9RUS 9n[R"XS-5nUSS2U4==UU-ss'UR#U5[%U5U SU S- -- nUcE[R&"S US--5[R("S[R*-5- nOU"U5nUU-U- n[R,"USS5nU$)a Calculate local FDR values for a list of Z-scores. Parameters ---------- zscores : array_like A vector of Z-scores null_proportion : float The assumed proportion of true null hypotheses null_pdf : function mapping reals to positive reals The density of null Z-scores; if None, use standard normal deg : int The maximum exponent in the polynomial expansion of the density of non-null Z-scores nbins : int The number of bins for estimating the marginal density of Z-scores. alpha : float Use Poisson ridge regression with parameter alpha to estimate the density of non-null Z-scores. Returns ------- fdr : array_like A vector of FDR values References ---------- B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22. Examples -------- Basic use (the null Z-scores are taken to be standard normal): >>> from statsmodels.stats.multitest import local_fdr >>> import numpy as np >>> zscores = np.random.randn(30) >>> fdr = local_fdr(zscores) Use a Gaussian null distribution estimated from the data: >>> null = EmpiricalNull(zscores) >>> fdr = local_fdr(zscores, null_pdf=null.pdf) r)GLM)families)OLSNr;r rDg:0yE>)family)L1_wtr> start_params)r)+statsmodels.genmod.generalized_linear_modelrr#statsmodels.regression.linear_modelrrPrTr linspace histogramvanderstdlogfitparamsPoissonfit_regularizedpredictr expsqrtpiclip)zscoresnull_proportionnull_pdfdegnbinsr>rrrminzmaxzbinszhistzbinsdmatsdrnstartmd dmat_fullfzf0fdrs rrr s`@D7 wSnSnSnSnT(a XnUS- nT(a[R"X5nUS- nT(aSS[R"X*5-- nXU4$)Nr:rr )r r)rmeanrprobrn estimate_meanestimate_null_proportionestimate_scales rxform(NullDistribution.__init__..xformsoDBDBzaVVFJ'a'A { 334T> !r)normc>T "U5upnT RT U- U- 5T RT U- U- 5- nX4-nT [R"U5-TT - [R"SU- 5--nTU- U- nU[R"US-*S- 5T [R"U5-- - nUT [R"U5--nU*$)a  Negative log-likelihood of z-scores. The function has three arguments, packed into a vector: mean : location parameter logscale : log of the scale parameter logitprop : logit of the proportion of true nulls The implementation follows section 4 from Efron 2008. r rD)cdfr rrx)rdrrt central_masscprvalzvn_zsn_zs0rnull_lbnull_ubrzscores0s rfun&NullDistribution.__init__..funsFmGA!!HHgkQ%67 HHgkQ%678L!B266":%B(GGDQ,!#B BFFBE6A:&):: :D EBFF<00 0D5Lr)minimize)rrz Nelder-Mead)r?r) r flatnonzeror rscipy.stats.distributionsrscipy.optimizerr_rrr)selfrrrrrrrnrrmzrrrrrrrrs ````` @@@@@r__init__NullDistribution.__init__s^^W/Gw4FG H r7a<MN N;'lCM e "& 3  D , c255?= Ar#w$ #rcXR- UR- n[R"SUS--[R"UR5- S[R"S[R -5-- 5$)a Evaluates the fitted empirical null Z-score density. Parameters ---------- zscores : scalar or array_like The point or points at which the density is to be evaluated. Returns ------- The empirical null Z-score density evaluated at the given points. rrDg?)rrr rrr)rrzvals rpdfNullDistribution.pdfs[ ))#tww.vvd47lRVVDGG_4s266!BEE'?7JJKKr)rrrN)r;r TTF)__name__ __module__ __qualname____firstlineno____doc__rr__static_attributes__rrrrps.`FJ?DM$bLrr)皙?rr FF)rr<F)rrBr NF)r:Nr)rnumpyr statsmodels.stats._knockoffr__all__rmultitest_methods_names _alias_listmultitest_aliasrlrkrrrrrrrrrs%5 A+ !- ' &!-!1!)%=%>'G(Q&N +W~V}l#&'h;>J'9{   AaDOAaD qrUqT  -1!$VBrW't6;#$ $%*V9r@AbJSLSLr