Help us understand the problem. What is going on with this article?

# Pystanで単回帰分析

More than 1 year has passed since last update.

「StanとRでベイズ統計モデリング」 Chapter7より

## 対数をとるか否か

### モデル式７－１

$\mu[n]= b_1+b_2Area[n]$
$Y[n] \sim Normal(\mu[n],\sigma_Y)$

d = pd.read_csv("input/data-rental.txt")
sns.set_style("whitegrid")
sns.jointplot(x="Area",y="Y",data=d)

d.plot.scatter(x='Area',y='Y')
plt.yscale('log')
plt.xscale('log')
plt.grid(which="both")

plt.xlabel("Area")
plt.ylabel("Y")
sns.set_style('whitegrid')
plt.title('Fig7_1')


mdl = glm("Y~Area",data=d,family=sm.families.Poisson()).fit()

plt.scatter(d['Area'], d['Y'], alpha=0.6)
xx = np.linspace(min(d['Area']),max(d['Area']),100)
plt.plot(xx, np.exp(mdl.params[0]+mdl.params[1]*xx), 'b-', label='OLS')
plt.legend()
plt.title('Fig7_1_OLS')


stanmodel = StanModel(file="model/model7-1.stan")
Area_new = np.linspace(10,120,50)
data_ = {'N':len(d),'Area':d['Area'],'Y':d['Y'],'N_new':50,'Area_new':Area_new}
fit1 = stanmodel.sampling(data=data_,n_jobs=-1,seed=1234)
ms1 = fit1.extract()

col = np.linspace(10,120,50)
df2 = pd.DataFrame(fit1['y_new'])
df2.columns = col

qua = [0.1, 0.25, 0.50, 0.75, 0.9]
d_est = pd.DataFrame()

for i in np.arange(len(df2.columns)):
for qu in qua:
d_est[qu] = df2.quantile(qu)

x = d_est.index
y1 = d_est[0.1].values
y2 = d_est[0.25].values
y3 = d_est[0.5].values
y4 = d_est[0.75].values
y5 = d_est[0.9].values

plt.fill_between(x,y1,y5,facecolor='blue',alpha=0.1)
plt.fill_between(x,y2,y4,facecolor='blue',alpha=0.5)
plt.plot(x,y3,'k-')
plt.scatter(d["Area"],d["Y"],c='b')
plt.xlabel("Area")
plt.ylabel("Y")
sns.set_style('whitegrid')
plt.title('Fig7_2')


80%ベイズ予測区間が負の値を含む

d_ori = d

quantile = [10,50,90]
colname = ['p'+str(x) for x in quantile]
d_qua = pd.DataFrame(np.percentile(ms1["y_pred"],q=quantile,axis=0).T,columns=colname)
d_ = pd.concat([d_ori,d_qua],axis=1)
d0 = d_

palette = sns.color_palette()
fig = plt.figure(figsize=(10,8))

ax.plot([-50,1900],[-50,1900],'k--',alpha=0.7)
ax.errorbar(d0.Y,d0.p50,yerr=[d0.p50-d0.p10,d0.p90-d0.p50],
fmt='o',ecolor='gray',ms=5,mfc=palette[0],alpha=0.8,marker='o')

ax.set_aspect('equal')
ax.set_xlim(-50,1900)
ax.set_ylim(-50,1900)
ax.set_xlabel("Observed")
ax.set_ylabel("Predicted")


N_mcmc = len(ms1['lp__'])
d_noise = pd.DataFrame(-ms1['mu']+np.array(d_ori['Y']))
col = d_noise.columns
d_noise.columns = ["noise" + str(col[i]+1) for i in np.arange(len(col))]

data = d.copy()
data = data.sort_values(by="Area")

d_est = pd.concat([pd.DataFrame({"mcmc":np.arange(1,N_mcmc+1)}),d_noise],axis=1)

col = d_est.columns
est = []

fig = plt.figure(figsize=(10,8))
sns.set_style('whitegrid')
sns.set(font_scale=1)

for i in np.arange(1,len(d_est.columns)):
data = d_est[col[i]]
density = gaussian_kde(data)
xs = np.linspace(min(data),max(data),100)
plt.plot(xs,density(xs),'k-',lw=0.5)
xx = xs[np.argmax(density(xs))]
plt.vlines(xx,0,max(density(xs)),colors='k',linestyle="-.",alpha=0.5,linewidth=0.5)

est.append(xs[np.argmax(density(xs))])

plt.xlabel("Value")
plt.ylabel("density")

s_dens = gaussian_kde(ms1['s_Y'])

xs = np.linspace(min(ms1['s_Y']),max(ms1['s_Y']),100)
s_MPA = xs[np.argmax(s_dens(xs))]
print(s_MPA)
rv = norm(loc=0,scale=s_MPA)

bw = 25
bins = np.arange(min(est),max(est),bw)

fig = plt.figure(figsize=(10,8))
sns.set_style('whitegrid')
sns.set(font_scale=1)

res = plt.hist(est,bins=bins,color='lightgray',edgecolor='black')
x = np.linspace(rv.ppf(0.01),rv.ppf(0.99), 100)

plt.plot(x,rv.pdf(x)*len(d)*bw,'k--')

data = est
density = gaussian_kde(data)
print(max(data))
xs = np.linspace(min(data),max(data),100)
plt.plot(xs,density(xs)*len(d)*bw,lw=3)

plt.title("7-4-L Result")
plt.xlabel("Value")
plt.ylabel("count")


