【Programming using PyMC3】Statistical Rethinking with Python and PyMC3

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Statistical Rethinking with Python and PyMC3

Statistical Rethinking is an incredible good introductory book to Bayesian Statistics, its follows a Jaynesian and practical approach with very good examples and clear explanations.

In this repository I am (slowly) porting the examples in the book to PyMC3. I am trying to keep the examples as close as possible to those in the book, while at the same time I am trying to express them in the most Pythonic and PyMC3onic way I can.

All contributions are wellcome!

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2016-12-11 10:32:13 上传

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关键词：Statistical Programming statistica Rethinking statistic practical examples possible trying close

1. %matplotlib inline
   
2. import pymc3 as pm
   
3. import numpy as np
   
4. import scipy.stats as stats
   
5. import matplotlib.pyplot as plt
   
6. import seaborn as sns; sns.set_palette('colorblind'); sns.set_color_codes()

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1. ways = np.array([0, 3, 8, 9, 0])
   
2. ways/ways.sum()

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1. stats.binom.pmf(6, n=9, p=0.5)

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感谢分享

1. ef posterior_grid_approx(grid_points=5, success=6, tosses=9):
   
2.     """
   
3.     """
   
4.     # define grid
   
5.     p_grid = np.linspace(0, 1, grid_points)
   
6. 
   
7.     # define prior
   
8.     prior = np.repeat(5, grid_points)  # uniform
   
9.     #prior = (p_grid >= 0.5).astype(int)  # truncated
   
10.     #prior = np.exp(- 5 * abs(p_grid - 0.5))  # double exp
    
11. 
    
12.     # compute likelihood at each point in the grid
    
13.     likelihood = stats.binom.pmf(success, tosses, p_grid)
    
14. 
    
15.     # compute product of likelihood and prior
    
16.     unstd_posterior = likelihood * prior
    
17. 
    
18.     # standardize the posterior, so it sums to 1
    
19.     posterior = unstd_posterior / unstd_posterior.sum()
    
20.     return p_grid, posterior

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1. data = np.repeat((0, 1), (3, 6))
   
2. with pm.Model() as normal_aproximation:
   
3.     p = pm.Uniform('p', 0, 1, transform=None)
   
4.     w = pm.Binomial('w', n=len(data), p=p, observed=data.sum())
   
5.     mean_q = pm.find_MAP()
   
6.     std_q = ((1/pm.find_hessian(mean_q))**0.5)[0]
   
7. mean_q['p'], std_q

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1. # analytical calculation
   
2. w, n = 6, 9
   
3. x = np.linspace(0, 1, 100)
   
4. plt.plot(x, stats.beta.pdf(x , w+1, n-w+1), label='True posterior')
   
5. # quadratic approximation
   
6. plt.plot(x, stats.norm.pdf(x, mean_q['p'], std_q), label='Quadratic approximation')
   
7. plt.legend(loc=0);

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1. import sys, IPython, scipy, matplotlib, platform
   
2. print("This notebook was createad on a computer %s running %s and using:\nPython %s\nIPython %s\nPyMC3 %s\nNumPy %s\nSciPy %s\nMatplotlib %s\nSeaborn %s\n" % (platform.machine(), ' '.join(platform.linux_distribution()[:2]), sys.version[:5], IPython.__version__, pm.__version__, np.__version__, scipy.__version__, matplotlib.__version__, sns.__version__))

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Applications of Differential Geometry to