Baseball

import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
# Retina display
%config InlineBackend.figure_format = 'retina'

from tueplots import bundles
plt.rcParams.update(bundles.beamer_moml())

# Also add despine to the bundle using rcParams
plt.rcParams['axes.spines.right'] = False
plt.rcParams['axes.spines.top'] = False

# Increase font size to match Beamer template
plt.rcParams['font.size'] = 12
# Make background transparent
plt.rcParams['figure.facecolor'] = 'none'

from ISLP import load_data
Hitters = load_data('Hitters')

Hitters

	AtBat	Hits	HmRun	Runs	RBI	Walks	Years	CAtBat	CHits	CHmRun	CRuns	CRBI	CWalks	League	Division	PutOuts	Assists	Errors	Salary	NewLeague
0	293	66	1	30	29	14	1	293	66	1	30	29	14	A	E	446	33	20	NaN	A
1	315	81	7	24	38	39	14	3449	835	69	321	414	375	N	W	632	43	10	475.0	N
2	479	130	18	66	72	76	3	1624	457	63	224	266	263	A	W	880	82	14	480.0	A
3	496	141	20	65	78	37	11	5628	1575	225	828	838	354	N	E	200	11	3	500.0	N
4	321	87	10	39	42	30	2	396	101	12	48	46	33	N	E	805	40	4	91.5	N
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
317	497	127	7	65	48	37	5	2703	806	32	379	311	138	N	E	325	9	3	700.0	N
318	492	136	5	76	50	94	12	5511	1511	39	897	451	875	A	E	313	381	20	875.0	A
319	475	126	3	61	43	52	6	1700	433	7	217	93	146	A	W	37	113	7	385.0	A
320	573	144	9	85	60	78	8	3198	857	97	470	420	332	A	E	1314	131	12	960.0	A
321	631	170	9	77	44	31	11	4908	1457	30	775	357	249	A	W	408	4	3	1000.0	A

322 rows × 20 columns

(Hitters.Hits/Hitters.AtBat).hist(bins=50)
plt.grid(False)
plt.xlabel("Batting Average")
plt.savefig("baseball-a.pdf")

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import torch.distributions as dist
import torch

params = {"A": (3, 10),
         "B": (250, 400),
         "C": (153, 450),
         }

colors = ["g", "b", "k"]
lines = ["--", "-.", ":", "-"]
(Hitters.Hits/Hitters.AtBat).hist(bins=50, alpha=0.2)

x_lin = torch.linspace(0.0, 0.5, 100)
for i, (name, d) in enumerate(params.items()):
    plt.plot(x_lin, dist.Beta(*d).log_prob(x_lin).exp(), 
             label=f"{name}: Beta{d}", lw=4, ls=lines[i], c=colors[i])
plt.legend(title="Prior")
plt.grid(False)
plt.xlabel("Batting Average")
plt.savefig("baseball-b.pdf")

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findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed
findfont: Generic family 'sans-serif' not found because none of the following families were found: Roboto Condensed

import numpy as np
from scipy import stats

# Your data
data = (Hitters.Hits / Hitters.AtBat).values

# Define the distribution you want to fit (for example, a beta distribution)
distribution = stats.beta



# Specify bounds for the parameters
bounds = ((1, 300), (1, 300))

# Fit the distribution with bounds
res = stats.fit(distribution, data, bounds=bounds)

res

  params: FitParams(a=33.704412916832084, b=96.02829213089092, loc=0.0, scale=1.0)
 success: True
 message: 'Optimization terminated successfully.'