
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

import seaborn as sns

%matplotlib inline 
%config InlineBackend.figure_format='retina' #Sharp graphs, higher resolution


x = np.random.random(100)
y=np.random.random([300,500])

x

array([0.72849772, 0.28634765, 0.51250514, 0.12223006, 0.20499995,
       0.97943066, 0.89593034, 0.93264747, 0.6990873 , 0.4476208 ,
       0.17922023, 0.88086146, 0.90034927, 0.85839652, 0.36774522,
       0.92775528, 0.1990322 , 0.70765016, 0.98386024, 0.6303022 ,
       0.33444369, 0.46200633, 0.67329615, 0.04208176, 0.01933778,
       0.64850699, 0.65444804, 0.50877939, 0.35702145, 0.74000317,
       0.26780376, 0.18268975, 0.64709331, 0.45530489, 0.21019303,
       0.07332238, 0.69304089, 0.0820179 , 0.2799592 , 0.33082313,
       0.58428732, 0.09025344, 0.7034371 , 0.73103803, 0.50399405,
       0.55354515, 0.62670808, 0.69993811, 0.03142535, 0.04919653,
       0.59894273, 0.29196858, 0.20118783, 0.41229857, 0.53640477,
       0.57474109, 0.17812323, 0.33802916, 0.38649237, 0.48716238,
       0.19490078, 0.94208024, 0.14982987, 0.45643282, 0.12844383,
       0.58477759, 0.64205975, 0.92245012, 0.65224673, 0.04545392,
       0.92779547, 0.88744108, 0.21585594, 0.36714833, 0.44339485,
       0.17460866, 0.41274068, 0.65362162, 0.43761918, 0.26878401,
       0.29845683, 0.51557875, 0.52447941, 0.8529765 , 0.61862564,
       0.76241719, 0.50328707, 0.28306359, 0.44934877, 0.0953664 ,
       0.39526117, 0.2019546 , 0.97922837, 0.66848224, 0.88907361,
       0.65501013, 0.26024173, 0.5920493 , 0.16029675, 0.51547966])


plt.hist(x)
plt.show()


bob=plt.hist(x)


bob[0][2]

9.0


x = np.random.random(1000000)


g=plt.hist(x,1000)


sns.histplot(x)

<AxesSubplot:ylabel='Count'>


x=np.random.random(1000)
sns.displot(x,kind="kde")

<seaborn.axisgrid.FacetGrid at 0x7f995b329b20>


sns.histplot(x,cumulative=True)

<AxesSubplot:ylabel='Count'>


x=np.random.normal(3,1,1000)


plt.plot(x,'.')

[<matplotlib.lines.Line2D at 0x7f9959e12b50>]


sns.histplot(x,cumulative=True)

<AxesSubplot:ylabel='Count'>


sns.boxplot(data=x, orient='h')

<AxesSubplot:>


np.mean(x)

2.9873071782799387


np.std(x)

0.9970066328090376


np.median(x)

3.011721881611428


np.var(x)

0.994022225865215


np.ptp(x)

6.208458175832762


np.amin(x)

-0.3795143648460684


np.min(x)

-0.3795143648460684


np.percentile(x,27)

2.365205037359119


x=np.random.randint(10,100,2000)
r=np.random.randint(1,10)
w = np.random.random(2000)
n = np.random.normal(0,1,2000)

z=r*x + w*n*x

z

array([117.73868384, 287.99460851, 319.70747003, ..., 310.588065  ,
        39.20358754, 300.62657006])


plt.plot(x,z,'.',alpha=0.052)

[<matplotlib.lines.Line2D at 0x7f9969948f70>]


dataX=pd.DataFrame(x,z)


dataX.head()


dataX=dataX.reset_index()


dataX.head()


dataX.columns =['z','x']


dataX.head()


dataX.tail(20)


dataX.describe()


sns.boxplot(data=dataX)

<AxesSubplot:>


sns.scatterplot(x='x',y='z',data=dataX)

<AxesSubplot:xlabel='x', ylabel='z'>


plt.scatter(dataX.x,dataX.z,alpha=0.5)

<matplotlib.collections.PathCollection at 0x7f996999a3a0>


sns.jointplot(x='x',y='z',data=dataX)

