rm(list=ls())
set.seed(11)
library(BayesVarSel)
## Loading required package: MASS
## Loading required package: mvtnorm
## Loading required package: parallel
library(mixdir)
p=200
n=50
nsim.gibbs=1000
m1=3
signaltonoise=3
Suppose we have 200 covariates and 50 iid observations from a regression model where intercept and 197 coefficients are zero while the first 3 covariates are 3 and errors with variance 1.
x=cbind(1,array(rnorm(n*p,0,1),dim=c(n,p)))
betas=c(0,c(1,1,1)*signaltonoise,rep(0,p-3))
colnames(x)=c("I",paste("x",1:p,sep=""))
true.mod=(betas>0)*1
names(true.mod)=colnames(x)
y=x%*%betas+rnorm(n,0,1)
simdat=data.frame(y,x)
Suppose to explore the model space with 1000 steps using Gibbs Sampling, starting from the full and assuming a constant prior on model space (only to perform Gibb Sampling). BF factors are calculated using the conventional prior.
res.GibbsBvs<- GibbsBvs(formula= y ~ ., data=simdat, prior.betas="gZellner",
prior.models="Constant", n.iter=nsim.gibbs, init.model="Null", n.burnin=100,
time.test = FALSE)
## Info. . . .
## Most complex model has 202 covariates
## From those 1 is fixed and we should select from the remaining 201
## I, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200
## The problem has a total of 3.213876e+60 competing models
## Of these, 1100 are sampled with replacement
## Then, 1000 are kept and used to construct the summaries
## Working on the problem...please wait.
From exploration steps we need at least the set of visited models in all performed Gibbs steps (BFs are ignored). These are our observations.
xx=res.GibbsBvs$modelslogBF
dim(xx)
## [1] 1000 202
ww=xx[,ncol(xx)]
xx=xx[,-ncol(xx)]
image(xx[,1:10])
This matrix is the of 0/1s that provides evidence for the true model into a part of the model space. In this case the explored models have the following sizes:
barplot(table(rowSums(xx)),xlab="Model sizes",las=2)
Not all models into the model space can be visited, only those with p − n − 1 covariates (149 in this case). The full model space is given by the hyper contingency table made by crossing p 0/1 categorical variables with 2 levels and thus by 2p cells (1.60693810^{60} in this case). On the probability distribution of such contingency table we assume a Dirichlet process prior (which is the prior on model space) and the data are the samples from Gibbs step. This model is proposed here Dunson and Xing (2009).
mdat=data.frame(xx)
for(i in 1:ncol(mdat)) mdat[,i]=factor(mdat[,i])
Posterior of cells probabilities (and thus models) is obtained using the variational algorithm detailed in Ahlmann-Eltze and Yau (2018) (otherwise Gibbs sampling would be used as originally proposed in Dunson and Xing (2009)). We assume that the latent space has dimension 2: the space with covariates with cells with high probabilities (in which it is supposed to lie the true model) and the set of cells with low probabilities (in which there is not the true model)
res <- mixdir(mdat, n_latent=2,max_iter = 1000)
cat(res$converged,"\n")
## TRUE
Given one of the latent spaces, each covariate has a probability to be 1 or 0 (i.e. included or not included in the model). Let’s analyse each latent space separately:
The posterior probability of each covariate for the first latent space is (first 3 covariates belong to this latent space with high probability):
pls1=unlist(lapply(res$category_prob,function(x) x[[2]][2]))
barplot(pls1[-1],col=c(rep(2,m1),rep(1,p-m1)),las=2,cex.axis=0.5,ylim=c(0,1))
The posterior probability of each covariate for the second latent space (which represents the null model):
pls2=unlist(lapply(res$category_prob,function(x) x[[1]][2]))
barplot(pls2[-1],col=c(rep(2,m1),rep(1,p-m1)),las=2,cex.axis=0.5,ylim=c(0,1))
Let’s compare the posterior inclusion probability with just Gibbs sampling with the posterior probability using the DPMP:
exdetail=paste("nGiibsBVS=",nsim.gibbs,
" signaltonoise=",signaltonoise,sep="")
par(mfrow=c(2,1))
barplot(pls1,col=true.mod+1,
main=exdetail,
ylab="Post. Prob. DMMP",ylim=c(0,1))
barplot(res.GibbsBvs$inclprob,col=true.mod+1,
ylab="Post. Inclusion Prob.",ylim=c(0,1))
par(mfrow=c(1,1))
plot(res.GibbsBvs$inclprob,pls1,col=true.mod+1,cex=1,pch=19,
xlab="Post. Inclusion Prob.",ylab="Post. Prob. DMMP",main=exdetail,ylim=c(0,1),xlim=c(0,1))
points(res.GibbsBvs$inclprob[true.mod==1],pls1[true.mod==1],col=2,cex=1,pch=23)
abline(0,1,lty=2)
Consider the Riboflavin data set. Dataset of riboflavin production by Bacillus subtilis containing n = 71 observations of p = 4088 predictors (gene expressions) and a one-dimensional response (riboflavin production).
library(hdi)
## Loading required package: scalreg
## Loading required package: lars
## Loaded lars 1.2
data(riboflavin)
dim(riboflavin)
## [1] 71 2
library(mombf)
## Loading required package: ncvreg
## Loading required package: mgcv
## Loading required package: nlme
## This is mgcv 1.8-31. For overview type 'help("mgcv-package")'.
res.nonlocal<- modelSelection(y=riboflavin$y, x=riboflavin$x,
scale=T, center=T,burnin = 100,
niter = nsim.gibbs+100)
## Using default prior for continuous outcomes priorCoef=momprior(tau=0.348), priorVar=igprior(.01,.01)
## Greedy searching posterior mode... Done.
## Running Gibbs sampler.......... Done.
res.nonlocal$margpp[res.nonlocal$margpp>.5]
## ARGF_at YOAB_at
## 0.6312150 0.9958803
res.conventional<- GibbsBvs(formula=y~., data=as.data.frame(cbind(y=riboflavin$y, riboflavin$x)),n.iter=nsim.gibbs+100, init.model="Null", n.burnin=100, time.test = FALSE)
