import numpy as np import pandas as pd from scipy import stats import matplotlib.pyplot as plt from scipy.stats import t

df1 = pd.read_csv("data1.csv")

def mean(df): return np.sum(df)/len(df) def std(df): DF = len(df)-1 m = mean(df) ssq = np.sum(np.power(df-m,2)) return np.sqrt(ssq/DF) N=len(df1["x"]) DF = N-1 t0975 = stats.t.ppf(0.975,DF, 0,1) x_bar = mean(df1["x"]) s = std(df1["x"]) CI = [x_bar-t0975*s/np.sqrt(N), x_bar+t0975*s/np.sqrt(N)] print(CI)

mu = mean(df1["x"]) var = np.power(std(df1["x"]), 2) print("The expected value: ", mu) print() print("The variance: ", var)

m = mean(df1["x"]) s = std(df1["x"]) print(np.exp(-np.power((3-m)/s, 2)/2)/(s*np.sqrt(2*np.pi)))

N = len(df1["x"]) m = mean(df1["x"]) s = std(df1["x"]) N*np.log(1/(s*np.sqrt(2*np.pi))) - np.sum(np.power(df1["x"]-m,2))/(2*np.power(s,2))

mini = np.min(df1["x"]) maxi = np.max(df1["x"]) r = (maxi - mini)/5 bins = [r*i + mini for i in range(0,6)] count = [] for i in range(len(bins)-1): if i < len(bins)-2: count.append(len(df1[(df1['x'] >= bins[i]) & (df1['x'] < bins[i+1])])) else: count.append(len(df1[(df1['x'] >= bins[i])])) print("Edges of bins: ", bins) print("How many values in each bin: ", count)

df2 = pd.read_csv("data2.csv") df2[df2["split"] == "train"]["x2"] freq = {} for i in df2[df2["split"] == "train"]["x2"]: if i in freq: freq[i] += 1 else: freq[i] = 1 relfreq = {} for i in freq: relfreq[i] = freq[i]/sum(freq.values()) for i in relfreq: print("class and relative frequency: ", i, relfreq[i])

ddof0 = len(df2[df2["y"]==0]["x1"])-1 ddof1 = len(df2[df2["y"]==1]["x1"])-1 x = np.linspace(stats.f.ppf(0.001, ddof1, ddof0),stats.f.ppf(0.999, ddof1, ddof0), 100) plt.plot(x, stats.f.pdf(x, ddof1, ddof0),'r-', lw=5, alpha=0.6, label='f pdf')

var_0 = np.var(df2[df2["y"]==0]["x1"], ddof=1) var_1 = np.var(df2[df2["y"]==1]["x1"], ddof=1) print("Var y = 0: ", var_0) print("Var y = 1: ", var_1) f = var_1/var_0 p = 2*(1-stats.f.cdf(f, ddof1, ddof0)) print("F statistic: ", f) print("P-value: ", p)

stats.f.ppf(0.05, ddof1, ddof0)

mu = mean(df2["x1"]) var = np.power(std(df2["x1"]), 2) print("The expected value: ", mu) print() print("The variance: ", var) mini = np.min(df2["x1"]) maxi = np.max(df2["x1"]) x = np.linspace(mini, maxi, 1000) y = stats.norm.pdf(x, mu, np.sqrt(var)) plt.plot(x,y) plt.show()

p = stats.norm.cdf(0.4, mu, np.sqrt(var))- stats.norm.cdf(0.2,mu,np.sqrt(var)) print(p)

train = df2[df2["split"]=="train"] def train(df): mean = df.groupby("y").mean().reset_index() prior = {} llh_d = {} llh_c = {}

df3 = pd.read_csv("data3.csv") df3

# TEST 1 x_bar = np.mean(df3[df3["group"] == 1]["active_time"]) y_bar = np.mean(df3[df3["group"] == 2]["active_time"]) N_x = len(df3[df3["group"] == 1]["active_time"]) N_y = len(df3[df3["group"] == 2]["active_time"]) s2_x = np.var(df3[df3["group"] == 1]["active_time"]) s2_y = np.var(df3[df3["group"] == 2]["active_time"]) dff = np.power(s2_x/N_x+s2_y/N_y, 2)/(np.power(s2_x/N_x, 2)/(N_x-1) + np.power(s2_y/N_y,2)/(N_y-1)) t0 = (x_bar-y_bar)/np.sqrt(s2_x/N_x + s2_y/N_y) p = 2*min(stats.t.cdf(t0, dff), 1-t.cdf(t0, dff)) print("P-value of test 1: ", p) #PDF x = np.linspace(t.ppf(0.01, dff), t.ppf(0.99, dff), 100) plt.plot(x, t.pdf(x, dff), 'r-', lw=5, alpha=0.6, label='t pdf')

# TEST 2 # NOT ENOUGH TIME TO COMPUTE v = df3.subject_id.value_counts() dftest2 = df3[df3.subject_id.isin(v.index[v.gt(1)])].reset_index() dfg1 = dftest2[dftest2["group"] == 1] dfg3 = dftest2[dftest2["group"] == 3] m = np.mean(df3) x_bar = np.mean(df3[df3["group"] == 1]["active_time"]) y_bar = np.mean(df3[df3["group"] == 2]["active_time"]) N_x = len(df3[df3["group"] == 1]["active_time"]) N_y = len(df3[df3["group"] == 2]["active_time"]) s2_x = np.var(df3[df3["group"] == 1]["active_time"]) s2_y = np.var(df3[df3["group"] == 2]["active_time"]) t0 p = 2*min(stats.t.cdf(t0, dff), 1-t.cdf(t0, dff)) print("P-value of test 1: ", p) #PDF x = np.linspace(t.ppf(0.01, dff), t.ppf(0.99, dff), 100) plt.plot(x, t.pdf(x, dff), 'r-', lw=5, alpha=0.6, label='t pdf')