### モデル式７－２

YおよびAreaの対数をとって単回帰に使う
$\mu[n]= b_1+b_2 log10(Area[n])$
$log10(Y[n]) \sim Normal(\mu[n],\sigma_Y)$

Area_new = np.linspace(10,120,50)
data_ = {'N':len(d),'Area':np.log10(d['Area']),'Y':np.log10(d['Y']),'N_new':50,'Area_new':np.log10(Area_new)}
fit2 = stanmodel.sampling(data=data_,n_jobs=-1,seed=1234)
ms2 = fit2.extract()

col = np.linspace(10,120,50)
df2 = pd.DataFrame(10**fit2['y_new'])
df2.columns = col

qua = [0.1, 0.25, 0.50, 0.75, 0.9]
d_est = pd.DataFrame()

for i in np.arange(len(df2.columns)):
for qu in qua:
d_est[qu] = df2.quantile(qu)

x = d_est.index
y1 = d_est[0.1].values
y2 = d_est[0.25].values
y3 = d_est[0.5].values
y4 = d_est[0.75].values
y5 = d_est[0.9].values

plt.fill_between(x,y1,y5,facecolor='blue',alpha=0.1)
plt.fill_between(x,y2,y4,facecolor='blue',alpha=0.5)
plt.plot(x,y3,'k-')
plt.scatter(d["Area"],d["Y"],c='b')

plt.xlabel("Area")
plt.ylabel("Y")
sns.set_style('whitegrid')
plt.title('Fig7_2')


d_ori = d

quantile = [10,50,90]
colname = ['p'+str(x) for x in quantile]
d_qua = pd.DataFrame(np.percentile(10**ms2["y_pred"],q=quantile,axis=0).T,columns=colname)
d_ = pd.concat([d_ori,d_qua],axis=1)
d0 = d_

palette = sns.color_palette()
fig = plt.figure(figsize=(10,8))

ax.plot([-50,1900],[-50,1900],'k--',alpha=0.7)
ax.errorbar(d0.Y,d0.p50,yerr=[d0.p50-d0.p10,d0.p90-d0.p50],
fmt='o',ecolor='gray',ms=5,mfc=palette[0],alpha=0.8,marker='o')

ax.set_aspect('equal')
ax.set_xlim(-50,1900)
ax.set_ylim(-50,1900)
ax.set_xlabel("Observed")
ax.set_ylabel("Predicted")


Areaが1000m2より大きい物件のベイズ予測区間は広くなっている

N_mcmc = len(ms2['lp__'])
d_noise = pd.DataFrame(-ms2['mu']+np.array(np.log10(d_ori['Y'])))
col = d_noise.columns
d_noise.columns = ["noise" + str(col[i]+1) for i in np.arange(len(col))]

data = d.copy()
data = data.sort_values(by="Area")

d_est = pd.concat([pd.DataFrame({"mcmc":np.arange(1,N_mcmc+1)}),d_noise],axis=1)

col = d_est.columns
est = []

fig = plt.figure(figsize=(10,8))
sns.set_style('whitegrid')
sns.set(font_scale=1)

for i in np.arange(1,len(d_est.columns)):
data = d_est[col[i]]
density = gaussian_kde(data)
xs = np.linspace(min(data),max(data),100)
plt.plot(xs,density(xs),'k-',lw=0.5)
xx = xs[np.argmax(density(xs))]
plt.vlines(xx,0,max(density(xs)),colors='k',linestyle="-.",alpha=0.5,linewidth=0.5)

est.append(xs[np.argmax(density(xs))])

plt.xlabel("Value")
plt.ylabel("density")

s_dens = gaussian_kde(ms2['s_Y'])

xs = np.linspace(min(ms2['s_Y']),max(ms2['s_Y']),100)
s_MPA = xs[np.argmax(s_dens(xs))]
print(s_MPA)
rv = norm(loc=0,scale=s_MPA)

bw = 0.02
bins = np.arange(min(est),max(est),bw)

fig = plt.figure(figsize=(10,8))
sns.set_style('whitegrid')
sns.set(font_scale=1)

res = plt.hist(est,bins=bins,color='lightgray',edgecolor='black')
x = np.linspace(rv.ppf(0.01),rv.ppf(0.99), 100)

plt.plot(x,rv.pdf(x)*len(d)*bw,'k--')

data = est
density = gaussian_kde(data)
print(max(data))
xs = np.linspace(min(data),max(data),100)
plt.plot(xs,density(xs)*len(d)*bw,lw=3)

plt.title("7-4-R Result")
plt.xlabel("Value")
plt.ylabel("count")


Why not register and get more from Qiita?
1. We will deliver articles that match you
By following users and tags, you can catch up information on technical fields that you are interested in as a whole
2. you can read useful information later efficiently
By "stocking" the articles you like, you can search right away