## Info. . . .
## Most complex model has 4089 covariates
## From those 1 is fixed and we should select from the remaining 4088
## AADK_at, AAPA_at, ABFA_at, ABH_at, ABNA_at, ABRB_at, ACCA_at, ACCB_at, ACCC_at, ACDA_at, ACKA_at, ACOA_at, ACOB_at, ACOC_at, ACOL_at, ACOR_at, ACPA_at, ACSA_at, ACUA_at, ACUB_at, ACUC_at, ADAA_at, ADAB_at, ADDA_at, ADDB_at, ADEC_at, ADHA_at, ADHB_at, ADK_at, AHPC_at, AHPF_at, AHRC_at, ALAS_at, ALD_at, ALDX_at, ALDY_at, ALKA_at, ALSD_at, ALSR_at, ALSS_at, ALST_at, AMHX_at, AMPS_at, AMYC_at, AMYD_at, AMYE_at, AMYX_at, ANSA_at, ANSB_at, ANSR_at, APPA_at, APPB_at, APPC_at, APPD_at, APPF_at, APRE_at, APRX_at, APT_at, ARAA_at, ARAB_at, ARAD_at, ARAE_at, ARAL_at, ARAM_at, ARAN_at, ARAP_at, ARAQ_at, ARAR_at, ARGB_at, ARGC_at, ARGD_at, ARGE_at, ARGF_at, ARGG_at, ARGH_at, ARGJ_at, ARGS_at, AROA_at, AROB_at, AROC_at, AROD_at, AROE_at, AROF_at, AROH_at, AROI_at, arsB_at, arsC_at, arsR_at, ASD_at, ASK_r_at, ASNB_at, ASNH_at, ASNS_at, ASPB_at, ASPS_at, ATPA_at, ATPB_at, ATPC_at, ATPD_at, ATPE_at, ATPF_at, ATPG_at, ATPH_at, ATPI_at, AZLB_at, AZLC_at, AZLD_at, bcd_at, BCSA_at, BEX_at, BFMBAA_at, BFMBAB_at, BFMBB_at, BGLA_at, BGLC_at, BGLH_at, BGLP_at, BGLS_at, bhlA_i_at, bhlB_at, BIOA_at, BIOB_at, BIOD_at, BIOF_at, BIOI_at, BIOW_at, BIRA_s_at, bkdR_at, BLT_at, BLTD_at, BLTR_at, blyA_at, BMR_at, BMRR_at, BMRU_at, BOFA_at, BOFC_at, BPR_at, BRAB_at, BRNQ_at, BSAA_at, CAH_at, CARA_at, CARB_at, cca_at, CCCA_at, CCCB_at, CCDA_at, CCPA_at, ccpB_at, CDD_at, CDSA_at, CGEA_at, CGEB_at, CGEC_at, CGED_at, CGEE_at, CHEA_at, CHEB_at, CHEC_at, CHED_at, CHER_at, CHEV_at, CHEW_at, CHEY_at, CINA_at, CITA_at, CITB_at, CITC_at, CITG_at, CITH_at, CITM_at, CITR_at, CITS_at, CITT_at, CITZ_at, CLPC_at, CLPE_at, CLPP_at, CLPQ_at, CLPX_at, CLPY_at, CMK_at, CODV_at, CODY_at, COMA_at, COMC_at, COMEA_at, COMEB_at, COMEC_at, COMER_at, COMFA_at, COMFB_at, COMFC_at, COMGA_at, COMGB_at, COMGC_at, COMGD_at, COMGE_at, COMGF_at, COMGG_at, COMK_at, COMP_at, COMQ_at, COMX_at, COTA_at, COTB_at, COTC_i_at, COTD_at, COTE_at, COTF_at, COTG_at, COTH_at, COTJA_at, COTJB_at, COTJC_at, COTK_at, COTL_r_at, COTM_at, cotSA_at, COTS_at, COTT_at, COTV_at, COTW_at, COTX_at, COTY_at, COTZ_at, CRH_at, CSAA_at, CSBA_at, CSBB_at, csbC_at, csbD_i_at, CSBX_at, CSFB_i_at, CSGA_at, CSN_at, CSPB_at, CSPC_at, CSPD_at, CSPR_at, CSRA_at, CSTA_at, CTAA_at, CTAB_at, CTAC_at, CTAD_at, CTAE_at, CTAF_at, CTAG_at, CTC_at, CTPA_at, CTRA_at, CTSR_at, CWLA_at, CWLC_at, CWLD_at, CWLJ_at, CYDA_at, CYDB_at, CYDC_at, CYDD_at, CYPA_at, CYPX_at, CYSE_at, CYSH_at, CYSK_at, CYSS_at, CZCD_at, DACA_at, DACB_at, dacC_at, DACF_at, DAL_at, DAPA_at, DAPB_at, DAPG_at, DAT_at, DDLA_at, DEAD_at, DEF_at, DEGA_at, DEGQ_r_at, DEGR_r_at, DEGS_at, DEGU_at, DEOD_at, DEOR_at, des_at, DFRA_at, DGKA_at, DHAS_at, DHBA_at, DHBB_at, DHBC_at, DHBE_at, DHBF_at, DINB_at, DING_at, DIVIB_at, DIVIC_at, DIVIVA_at, DLTA_at, DLTB_at, DLTC_at, DLTD_at, DLTE_at, DNAA_at, DNAB_at, DNAC_at, DNAD_at, DNAE_at, DNAG_at, DNAI_at, DNAJ_at, DNAK_at, DNAN_at, DNAX_at, DPPA_at, DPPB_at, DPPC_at, DPPD_at, DPPE_at, DPS_at, DRA_at, DRM_at, EAG_at, EBRA_at, EBRB_at, ECSA_at, ECSB_at, ECSC_at, EFP_at, ENO_at, EPR_at, ETFA_at, ETFB_at, EXOA_at, EXPZ_at, exuR_at, exuT_at, FABD_at, FABG_at, FBAA_at, FBP_at, FER_at, FEUA_at, FEUB_at, FEUC_at, FFH_at, FHUB_at, FHUC_at, FHUD_at, FHUG_at, FLGB_at, FLGC_at, FLGE_at, FLGK_at, FLGL_at, FLGM_at, FLHA_at, FLHB_at, FLHF_at, FLHO_at, FLHP_at, FLID_at, FLIE_at, FLIF_at, FLIG_at, FLIH_at, FLII_at, FLIJ_at, FLIK_at, FLIL_at, FLIM_at, FLIP_at, FLIQ_at, FLIR_at, FLIS_at, FLIT_at, FLIY_at, FLIZ_at, FMT_at, FNR_at, FOLA_at, FOLC_at, FOLD_at, FOLK_at, FRR_at, FRUA_at, FRUB_at, FRUR_at, FTSA_at, FTSE_at, FTSH_at, FTSL_at, FTSX_at, FTSY_at, FTSZ_at, fur_at, FUS_at, GABP_at, GALE_at, GALK_at, GALT_at, `GAP129A-F_at`, `GAP136-F_at`, `GAP181-F_at`, `GAP229-F_at`, `GAP275-