ó áp7]c @sîdZddlmZddlmZddlZddlmZdddd d d gZ d „Z i d d6dd6dd6dd6dd6dd6dd6dd6dd6dd 6d!d"6Z dd#d$gdd%gdd&gdd'gdd(gdd)gdd*d+d,d-gdd.d/d0d1gdd2gd d3d4gd"gg Z eƒZ xCe D];Zed5e ed5d?d@„Zd efdA„ƒYZdS(BsQMultiple Testing and P-Value Correction Author: Josef Perktold License: BSD-3 iÿÿÿÿ(trange(t OrderedDictN(t RegressionFDRt fdrcorrectiontfdrcorrection_twostaget local_fdrt multipleteststNullDistributionRcCs*t|ƒ}tjd|dƒt|ƒS(s2no frills empirical cdf used in fdrcorrection i(tlentnptarangetfloat(txtnobs((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyt_ecdfs t BonferronitbtSidaktstHolmths Holm-SidakthssSimes-HochbergtshtHommelthosFDR Benjamini-Hochbergtfdr_bhsFDR Benjamini-Yekutielitfdr_bysFDR 2-stage Benjamini-Hochbergtfdr_tsbhs'FDR 2-stage Benjamini-Krieger-Yekutielit fdr_tsbkys&FDR adaptive Gavrilov-Benjamini-Sarkartfdr_gbstbonft bonferronitsidaktholms holm-sidakssimes-hochbergthommeltfdr_itfdr_ptfdritfdrptfdr_ntfdr_ctfdrntfdrcorrtfdr_2sbht fdr_2sbkyt fdr_twostageiigš™™™™™©?cCs5ddl}tj|ƒ}|}|sKtj|ƒ}tj||ƒ}nt|ƒ}dtjd|d|ƒ} |t|ƒ} |jƒd,kr¶|| k} |t|ƒ} nû|jƒd-krñ|| k} dtjd||ƒ} nÀ|jƒd.krÔdtjd|dtj |d dƒƒ} || k}~ tj |ƒd }|j d krpt|ƒ}ntj |ƒ}t ||)|} ~dtjd|tj |d dƒƒ}tjj|ƒ} ~nÝ|jƒd/kr‘||tj |d dƒk}tj |ƒd }|j d kr6t|ƒ}ntj |ƒ}t ||)|} |tj |d dƒ}tjj|ƒ} ~|jƒn |jƒd0krZ|tj |d dƒ}||k} tj | ƒ}|d j d krtjtj | ƒƒ}t | |*ntj |d dƒ|}tjj|ddd…ƒddd…} ~nW|jƒd1kr#|jƒ}x“t|ddƒD]}tj ||| tj d|dƒƒ}tj|| |ƒ|| )tj|| tj||| |ƒƒ|| *q‹W|} ||k} nŽ|jƒd2kr\t|d|dddt ƒ\} } nU|jƒd3kr•t|d|dd!dt ƒ\} } n|jƒd4krÒt|d|dd%dt ƒd& \} } nß|jƒd5krt|d|dd)dt ƒd& \} } n¢|jƒd6kr¥tj d|dƒ}|d|||d|}tjj|ƒ}tjj|ddd…ƒddd…} ~| |k} n td+ƒ‚| dk rÐd| | dkRCR@RG(RHR.R/R1t pvals_sortindt pvals_sortedt ecdffactortcmRORXRURPR^R_((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyR s6'  )    ,   R3cCs2tj|ƒ}|s9tj|ƒ}tj||ƒ}nt|ƒ}|dkrhd|}||}n'|dkrƒd}|}n tdƒ‚|g} t|d|dddtƒ\} } | jƒ} | d ksà| |krø| | ||| | fS| } x›tr›d|| }|||}| j |ƒt|d|dddtƒ\} } | jƒ}| ss|| krwPn|| kr’t d ƒ‚n|} qW| |d|9} |dkrË| d|9} n|stj | ƒ}| ||<~ tj | ƒ}| ||<||||| fS| | ||| fSd S( sÞ(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 iter : bool Returns ------- rejected : array, bool True if a hypothesis is rejected, False if not pvalue-corrected : array pvalues adjusted for multiple hypotheses testing to limit FDR m0 : int ntest - rej, estimated number of true 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 origianal 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? R3gð?R4s+only 'bky' and 'bh' are available as methodR.R/R0R1is oops - shouldn't be hereN( R R6R7R8RRERR>Rdtappendt RuntimeErrorRG(RHR.R/titerR1RfRLtfactt alpha_primet alpha_stagestrejt pvalscorrtr1tri_oldtntests0t alpha_startrit pvalscorr_RO((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyRZsT5                 gð?iicCs—ddlm}ddlm}ddlm}t|ƒ}t|ƒ} tj|| |ƒ} tj || ƒd} | d | dd} tj | |dƒ} |tj d| ƒ| ƒj ƒ}|| | d|j ƒƒj d |jƒ}tj ||dƒ}|j|ƒt|ƒ| d| d}|d krdtjd |dƒtjdtjƒ}n ||ƒ}|||}tj|ddƒ}|S( s± 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 : integer The maximum exponent in the polynomial expansion of the density of non-null Z-scores nbins : integer The number of bins for estimating the marginal density of 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) iÿÿÿÿ(tGLM(tfamilies(tOLSiiitfamilyt start_paramsgà¿N(t+statsmodels.genmod.generalized_linear_modelRxRyt#statsmodels.regression.linear_modelRzR=RBR tlinspacet histogramtvandertlogtfittPoissontparamstpredictRRFtexptsqrttpitclip(tzscorestnull_proportiontnull_pdftdegtnbinsRxRyRztminztmaxztbinstzhisttzbinstdmattmdt dmat_fulltfztf0tfdr((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyRÇs&-  "*) . cBs/eZdZddeeed„Zd„ZRS(s) Estimate a Gaussian distribution for the null Z-scores. The observed Z-scores consist of both null and non-null values. The fitted distribution of null Z-scores is Gaussian, but may have non-zero mean and/or non-unit scale. Parameters ---------- zscores : array-like The observed Z-scores. null_lb : float Z-scores between `null_lb` and `null_ub` are all considered to be true null hypotheses. null_ub : float See `null_lb`. estimate_mean : bool If True, estimate the mean of the distribution. If False, the mean is fixed at zero. estimate_scale : bool If True, estimate the scale of the distribution. If False, the scale parameter is fixed at 1. estimate_null_proportion : bool If True, estimate the proportion of true null hypotheses (i.e. the proportion of z-scores with expected value zero). If False, this parameter is fixed at 1. Attributes ---------- mean : float The estimated mean of the empirical null distribution sd : float The estimated standard deviation of the empirical null distribution null_proportion : float The estimated proportion of true null hypotheses among all hypotheses References ---------- B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22. Notes ----- See also: http://nipy.org/nipy/labs/enn.html#nipy.algorithms.statistics.empirical_pvalue.NormalEmpiricalNull.fdr iÿÿÿÿics tj|ˆk|ˆk@ƒ}t|ƒdkr@tdƒ‚n||‰ t|ƒtˆ ƒ‰‰‡‡‡fd†‰ddlm‰‡‡‡‡‡‡‡ fd†}ddlm} | |tjd d d ƒ} ˆ| d ƒ\} } } | |_ | |_ | |_ dS(Nis,No Z-scores fall between null_lb and null_ubcsd}d}d}d}ˆr5||}|d7}nˆr[tj||ƒ}|d7}nˆr€ddtj|| ƒ}n|||fS(Nggð?ii(R R‡(R…tmeantsdtprobR\(t estimate_meantestimate_null_proportiontestimate_scale(s:lib/python2.7/site-packages/statsmodels/stats/multitest.pytxform`s   iÿÿÿÿ(tnormcsΈ|ƒ\}}}ˆjˆ||ƒˆjˆ||ƒ}||}ˆtj|ƒˆˆtjd|ƒ}ˆ||}|tj|d dƒˆtj|ƒ7}|ˆtj|ƒ8}| S(s] 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. ii(tcdfR R‚Rd(R…tdRRat central_masstcptrvaltzv(tn_zstn_zs0R¢tnull_lbtnull_ubR¡tzscores0(s:lib/python2.7/site-packages/statsmodels/stats/multitest.pytfunvs  ,-(tminimizegiR/s Nelder-MeadR (gii( R t flatnonzeroRRktscipy.stats.distributionsR¢tscipy.optimizeR¯tr_R›RœRŒ(tselfR‹R«R¬RžR RŸR\R®R¯tmzR›RœR(( RžRŸR R©RªR¢R«R¬R¡R­s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyt__init__Rs !"  cCsQ||j|j}tjd|dtj|jƒdtjdtjƒƒS(s[ Evaluates the fitted emirical 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. gà¿igà?(R›RœR R‡R‚R‰(R´R‹tzval((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pytpdf£s(t__name__t __module__t__doc__R>tFalseR¶R¸(((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pyR!s/ P(R»tstatsmodels.compat.pythonRt collectionsRtnumpyR tstatsmodels.stats._knockoffRt__all__Rtmultitest_methods_namest _alias_listtmultitest_aliasRZRYR¼RRRRFRtobjectR(((s:lib/python2.7/site-packages/statsmodels/stats/multitest.pytsT                  ÊM  l  Y