import pymc3 as pm import pandas as pd import numpy as np import matplotlib.pyplot as plt import pandas as pd from scipy import stats gene_data = { 'gene1': { 'class1': [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 10, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 1] }, 'gene3': { 'class1': [13, 3, 9, 12, 24, 6, 22, 14, 5, 14, 18, 18, 7, 9, 13, 20, 9, 24, 12, 14, 4, 9, 5, 13, 5, 7, 16, 4, 13, 15, 2, 15, 8, 4, 4, 5, 8, 12, 2, 18, 11, 7, 7, 12, 25, 9, 8, 12, 2, 2, 14, 1, 2, 7, 9, 21, 7, 7, 8, 6, 5, 19, 36, 9, 6, 12, 8, 7, 3, 7, 7, 7, 6, 9, 7, 0, 12, 22, 13, 7, 5, 17, 3, 9, 8, 9, 3, 6, 20, 8, 15, 7, 8, 9, 13, 5, 4, 13, 6, 4, 10, 9, 6, 18, 13, 16, 16, 8, 10, 18, 8, 11, 5, 13, 22, 13, 5, 4, 3, 7, 6, 6, 8, 27, 9, 20, 5, 9, 12, 8, 19, 11, 8, 8, 23, 4, 4, 6, 9, 8, 4, 14, 6, 14, 2, 12, 3, 10, 11, 6, 5, 17, 20, 5, 4, 5, 1, 14, 16, 8, 13, 10, 12, 9, 3, 28, 24, 8, 5, 5, 2, 6, 19, 4, 15, 3, 4, 2, 9, 8, 4, 13, 11, 30, 10, 2, 8, 8, 11, 17, 17, 14, 6, 6, 3, 24, 7, 22, 9, 33, 6, 9, 12, 22, 10, 13, 12, 31, 4, 3, 11, 1, 2, 9, 7, 0, 2, 10, 7, 4, 9, 5, 9, 7, 18, 15, 5, 14, 8, 2, 13, 4, 7, 3, 14, 9, 6, 7, 6, 15, 4, 14, 4, 2, 8, 21, 10, 9, 12, 7, 3, 12, 3, 5, 4, 13, 4, 14, 48, 6, 7, 7, 9, 4, 8, 8, 8, 15, 5, 7, 8, 10, 9, 3, 6, 10, 6, 5, 8, 1, 2, 5, 7, 8, 14, 2, 11, 5, 7, 7, 7, 10, 17, 7, 7, 8, 12, 8, 9, 2, 11, 14, 7, 8, 9, 10, 15, 5, 6, 4, 16, 9, 19, 14, 12, 16, 6, 10, 7, 8, 11, 7, 4, 9, 3, 12, 5, 2, 32, 17, 6, 6, 12, 7, 15, 4, 7, 10, 4, 5, 8, 6, 6, 3, 10, 11, 14, 22, 11, 9, 9, 11, 18, 10, 3, 9, 11, 6, 9, 6, 5, 14, 6, 9, 8, 8, 13, 12, 19, 13, 8, 7, 15, 4, 17, 15, 10, 3, 5, 9, 14, 4, 7, 8, 11, 16, 6, 7, 4, 9, 12, 7, 5, 8, 17, 7, 1, 1, 11, 16], 'class2': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0] } } def beta_params(data): params = stats.beta.fit(data, loc=0, scale=1) return params[0], params[1] # grab the per-gene beta parameters beta_pars = dict() for gene in gene_data.keys(): c1_vec = np.array(gene_data[gene]['class1'])/5000. c2_vec = np.array(gene_data[gene]['class2'])/5000. beta_pars[gene] = beta_params(np.concatenate((c1_vec, c2_vec))) beta_pars = pd.DataFrame.from_dict(beta_pars) genes = ['gene1', 'gene2', 'gene3', 'gene4'] class1_data = np.concatenate([gene_data[g]['class1'] for g in genes]) class2_data = np.concatenate([gene_data[g]['class2'] for g in genes]) idx = np.repeat(range(4), [400] * 4) beta_pars_0 = beta_pars[genes].iloc[0].values beta_pars_1 = beta_pars[genes].iloc[1].values laplace_FC = 0.25 nbinom_n = 25. nbinom_mu = 5000. nbinom_p = 1.-nbinom_mu/(nbinom_mu + nbinom_n) nbinom_alpha = nbinom_n with pm.Model() as model: c_reads_prior = pm.NegativeBinomial('c_reads_prior', mu=nbinom_mu, alpha=nbinom_alpha, shape=2) lfc_prior = pm.Laplace('lfc_prior', mu=0, b=laplace_FC) c2_a_prior = pm.Gamma('c2_a_prior', alpha=(beta_pars_0 ** 2)/1e-2, beta=beta_pars_0 /1e-2, shape=4) c2_b_prior = pm.Gamma('c2_b_prior', alpha=(beta_pars_1 ** 2)/2, beta=beta_pars_1 /2, shape=4) c2_proba = pm.Beta('c2_proba', c2_a_prior, c2_b_prior, shape=4) c1_proba = pm.Deterministic('c1_proba', c2_proba * np.exp(lfc_prior)) class2_counts_obs = pm.Binomial('class2_counts_obs', n=c_reads_prior[1], p=c2_proba[idx], observed=class2_data) class1_counts_obs = pm.Binomial('class1_counts_obs', n=c_reads_prior[0], p=c1_proba[idx], observed=class1_data) trace = pm.sample(1000, step=pm.SMC(tune=False)) pm.traceplot(trace);