R_at`, `GAP317-F_at`, `GAP68D-R_at`, `GAP83-R_at`, GAP_at, GAPB_at, gatA_at, gatB_at, gatC_at, GBSA_at, GBSB_at, GCAD_at, GDH_at, GERAA_at, GERAB_at, GERAC_at, GERBA_at, GERBB_at, GERBC_at, GERCA_at, GERCB_at, GERCC_at, GERD_at, GERE_at, GERKA_at, GERKB_at, GERKC_at, GERM_at, GGAA_at, GGAB_at, GGT_at, GIDA_at, GID_at, GIDB_at, GLCK_at, glcP_at, GLCR_at, GLCT_at, GLGA_at, GLGB_at, GLGC_at, GLGD_at, GLGP_at, GLMS_at, GLNA_at, GLNH_at, GLNM_at, GLNP_at, GLNQ_at, GLNR_at, GLPD_at, GLPF_at, GLPK_at, GLPP_at, GLPQ_at, GLPT_at, GLTA_at, GLTB_at, GLTC_at, GLTP_at, GLTR_at, GLTT_at, GLTX_at, GLVA_at, GLVC_at, GLYA_at, GLYQ_at, GLYS_at, GNTK_at, GNTP_at, GNTR_at, GNTZ_at, goxB_at, GPR_at, GPSA_at, GREA_at, GROEL_at, GROES_at, GRPE_at, GSAB_at, GSIB_at, GSPA_at, GTAB_at, GUAA_at, GUAB_at, gudB_at, GUTB_at, GUTR_at, GYRA_at, GYRB_at, HAG_at, HBS_at, HEMA_at, HEMB_at, HEMC_at, HEMD_at, HEME_at, HEMH_at, HEML_at, HEMN_at, HEMX_at, HEMY_at, HIPO_at, HISA_at, HISB_at, HISC_at, HISD_at, HISF_at, HISG_at, HISH_at, HISI_at, hisJ_at, HISP_at, HISS_at, HISZ_at, HIT_at, HMP_at, HOLB_at, HOM_at, HPR_at, hprK_at, hprP_at, HPRT_at, HRCA_at, HTPG_at, HTRA_at, HUTG_at, HUTH_at, HUTI_at, HUTM_at, HUTP_at, HUTU_at, ILES_at, ILVA_at, ILVB_at, ILVC_at, ILVD_at, ILVN_at, INFA_at, INFB_at, INFC_at, IOLA_at, IOLB_at, IOLC_at, IOLD_at, IOLE_at, IOLF_at, IOLG_at, IOLH_at, IOLI_at, IOLJ_at, IOLR_at, IOLS_at, IPI_at, ISPA_at, ISPU_at, JAG_at, KAPB_at, KAPD_at, KATA_at, KATB_at, KATX_at, KBAA_at, KBL_at, KDGA_at, KDGK_at, KDGR_at, KDGT_at, KDUD_at, KDUI_at, KINA_at, KINB_at, KINC_at, kipR_at, KSGA_at, LACA_at, LACR_at, LCFA_at, LCTE_at, LCTP_at, LEPA_at, LEUA_at, LEUB_at, LEUC_at, LEUD_at, LEUS_at, LEVD_at, LEVE_at, LEVF_at, LEVG_at, LEVR_at, LEXA_at, LGT_at, LICA_at, LICB_at, LICC_at, LICH_at, LICR_at, LICT_at, LIPA_at, LIPB_at, LMRA_at, LMRB_at, LONA_at, LONB_at, LPLA_at, LPLB_at, LPLC_at, LPLD_at, LRPA_at, LRPB_at, LRPC_at, LSP_at, LYSA_at, LYSC_at, LYSS_at, LYTA_at, LYTB_at, LYTC_at, LYTD_at, LYTE_at, lytF_at, LYTR_at, LYTS_at, LYTT_at, MAF_at, malL_at, MALS_at, MAP_at, MBL_at, MCPA_at, MCPB_at, MCPC_at, MDR_at, MECA_at, MED_at, MELA_at, MENB_at, menC_at, MEND_at, MENE_at, MENF_at, METB_at, METC_at, METK_at, METS_at, MFD_at, MIAA_at, MINC_at, MIND_at, MMGA_at, MMGB_at, MMGC_at, MMGD_at, MMGE_at, MMR_at, MOAB_at, MOAD_at, MOAE_at, MOBA_at, MOBB_at, MOEA_at, MOEB_at, MOTA_at, MOTB_at, MPR_at, MRAY_at, MREB_at, MREBH_at, MREC_at, MRED_at, MRGA_at, mrpA_at, mrpB_at, mrpC_at, mrpD_at, mrpF_at, mrpG_at, MSME_at, MSMR_at, MSMX_at, msrA_at, MTA_at, MTBP_at, MTLA_at, MTLD_at, MTRA_at, MTRB_at, MURA_at, MURB_at, MURC_at, MURD_at, MURE_at, MURF_at, MURG_at, MURZ_at, MUTL_at, MUTM_at, MUTS_at, MUTT_at, NADA_at, NADB_at, NADC_at, NADE_at, NAGA_at, NAGB_at, NAP_at, NARA_at, NARG_at, NARH_at, NARI_at, NARJ_at, NARK_at, NARQ_at, NASA_at, NASB_at, NASC_at, NASD_at, NASE_at, NASF_at, NATA_at, NATB_at, NDHF_at, NDK_at, nfrA_at, NIFS_at, NIFZ_at, NIN_at, NPRB_at, NPRE_at, NRDE_at, NRDF_at, NRGA_at, NRGB_at, NTH_at, NUCA_at, NUCB_at, NUPC_at, NUSA_at, NUSG_at, OBG_s_at, ODHA_at, ODHB_at, OPPA_at, OPPB_at, OPPC_at, OPPD_at, OPPF_at, OPUAA_at, OPUAB_at, OPUAC_at, OPUBA_at, OPUBB_at, OPUBC_at, OPUBD_at, OPUCA_at, OPUCB_at, OPUCC_at, OPUCD_at, OPUD_at, OPUE_at, PABA_at, PABB_at, PABC_at, PADC_at, PAIA_at, PAIB_at, PANB_at, PANC_at, PAND_at, parC_at, parE_at, PATA_at, PATB_at, PBPA_at, PBPB_at, PBPC_at, PBPD_at, PBPE_at, PBPF_at, PBPX_at, PBUX_at, PCKA_at, PCP_at, pcrA_at, PDHA_at, PDHB_at, PDHC_at, PDHD_at, PDP_at, PEL_at, PELB_at, PENP_at, PEPT_at, perR_at, PFK_at, PGI_at, PGK_at, PGM_at, PGSA_at, PHEA_s_at, PHEB_s_at, PHES_at, PHET_at, PHOA_at, PHOB_at, PHOD_at, PHOH_at, PHOP_at, PHOR_at, PHRA_at, PHRC_at, PHRE_at, PHRF_at, PHRG_i_at, PHRI_r_at, PHRK_at, PKSA_at, PKSB_at, PKSC_at, PKSD_at, PKSE_at, PKSF_at, PKSG_at, PKSH_at, PKSI_at, PKSJ_at, PKSL_at, PKSM_at, PKSN_at, PKSR_at, PKSS_at, PLSX_at, PMI_at, PNBA_at, PNPA_at, PNP_at, POLA_at, POLC_at, PONA_at, PPIB_at, PPSA_at, PPS_at, PPSB_at, PPSC_at, PPSD_at, PPSE_at, PRFA_at, PRFB_at, PRIA_at, PRKA_at, PROA_at, PROB_at, PROH_at, PROJ_at, PROS_at, PRSA_at, PRS_at, PSD_at, PSSA_at, PTA_at, PTSG_at, PTSH_at, PTSI_at, PURA_at, PURB_at, PURC_at, PURD_at, PURE_at, PURF_at, PURH_at, PURK_at, PURL_at, PURM_at, PURN_at, PURQ_at, PURR_at, PURT_at, PYCA_at, PYKA_at, PYRAA_at, PYRAB_at, PYRB_at, PYRC_at, PYRD_at, PYRDII_at, PYRE_at, PYRF_at, PYRP_at, PYRR_at, QCRA_at, QCRB_at, QCRC_at, QOXA_at, QOXB_at, QOXC_at, QOXD_at, QUEA_at, RACE_at, RACX_at, RAPA_at, RAPB_at, RAPC_at, RAPD_at, RAPE_at, RAPF_at, RAPG_at, RAPH_at, RAPI_at, RAPJ_at, RAPK_at, RBFA_at, RBSA_at, RBSB_at, RBSC_at, RBSD_at, RBSK_at, RBSR_at, RECA_at, RECF_at, RECN_at, recO_at, RECR_at, recS_at, recU_at, RELA_at, RESA_at, RESB_at, RESC_at, RESD_at, RESE_at, RHO_at, RIBA_at, RIBB_at, RIBC_at, RIBG_at, RIBH_at, RIBR_at, RIBT_at, RIPX_at, rluB_at, RNCS_at, rnhB_at, rnhC_at, RNPA_at, ROCA_at, ROCB_at, ROCC_at, ROCD_at, ROCE_at, ROCF_at, rocG_at, ROCR_at, rodA_at, RPH_at, RPLA_at, RPLB_at, RPLC_at, RPLD_at, RPLE_at, RPLF_at, RPLI_at, RPLJ_at, RPLK_at, RPLL_at, RPLM_at, RPLN_at, RPLO_at, RPLP_at, RPLQ_at, RPLR_at, RPLS_at, RPLT_at, RPLU_at, RPLV_at, RPLW_at, RPLX_at, RPMA_at, RPMB_at, RPMC_at, RPMD_at, RPME_at, RPMF_at, RPMG_at, RPMH_at, RPMI_at, RPMJ_i_at, RPOA_at, RPOB_at, RPOC_at, RPOE_at, RPSB_at, RPSC_at, RPSD_at, RPSE_at, RPSF_at, RPSG_at, RPSH_at, RPSI_at, RPSJ_at, RPSK_at, RPSL_at, RPSM_at, RPSN_at, RPSO_at, RPSP_at, RPSQ_at, RPSR_at, RPSS_at, RPST_at, RPSU_at, RSBR_at, RSBS_at, RSBT_at, RSBU_at, RSBV_at, RSBW_at, RSBX_at, rsiX_at, RTP_at, RUVA_at, RUVB_at, SACA_at, SACB_at, SACC_at, SACP_at, SACT_at, SACV_r_at, SACX_at, SACY_at, SAPB_at, SBCD_at, SBO_at, SBP_at, SDHA_at, SDHB_at, SDHC_at, SECA_at, SECE_r_at, SECF_at, secG_at, SECY_at, SENS_at, SERA_at, SERC_at, SERS_at, SFP_at, SIGA_at, SIGB_at, SIGD_at, SIGE_at, SIGF_at, SIGG_at, SIGH_at, SIGL_at, sigM_at, SIGV_at, SIGW_at, SIGX_at, SIGY_at, SIGZ_at, SINI_at, SINR_at, SIPS_at, SIPT_at, SIPU_at, SIPV_at, SIPW_at, SLEB_at, SLP_at, SLR_at, SMBA_at, SMC_at, SMF_at, SMS_at, SODA_at, SODF_at, SOJ_at, speA_at, speB_at, speE_at, SPLA_at, SPLB_at, SPMA_at, SPMB_at, SPO0A_at, SPO0B_s_at, SPO0E_at, SPO0F_at, SPO0J_at, spo0M_at, SPOIIAA_at, SPOIIAB_at, SPOIIB_at, SPOIID_at, SPOIIE_at, SPOIIGA_at, SPOIIIAA_at, SPOIIIAB_at, SPOIIIAC_at, SPOIIIAD_at, SPOIIIAE_at, SPOIIIAF_at, SPOIIIAG_at, SPOIIIAH_at, SPOIIIC_at, SPOIIID_at, SPOIIIE_at, SPOIIIJ_at, SPOIIM_at, SPOIIP_at, SPOIIQ_at, SPOIIR_at, SPOIISA_at, SPOIISB_at, SPOIVA_at, SPOIVB_at, SPOIVCA_at, SPOIVCB_at, SPOIVFA_at, SPOIVFB_at, SPOVAA_at, SPOVAB_at, SPOVAC_at, SPOVAD_at, SPOVAE_at, SPOVAF_at, SPOVB_at, SPOVC_at, SPOVD_at, SPOVE_at, SPOVFA_at, SPOVFB_at, SPOVG_at, SPOVID_at, SPOVK_at, SPOVM_r_at, SPOVR_at, SPOVS_at, SPOVT_at, SPSA_at, SPSB_at, SPSC_at, SPSD_at, SPSE_at, SPSF_at, SPSG_at, SPSI_at, SPSJ_at, SQHC_at, SRFAA_at, SRFAB_at, SRFAC_at, SRFAD_at, SSB_at, SSPA_at, SSPB_at, SSPC_at, SSPD_at, SSPE_at, SSPF_at, sspG_at, sspH_at, sspI_at, sspJ_at, sspK_at, sspL_at, sspM_r_at, sspN_at, ssuA_at, ssuB_at, ssuC_at, ssuD_at, SUCC_at, SUCD_at, SUL_at, SUNA_at, SUNT_at, TAGA_at, TAGB_at, TAGC_at, TAGD_at, TAGE_at, TAGF_at, TAGG_at, TAGH_at, TAGO_at, tasA_at, TDH_at, TDK_at, TENA_at, TENI_at, TETB_at, TETL_n_at, TGL_at, TGT_at, THDF_at, THIA_at, THIC_at, THID_at, THIK_at, THRB_s_at, THRC_s_at, THRS_at, THRZ_at, THYA_at, THYB_at, TIG_at, TKT_at, TLPA_at, TLP_at, TLPB_at, TLPC_at, TMK_at, TMRB_at, TNRA_at, TOPA_at, TOPB_at, TPI_at, TREA_at, TREP_at, TRER_at, TRKA_at, TRMD_at, TRPA_at, TRPB_at, TRPD_s_at, TRPE_at, TRPS_at, TRUA_at, TRUB_at, TRXA_at, TRXB_at, TSF_at, TUAA_at, TUAB_at, TUAC_at, TUAD_at, TUAE_at, TUAF_at, TUAG_at, TUAH_at, TUFA_at, TYRA_at, TYRS_at, TYRZ_at, UDK_at, UNG_at, UPP_at, UREA_at, UREB_at, UREC_at, USD_i_at, UVRA_at, UVRB_at, UVRC_at, UVRX_at, UVRX_g_at, uxaA_at, uxaB_at, uxaC_at, uxuA_at, VALS_at, VEG_at, VPR_at, WAPA_at, WPRA_at, xepA_at, XHLA_at, XHLB_at, XKDA_at, XKDB_at, XKDC_at, XKDD_at, XKDE_at, XKDF_at, XKDG_at, XKDH_at, XKDI_at, XKDJ_at, XKDK_at, XKDM_at, XKDN_at, XKDO_at, XKDP_at, XKDQ_at, XKDR_at, XKDS_at, XKDT_at, XKDU_at, XKDV_at, XKDW_at, XKDX_at, XLYA_at, XLYB_at, XPAC_at, XPF_at, XPT_at, XRE_at, XSA_at, XTMA_at, XTMB_at, XTRA_at, XYLA_at, XYLB_at, XYLR_at, XYNA_at, XYNB_at, XYND_at, YAAA_at, YAAB_at, YAAC_at, YAAD_at, YAAE_at, YAAF_at, YAAG_at, YAAH_at, YAAI_at, YAAJ_at, YAAK_at, YAAL_at, YAAN_at, YAAO_at, YAAQ_at, YAAR_at, YAAT_at, YABA_at, YABB_at, YABC_at, YABD_at, YABE_at, YABF_at, YABG_at, YABH_at, YABJ_at, YABK_at, YABM_at, YABN_at, YABO_at, YABP_at, YABQ_at, YABR_at, YABS_at, YABT_at, YACA_at, YACB_at, YACC_at, YACD_at, YACF_at, YACH_at, YACI_at, YACK_at, YACL_at, YACM_at, YACN_at, YACO_at, YACP_at, YAZA_at, YAZB_at, YAZC_at, YBAC_at, YBAE_at, YBAF_at, YBAJ_at, YBAK_at, YBAL_at, YBAN_at, YBAR_at, YBAS_at, YBBA_at, YBBB_at, YBBC_at, YBBD_at, YBBE_at, YBBF_at, YBBH_at, YBBI_at, YBBJ_at, YBBK_at, YBBM_at, YBBP_at, YBBR_at, YBBT_at, YBBU_at, YBCC_at, YBCD_at, YBCF_at, YBCH_at, YBCI_at, YBCL_at, YBCM_at, YBCO_at, YBCP_at, YBCS_at, YBCT_at, YBDA_at, YBDB_at, YBDD_at, YBDE_at, YBDG_at, YBDJ_at, YBDK_at, YBDL_at, YBDM_at, YBDN_at, YBDO_at, YBDT_at, YBEC_at, YBEF_at, YBFA_at, YBFB_at, YBFE_at, YBFF_at, YBFG_at, YBFH_at, YBFI_at, YBFJ_at, YBFK_at, YBFM_at, YBFN_at, YBFO_at, YBFP_at, YBFQ_at, YBFS_at, YBFT_at, YBGA_at, YBGB_at, YBGE_at, YBGF_at, YBGG_at, YBGH_at, YBGJ_at, YBXA_at, YBXB_at, YBXF_at, YBXG_at, YBXH_at, YBXI_at, YBYB_at, YCBA_at, YCBB_at, YCBC_at, YCBD_at, YCBE_at, YCBF_at, YCBG_at, YCBH_at, YCBJ_at, YCBK_at, YCBL_at, YCBM_at, YCBN_at, YCBO_at, YCBP_at, YCBR_at, YCBT_at, YCBU_at, YCCC_at, YCCF_at, YCCG_at, YCCH_at, YCCK_at, YCDA_at, YCDB_at, YCDC_at, YCDD_at, YCDF_at, YCDG_at, YCDH_at, YCDI_at, YCEA_at, YCEB_at, YCEC_at, YCED_at, YCEE_at, YCEF_at, YCEG_at, YCEH_at, YCEI_at, YCEJ_at, YCEK_at, YCGA_at, YCGB_at, YCGE_at, YCGF_at, YCGG_at, YCGH_at, YCGI_at, YCGJ_at, YCGK_at, YCGL_at, YCGM_at, YCGN_at, YCGO_at, YCGP_at, YCGQ_at, YCGR_at, YCGS_at, YCGT_at, YCIA_at, YCIB_at, YCIC_at, YCKA_at, YCKB_at, YCKC_at, YCKD_at, YCKE_at, YCKF_at, YCKG_at, YCKH_at, YCKI_at, YCKJ_at, YCKK_at, YCLA_at, YCLB_at, YCLC_at, YCLD_at, YCLE_at, YCLF_at, YCLG_at, YCLH_at, YCLI_at, YCLJ_at, YCLK_at, YCLM_at, YCLN_at, YCLO_at, YCLP_at, YCLQ_at, YCNB_at, YCNC_at, YCND_at, YCNE_at, YCNF_at, YCNG_at, YCNH_at, YCNI_at, YCNJ_at, YCNK_at, YCNL_at, YCSA_at, YCSD_at, YCSE_at, YCSF_at, YCSG_at, YCSI_at, YCSK_at, YCSN_at, YCXA_at, YCXB_at, YCXC_at, YCXD_at, YCXE_at, YCZA_at, YCZB_at, YCZC_at, YCZE_at, YCZF_at, YCZG_at, YCZH_at, YCZI_at, YCZJ_at, YDAA_at, YDAB_at, YDAC_at, YDAD_at, YDAE_at, YDAF_at, YDAG_at, YDAH_at, YDAJ_at, YDAK_at, YDAL_at, YDAM_at, YDAN_at, YDAO_at, YDAP_at, YDAQ_at, YDAR_at, YDAS_at, YDAT_at, YDBA_at, YDBB_at, YDBC_at, YDBD_at, YDBE_at, YDBF_at, YDBG_at, YDBH_at, YDBI_at, YDBJ_at, YDBK_at, YDBL_at, YDBM_at, YDBN_at, YDBO_at, YDBP_at, YDBR_at, YDBS_at, YDBT_at, YDCA_at, YDCB_at, YDCC_at, YDCD_at, YDCE_at, YDCF_at, YDCG_at, YDCH_at, YDCI_at, YDCK_at, YDCL_at, YDCM_at, YDCN_at, YDCO_at, YDCP_at, YDCQ_at, YDCR_at, YDCS_at, YDCT_at, YDDA_at, YDDB_at, YDDC_at, YDDD_at, YDDE_at, YDDF_at, YDDG_at, YDDH_at, YDDI_at, YDDJ_r_at, YDDK_at, YDDM_at, YDDN_at, YDDQ_at, YDDR_at, YDDS_at, YDDT_s_at, YDEA_at, YDEB_at, YDEC_at, YDED_at, YDEE_at, YDEF_at, YDEG_at, YDEH_at, YDEI_at, YDEJ_at, YDEK_at, YDEL_at, YDEM_at, YDEN_at, YDEO_at, YDEP_at, YDEQ_at, YDER_at, YDES_at, YDET_at, YDFA_at, YDFB_at, YDFC_at, YDFD_at, YDFE_at, YDFF_at, YDFG_at, YDFH_at, YDFI_at, YDFJ_at, YDFK_at, YDFL_at, YDFM_at, YDFN_at, YDFO_at, YDFP_at, YDFQ_at, YDFR_at, YDFS_at, YDFT_at, YDGA_at, YDGB_at, YDGC_at, YDGD_at, YDGE_at, YDGF_at, YDGG_at, YDGH_at, YDGI_at, YDGJ_at, YDGK_at, YDHB_at, YDHC_at, YDHD_at, YDHE_at, YDHF_at, YDHG_at, YDHH_at, YDHI_at, YDHJ_at, YDHK_at, YDHL_at, YDHM_at, YDHN_at, YDHO_at, YDHP_at, YDHQ_at, YDHR_at, YDHS_at, YDHT_at, YDHU_at, YDIA_at, YDIB_at, YDIC_at, YDID_at, YDIE_at, YDIF_at, YDIG_at, YDIH_at, YDII_at, YDIJ_at, YDIK_at, YDIL_at, YDIM_at, YDIN_r_at, YDIO_at, YDIP_at, YDIQ_at, YDIR_at, YDIS_at, YDJA_at, YDJB_at, YDJC_at, YDJD_at, YDJE_at, YDJF_at, YDJG_at, YDJH_at, YDJI_at, YDJJ_at, YDJK_at, YDJL_at, YDJM_at, YDJN_at, YDJO_at, YDJP_at, YDZA_at, YDZE_at, YDZF_at, YDZH_at, YEAA_at, YEAB_at, YEAC_at, YEAD_at, YEBA_at, YEBB_at, YEBC_at, YEBD_at, YEBF_at, YEBG_at, YECA_at, YEEA_at, YEEB_at, YEEC_at, YEED_at, YEEF_at, YEEG_at, YEEI_at, YEFA_at, YEFB_at, YEFC_at, YERA_at, YERB_at, YERC_at, YERD_at, YERE_at, YERG_at, YERH_at, YERI_at, YERO_at, YERP_at, YERQ_at, YESE_at, YESF_at, YESJ_at, YESK_at, YESL_at, YESM_at, YESN_at, YESO_at, YESP_at, YESQ_at, YESR_at, YESS_at, YEST_at, YESU_at, YESV_at, YESW_at, YESX_at, YESY_at, YESZ_at, YETA_at, YETF_at, YETG_at, YETH_at, YETI_at, YETJ_at, YETK_at, YETL_at, YETM_at, YETN_at, YETO_at, YEXA_at, YEZA_at, YEZB_at, YEZC_at, YEZD_at, YFHA_at, YFHB_at, YFHC_at, YFHD_at, YFHE_r_at, YFHF_at, YFHG_at, YFHH_at, YFHI_at, YFHJ_at, YFHK_at, YFHL_at, YFHM_at, YFHO_at, YFHP_at, YFHQ_at, YFHR_at, YFHS_i_at, YFIA_at, YFIB_at, YFIC_at, YFID_at, YFIE_at, YFIF_at, YFIG_at, YFIH_at, YFII_at, YFIJ_at, YFIK_at, YFIL_at, YFIM_at, YFIN_at, YFIO_at, YFIQ_at, YFIR_at, YFIS_at, YFIT_at, YFIU_at, YFIV_at, YFIW_at, YFIX_at, YFIY_at, 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YRHL_at, YRHM_at, YRHO_at, YRHP_at, YRKA_at, YRKB_at, YRKC_at, YRKD_at, YRKE_at, YRKF_at, YRKG_r_at, YRKH_at, YRKI_at, YRKJ_at, YRKK_at, YRKL_at, YRKM_i_at, YRKN_at, YRKO_at, YRKP_at, YRKQ_at, YRKR_at, YRKS_f_at, YRPB_at, YRPC_at, YRPD_at, YRPE_at, YRPG_at, YRRA_at, YRRB_at, YRRC_at, YRRD_at, YRRI_at, YRRK_at, YRRL_at, YRRM_at, YRRN_at, YRRO_at, YRRR_at, YRRS_at, YRRT_at, YRRU_at, YRVC_at, YRVD_at, YRVE_at, YRVI_at, YRVJ_at, YRVM_at, YRVN_at, YRVO_at, YRXA_at, YRZA_at, YRZB_at, YRZC_at, YRZD_at, YRZE_at, YRZF_at, YRZG_at, YRZH_at, YRZI_r_at, YRZK_at, YSAA_at, YSBA_at, YSBB_at, YSCA_at, YSCB_at, YSDA_at, YSDB_at, YSDC_at, YSFB_at, YSFC_at, YSFD_at, YSFE_at, YSGA_at, YSHA_at, YSHB_at, YSHC_at, YSHD_at, YSHE_at, YSIA_at, YSIB_at, YSLB_at, YSMA_at, YSMB_at, YSNA_at, YSNB_at, YSND_at, YSNE_at, YSNF_at, YSOA_at, YSXA_at, YSXB_at, YSXC_at, YSXD_at, YSXE_at, YTAA_at, YTAB_at, YTAF_at, YTAG_at, YTAP_at, YTBD_at, YTBE_at, YTBJ_at, YTBQ_at, YTCA_at, YTCB_at, YTCC_at, YTCD_at, YTCF_at, YTCG_at, YTCI_at, YTCJ_at, YTCP_at, YTCQ_at, YTDA_at, YTDI_at, YTDP_at, YTEA_at, YTEI_at, YTEJ_at, YTEP_at, YTEQ_at, YTER_at, YTES_at, YTET_at, YTEU_at, YTEV_i_at, YTFI_at, YTFJ_at, YTFP_at, YTGA_at, YTGB_at, YTGC_at, YTGD_at, YTGI_at, YTGP_at, YTHA_at, YTHB_at, YTHC_at, YTHP_at, YTHQ_at, YTIA_at, YTIB_at, YTIP_at, YTJA_at, YTJB_at, YTJP_at, YTKA_at, YTKC_at, YTKD_at, YTKK_at, YTKL_at, YTKP_at, YTLA_at, YTLB_at, YTLC_at, YTLD_at, YTLI_at, YTLP_at, YTLQ_at, YTLR_at, YTMA_at, YTMB_at, YTMI_at, YTMJ_at, YTMK_at, YTML_at, YTMM_at, YTMO_at, YTMP_at, YTMQ_at, YTNA_at, YTNI_at, YTNJ_at, YTNM_at, YTNP_at, YTOA_at, YTOI_at, YTOP_at, YTOQ_at, YTPA_at, YTPB_at, YTPI_at, YTPP_at, YTPQ_at, YTPR_at, YTPS_at, YTPT_at, YTQA_at, YTQB_at, YTQI_at, YTRA_at, YTRB_at, YTRC_at, YTRD_at, YTRE_at, YTRF_at, YTRI_at, YTRP_at, YTSA_at, YTSB_at, YTSC_at, YTSD_at, YTSJ_at, YTSP_at, YTTA_at, YTTB_at, YTTI_at, YTTP_at, YTVA_at, YTVB_at, YTVI_at, YTWF_at, YTWI_at, YTWP_at, YTXB_at, YTXC_at, YTXD_at, YTXE_at, YTXG_at, YTXH_at, YTXJ_at, YTXK_at, YTXM_at, YTXO_at, YTZA_at, YTZB_at, YTZC_at, YTZD_at, YTZE_at, YTZF_at, YTZG_at, YTZH_at, YUAA_at, YUAB_