[Case Study]Bayesian GLMs made easy with PyMC3

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Author: Thomas Wiecki

In this blog post I will talk about:

• How the Bayesian Revolution in many scientific disciplines is hindered by poor usability of current Probabilistic Programming languages.
• A gentle introduction to Bayesian linear regression and how it differs from the frequentist approach.
• A preview of PyMC3 (currently in alpha) and its new GLM submodule I wrote to allow creation and estimation of Bayesian GLMs as easy as frequentist GLMs in R.
  

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Bayesian GLMs made easy with PyMC3.pdf (1.01 MB)

2016-12-18 07:11:03 上传

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关键词：Case study Bayesian Bayes study baye scientific currently creation about blog

1. size = 200
   
2. true_intercept = 1
   
3. true_slope = 2
   
4. 
   
5. x = np.linspace(0, 1, size)
   
6. # y = a + b*x
   
7. true_regression_line = true_intercept + true_slope * x
   
8. # add noise
   
9. y = true_regression_line + np.random.normal(scale=.5, size=size)
   
10. 
    
11. data = dict(x=x, y=y)

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1. fig = plt.figure(figsize=(7, 7))
   
2. ax = fig.add_subplot(111, xlabel='x', ylabel='y', title='Generated data and underlying model')
   
3. ax.plot(x, y, 'x', label='sampled data')
   
4. ax.plot(x, true_regression_line, label='true regression line', lw=2.)
   
5. plt.legend(loc=0);

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1. Here we use the awesome new NUTS sampler (our Inference Button) to draw 2000 posterior samples.
   
2. 
   
3. In [ ]:
   
4. with Model() as model: # model specifications in PyMC3 are wrapped in a with-statement
   
5.     # Define priors
   
6.     sigma = HalfCauchy('sigma', beta=10, testval=1.)
   
7.     intercept = Normal('Intercept', 0, sd=20)
   
8.     x_coeff = Normal('x', 0, sd=20)
   
9.    
   
10.     # Define likelihood
    
11.     likelihood = Normal('y', mu=intercept + x_coeff * x,
    
12.                         sd=sigma, observed=y)
    
13.    
    
14.     # Inference!
    
15.     start = find_MAP() # Find starting value by optimization
    
16.     step = NUTS(scaling=start) # Instantiate MCMC sampling algorithm
    
17.     trace = sample(2000, step, start=start, progressbar=False) # draw 2000 posterior samples using NUTS sampling

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