from?__future__?import?division
import?numpy?as?np
import?scipy.stats.kde?as?kde

def?hpd_grid（sample?alpha=0.05?roundto=2）:
????“““Calculate?highest?posterior?density?（HPD）?of?array?for?given?alpha.?
????The?HPD?is?the?minimum?width?Bayesian?credible?interval?（BCI）.?
????The?function?works?for?multimodal?distributions?returning?more?than?one?mode

????Parameters
????----------
????
????sample?:?Numpy?array?or?python?list
????????An?array?containing?MCMC?samples
????alpha?:?float
????????Desired?probability?of?type?I?error?（defaults?to?0.05）
????roundto:?integer
????????Number?of?digits?after?the?decimal?point?for?the?results

????Returns
????----------
????hpd:?array?with?the?lower?
??????????
????“““
????sample?=?np.asarray（sample）
????sample?=?sample[~np.isnan（sample）]
????#?get?upper?and?lower?bounds
????l?=?np.min（sample）
????u?=?np.max（sample）
????density?=?kde.gaussian_kde（sample）
????x?=?np.linspace（l?u?2000）
????y?=?density.evaluate（x）
????#y?=?density.evaluate（x?l?u）?waitting?for?PR?to?be?accepted
????xy_zipped?=?zip（x?y/np.sum（y））
????xy?=?sorted（xy_zipped?key=lambda?x:?x[1]?reverse=True）
????xy_cum_sum?=?0
????hdv?=?[]
????for?val?in?xy:
????????xy_cum_sum?+=?val[1]
????????hdv.append（val[0]）
????????if?xy_cum_sum?>=?（1-alpha）:
????????????break
????hdv.sort（）
????diff?=?（u-l）/20??#?differences?of?5%
????hpd?=?[]
????hpd.append（round（min（hdv）?roundto））
????for?i?in?range（1?len（hdv））:
????????if?hdv[i]-hdv[i-1]?>=?diff:
????????????hpd.append（round（hdv[i-1]?roundto））
????????????hpd.append（round（hdv[i]?roundto））
????hpd.append（round（max（hdv）?roundto））
????ite?=?iter（hpd）
????hpd?=?list（zip（ite?ite））
????modes?=?[]
????for?value?in?hpd:
?????????x_hpd?=?x[（x?>?value[0]）?&?（x??????????y_hpd?=?y[（x?>?value[0]）?&?（x??????????modes.append（round（x_hpd[np.argmax（y_hpd）]?roundto））
????return?hpd?x?y?modes

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?1\
?????文件??????295868??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?1\01_Thinking_Probabilistically_a_Bayesian_Inference_Primer?（3）.ipynb
?????文件????????1886??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?1\hpd?（1）.py
?????文件???????23400??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?1\mauna_loa_CO2?（1）.csv
?????文件????????3670??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?1\plot_post?（1）.py
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?2\
?????文件??????475295??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?2\02_Programming_probabilistically_a_PyMC3_primer?（1）.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?3\
?????文件?????1098467??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?3\03_Juggling?with?multiparametric?and?Hierarchical?models.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?4\
?????文件?????2722708??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?4\04_Understanding_and_predicting_data_with_linear_regression_models?（2）.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?5\
?????文件?????1130805??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?5\05_Classifying_outcomes_with_logistic_regression?（2）.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?6\
?????文件??????597576??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?6\06_Model_comparison.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?7\
?????文件??????764114??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?7\07_Mixture_Models?（1）.ipynb
?????目錄???????????0??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?8\
?????文件??????829985??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\Chapter?8\08_Gaussian_processes.ipynb
?????文件????????1062??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\LICENSE
?????文件????????1595??2017-12-19?11:16??Bayesian-Analysis-with-Python-master\README.md