at, YUAC_at, YUAD_at, YUAE_at, YUAF_at, YUAG_at, YUAI_at, YUAJ_at, YUBA_at, YUBB_at, YUBC_at, YUBD_at, YUBE_at, YUBF_at, YUBG_at, YUEB_at, YUEC_at, YUED_at, YUEE_at, YUEF_at, YUEG_at, YUEH_at, YUEI_at, YUEJ_at, YUEK_at, YUFK_at, YUFL_at, YUFM_at, YUFN_at, YUFO_at, YUFP_at, YUFQ_at, YUFR_at, YUFS_at, YUGE_at, YUGF_at, YUGG_at, YUGH_at, YUGI_at, YUGJ_at, YUGK_at, YUGM_at, YUGN_at, YUGO_at, YUGP_at, YUGS_at, YUGT_at, YUGU_at, YUIA_at, YUIB_at, YUIC_at, YUID_at, YUIE_at, YUIF_at, YUIG_at, YUIH_at, YUII_at, YUKA_at, YUKB_at, YUKC_at, YUKD_at, YUKE_at, YUKF_at, YUKJ_at, YULB_at, YULC_at, YULD_at, YULE_at, YULF_at, YUMB_at, YUMC_at, YUMD_at, YUNA_at, YUNB_at, YUNC_at, YUND_at, YUNE_at, YUNF_at, YUNG_at, YUNH_at, YUNI_at, YUNJ_at, YUNK_at, YUNL_at, YUNM_at, YURB_at, YURC_at, YURD_at, YURE_at, YURF_at, YURG_at, YURH_at, YURI_at, YURJ_at, YURK_at, YURL_at, YURM_at, YURN_at, YURO_at, YURP_at, YURQ_at, YURR_at, YURS_at, YURT_at, YURU_at, YURV_at, YURW_at, YURX_at, YURY_at, YURZ_at, YUSA_at, YUSB_at, YUSC_at, YUSD_at, YUSE_at, YUSF_at, YUSG_at, YUSH_at, YUSI_at, YUSJ_at, YUSK_at, YUSL_at, YUSM_at, YUSN_at, YUSO_at, YUSP_at, YUSQ_at, YUSR_at, YUSS_at, YUST_at, YUSU_at, YUSV_at, YUSW_at, YUSX_at, YUSY_at, YUSZ_at, YUTB_at, YUTC_at, YUTD_at, YUTE_at, YUTF_at, YUTG_at, YUTH_at, YUTI_at, YUTJ_at, YUTK_at, YUTL_at, YUTM_at, YUXG_at, YUXH_at, YUXI_at, YUXJ_at, YUXK_at, YUXL_at, YUXN_at, YUXO_at, YUZA_at, YUZB_at, YUZC_at, YUZD_at, YUZE_at, YUZF_at, YUZG_at, YVAA_at, YVAB_at, YVAC_at, YVAD_at, YVAE_at, YVAF_at, YVAG_at, YVAI_at, YVAJ_at, YVAK_at, YVAM_at, YVAN_at, YVAO_at, YVAP_at, YVAQ_at, YVAV_at, YVAW_at, YVAX_at, YVAY_at, YVAZ_at, YVBA_at, YVBF_at, YVBG_at, YVBH_at, YVBI_at, YVBJ_at, YVBK_at, YVBQ_at, YVBT_at, YVBU_at, YVBV_at, YVBW_at, YVBX_at, YVBY_at, YVCA_at, YVCB_at, YVCC_at, YVCD_at, YVCE_at, YVCI_at, YVCJ_at, YVCK_at, YVCL_at, YVCN_at, YVCP_at, YVCQ_at, YVCR_at, YVCS_at, YVCT_at, YVDA_at, YVDB_at, YVDC_at, YVDD_at, YVDE_at, YVDF_at, YVDG_at, YVDH_at, YVDI_at, YVDJ_at, YVDK_at, YVDM_at, YVDO_at, YVDP_at, YVDQ_at, YVDR_at, YVDS_at, YVDT_at, YVEA_at, YVEB_at, YVEF_at, YVEG_at, YVEK_at, YVEL_at, YVEM_at, YVEN_at, YVEO_at, YVEP_at, YVEQ_at, YVER_at, YVES_at, YVET_at, YVFA_at, YVFB_at, YVFC_at, YVFD_at, YVFE_at, YVFF_at, YVFG_at, YVFH_at, YVFI_at, YVFK_at, YVFL_at, YVFM_at, YVFO_at, YVFP_at, YVFQ_at, YVFR_at, YVFS_at, YVFT_at, YVFU_at, YVFV_at, YVFW_at, YVGJ_at, YVGK_at, YVGL_at, YVGM_at, YVGN_at, YVGO_at, YVGP_at, YVGQ_at, YVGR_at, YVGS_at, YVGT_at, YVGU_at, YVGV_at, YVGW_at, YVGX_at, YVGY_at, YVGZ_at, YVHJ_at, YVIA_at, YVIE_at, YVIF_at, YVJA_at, YVJB_at, YVJD_at, YVKA_at, YVKB_at, YVKC_at, YVKN_at, YVLA_at, YVLB_at, YVLC_at, YVLD_at, YVMA_at, YVMB_at, YVMC_at, YVNA_at, YVNB_at, YVOA_at, YVOD_at, YVOF_at, YVPA_at, YVPB_at, YVQA_at, YVQB_at, YVQC_at, YVQE_at, YVQF_at, YVQG_at, YVQH_at, YVQI_at, YVQJ_at, YVQK_at, YVRA_at, YVRB_at, YVRC_at, YVRD_at, YVRE_at, YVRG_at, YVRH_at, YVRI_at, YVRK_at, YVRL_at, YVRN_at, YVRO_at, YVRP_at, YVSG_at, YVSH_at, YVTA_at, YVYC_at, YVYD_at, YVYE_at, YVYF_at, YVYG_at, YVYH_at, YVZA_at, YVZB_at, YVZC_at, YVZD_at, YWAA_at, YWAB_at, YWAC_at, YWAD_at, YWAE_at, YWAF_at, YWBA_at, YWBB_at, YWBC_at, YWBD_at, YWBE_at, YWBF_at, YWBG_at, YWBH_at, YWBI_at, YWBL_at, YWBM_at, YWBN_at, YWBO_at, YWCA_at, YWCB_at, YWCC_at, YWCD_at, YWCE_at, YWCH_at, YWCI_at, YWCJ_at, YWDA_at, YWDC_at, YWDD_at, YWDE_at, YWDF_at, YWDH_at, YWDI_at, YWDJ_at, YWDK_at, YWDL_at, YWEA_at, YWFA_at, YWFB_at, YWFC_at, YWFD_at, YWFE_at, YWFF_at, YWFG_at, YWFH_at, YWFI_at, YWFK_at, YWFL_at, YWFM_at, YWFN_at, YWFO_at, YWGA_at, YWGB_at, YWHA_at, YWHB_at, YWHC_at, YWHD_at, YWHE_at, YWHH_at, YWHK_at, YWHL_at, YWHM_at, YWHN_at, YWHO_at, YWHP_at, YWHQ_at, YWHR_at, YWIA_at, YWIB_at, YWIC_at, YWID_at, YWIE_at, YWJA_at, YWJB_at, YWJC_at, YWJD_at, YWJE_at, YWJF_at, YWJG_at, YWJH_at, YWJI_at, YWKA_at, YWKB_at, YWKC_at, YWKD_