<seaborn.axisgrid.JointGrid at 0x7f993c772c40>


sns.pairplot(dataX)

<seaborn.axisgrid.PairGrid at 0x7f993ce69bb0>


sns.lmplot(x='x',y='z',data=dataX)

<seaborn.axisgrid.FacetGrid at 0x7f99697dcaf0>


sns.regplot(x='x',y='z',data=dataX)

<AxesSubplot:xlabel='x', ylabel='z'>


sns.kdeplot(x='x',y='z',data=dataX,cmap='Reds',shade=True)

<AxesSubplot:xlabel='x', ylabel='z'>


dataX=pd.read_csv('data/110Statdata.csv')


dataX.head(20)


dataX.tail()

	z	x
1980	279.340770	70
1981	197.818556	49
1982	82.450744	21
1983	80.472200	31
1984	376.640677	88
1985	290.713836	58
1986	396.367726	88
1987	36.453017	12
1988	50.136872	12
1989	207.226602	53
1990	210.339484	53
1991	78.749481	20
1992	338.592799	90
1993	77.569325	19
1994	237.376062	70
1995	346.193869	83
1996	229.938570	64
1997	310.588065	76
1998	39.203588	10
1999	300.626570	64

	z	x
count	2000.000000	2000.000000
mean	213.523321	53.601500
std	107.747149	25.817959
min	26.955958	10.000000
25%	118.727254	30.000000
50%	210.185950	53.000000
75%	296.533153	75.000000
max	543.385580	99.000000

	Q	M	M .1	M .2	M .3	M .4	F	F.1	F.2	F.3	F.4
0	1	71.0	67.0	75	72.0	72.0	69.0	70.0	67	61	67
1	2	162.0	140.0	177	210.0	180.0	136.0	162.0	152	135	150
2	3	10.0	11.0	12	11.0	11.0	9.0	10.0	8	8	7
3	4	35.0	7.0	3	11.0	20.0	63.0	1.0	5	9	8
4	5	7.0	28.0	3	14.0	15.0	21.0	0.0	3	7	3
5	1	70.0	70.0	72	71.0	71.0	68.0	65.0	62	64	64
6	2	140.0	175.0	190	240.0	280.0	124.0	140.0	110	147	125
7	3	10.0	8.0	11	11.0	11.0	7.0	9.0	7.5	8	6.5
8	4	14.0	2.0	2	6.0	10.0	4.0	5.0	1	10	20
9	5	5.0	0.0	20	12.0	10.0	10.0	2.0	1	28	3
10	1	69.0	70.0	76	69.0	68.0	69.0	63.0	64	60	60
11	2	190.0	175.0	335	225.0	136.0	140.0	130.0	135	115	135
12	3	11.0	12.0	13	11.0	10.0	11.0	7.0	9	7	7
13	4	6.0	20.0	7	6.0	7.0	6.0	5.0	1	42	10
14	5	0.0	48.0	20	10.0	0.0	0.0	0.0	2	0	2
15	1	72.0	71.0	73	75.0	71.0	65.0	68.0	65	66	66
16	2	310.0	140.0	180	200.0	160.0	140.0	130.0	145	140	150
17	3	13.0	11.0	12	13.0	11.0	8.0	7.5	8	7.5	7.5
18	4	26.0	2.0	5	10.0	4.0	5.0	10.0	7	12	20
19	5	20.0	8.0	5	15.0	3.0	12.0	8.0	3	3	15

	Q	M	M .1	M .2	M .3	M .4	F	F.1	F.2	F.3	F.4
820	1	71.0	70.0	71	72.0	68.0	71.0	65.0	64	70	73
821	2	149.0	164.0	127	213.0	180.0	148.0	110.0	116	134	185
822	3	12.0	11.5	10	12.0	11.0	6.0	4.0	5	8	7
823	4	15.0	30.0	25	0.0	30.0	15.0	5.0	5	15	30
824	5	5.0	11.0	0	0.0	20.0	1.0	0.0	0	0	5

MAT411 Bayesian Data Analysis¶

Combining sets¶

Pandas Dataframe¶

Real Data¶

	0
117.738684	27
287.994609	77
319.707470	84
182.845268	52
175.606768	44