at, YWKE_at, YWKF_at, YWLA_at, YWLB_at, YWLC_at, YWLD_at, YWLE_at, YWLF_at, YWLG_at, YWMA_at, YWMB_at, YWMC_at, YWMD_at, YWME_at, YWMF_at, YWNA_at, YWNB_at, YWNC_at, YWNE_at, YWNF_at, YWNG_at, YWNH_at, YWNJ_at, YWOA_at, YWOB_at, YWOC_at, YWOD_at, YWOE_at, YWOF_at, YWOG_at, YWOH_at, YWPB_at, YWPC_at, YWPD_at, YWPE_at, YWPF_at, YWPG_at, YWPH_at, YWPJ_at, YWQA_at, YWQB_at, YWQC_at, YWQD_at, YWQE_at, YWQF_at, YWQG_at, YWQH_at, YWQI_at, YWQJ_at, YWQK_at, YWQL_at, YWQM_at, YWQN_at, YWQO_at, YWRA_at, YWRB_at, YWRC_at, YWRD_at, YWRE_at, YWRF_at, YWRJ_at, YWRK_at, YWRO_at, YWSA_at, YWSB_at, YWSC_at, YWTA_at, YWTB_at, YWTC_at, YWTD_at, YWTE_at, YWTF_at, YWTG_at, YWZA_at, YWZB_at, YWZC_at, YXAA_at, YXAB_at, YXAC_at, YXAD_at, YXAF_at, YXAG_at, YXAH_at, YXAI_at, YXAJ_at, YXAL_at, YXAM_at, YXBA_at, YXBB_at, YXBC_at, YXBD_at, YXBF_at, YXBG_at, YXCA_at, YXCD_at, YXCE_at, YXDJ_at, YXDK_at, YXDL_at, YXDM_at, YXEA_at, YXEB_at, YXEC_at, YXED_at, YXEE_at, YXEF_at, YXEG_at, YXEH_at, YXEI_at, YXEJ_at, YXEK_at, YXEL_at, YXEM_at, YXEN_at, YXEO_at, YXEP_at, YXEQ_at, YXER_at, YXIA_at, YXIB_at, YXIC_at, YXID_at, YXIE_at, YXIF_at, YXIG_at, YXIH_at, YXII_at, YXIJ_at, YXIK_at, YXIL_at, YXIM_at, YXIO_at, YXIP_at, YXIQ_at, YXIS_at, YXIT_at, YXJA_at, YXJB_at, YXJC_at, YXJD_at, YXJE_at, YXJF_at, YXJG_at, YXJH_at, YXJI_at, YXJJ_at, YXJL_at, YXJM_at, YXJN_at, YXJO_at, YXKA_at, YXKC_at, YXKD_at, YXKF_at, YXKH_at, YXKI_at, YXKJ_at, YXKO_at, YXLA_at, YXLC_at, YXLD_at, YXLE_at, YXLF_at, YXLG_at, YXLH_at, YXLJ_at, YXNA_at, YXNB_at, YXXB_at, YXXD_i_at, YXXE_at, YXXF_at, YXXG_at, YXZC_at, YXZE_at, YXZF_at, YXZG_at, YYAA_at, YYAB_at, YYAC_at, YYAD_at, YYAE_at, YYAF_at, YYAH_at, YYAI_at, YYAJ_at, YYAK_at, YYAL_at, YYAM_at, YYAN_at, YYAO_at, YYAP_at, YYAQ_at, YYAR_at, YYAS_at, YYAT_at, YYBA_at, YYBB_at, YYBC_at, YYBD_at, YYBE_at, YYBF_at, YYBG_at, YYBH_at, YYBI_at, YYBJ_at, YYBK_at, YYBL_at, YYBM_at, YYBN_at, YYBO_at, YYBP_at, YYBQ_at, YYBR_at, YYBS_at, YYBT_at, YYCA_at, YYCB_at, YYCC_at, YYCD_at, YYCE_at, YYCF_at, YYCG_at, YYCH_at, YYCI_at, YYCJ_at, YYCN_at, YYCO_at, YYCP_at, YYCQ_at, YYCR_at, YYCS_at, YYDA_at, YYDB_at, YYDC_r_at, YYDD_at, YYDF_i_at, YYDG_at, YYDH_at, YYDI_at, YYDJ_at, YYDK_at, YYXA_at, YYZB_at, YYZE_at, zur_at
## The problem has a total of Inf competing models
## Of these, 1200 are sampled with replacement
## Then, 1100 are kept and used to construct the summaries
## Working on the problem...please wait.
res.conventional$inclprob[res.conventional$inclprob>0.5]
## ARGF_at YOAB_at YXLE_at
## 0.5672727 0.9509091 0.9209091
Size of explored models
nlp.gibbs=res.nonlocal$postSample
nlp.gibbs=nlp.gibbs[,colSums(nlp.gibbs)>20]
dim(nlp.gibbs)
## [1] 1000 61
barplot(table(rowSums(nlp.gibbs)))
res.nlp <- mixdir(nlp.gibbs, n_latent=2,max_iter = 1000)
pls.nlp=unlist(lapply(res.nlp$category_prob,function(x) x[[1]][2]))
cat(res.nlp$converged,"\n")
## TRUE
pls.nlp[pls.nlp>0.5]
## CARB_at.1 YOAB_at.1 YXLD_at.1
## 0.5605836 0.9990099 0.6848181
Size of Explored Models
conv.gibbs=res.conventional$modelslogBF[,-ncol(res.conventional$modelslogBF)]
conv.gibbs=conv.gibbs[,colSums(conv.gibbs)>20]
dim(conv.gibbs)
## [1] 1100 40
barplot(table(rowSums(conv.gibbs)))
res.conv <- mixdir(conv.gibbs, n_latent=2,max_iter = 1000)
pls.conv=unlist(lapply(res.conv$category_prob,function(x) x[[1]][2]))
cat(res.conv$converged,"\n")
## TRUE
pls.conv[pls.conv>0.5]
## DNAJ_at.1 YOAB_at.1 YRHE_at.1 YXLE_at.1
## 0.5447155 0.9895253 0.5586710 0.8198246
Ahlmann-Eltze, Constantin, and Christopher Yau. 2018. “MixDir: Scalable Bayesian Clustering for High-Dimensional Categorical Data.” In 2018 Ieee 5th International Conference on Data Science and Advanced Analytics (Dsaa), 526–39. IEEE.
Dunson, David B, and Chuanhua Xing. 2009. “Nonparametric Bayes Modeling of Multivariate Categorical Data.” Journal of the American Statistical Association 104 (487): 1042–51.