

In [1]:

    
import numpy as np
import spacepy.plot as spp

import pymc

%matplotlib inline









    



This unreleased version of SpacePy is not supported by the SpacePy team.






    



/Users/balarsen/miniconda3/envs/python3/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
  warnings.warn(self.msg_depr % (key, alt_key))

Page 45 example

Using a uniform Prior



In [3]:

    
mu = pymc.Uniform('mu', 0, 1e5)
deaths = pymc.Poisson('deaths', mu = 2.0*mu, observed=True, value=[3])
model = pymc.MCMC((mu, deaths))



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model.sample(10000, burn=100, burn_till_tuned=True)









    



 [----------------------------------------------253%----------------------------------------------] 37816 of 14900 complete in 1.5 sec



In [6]:

    
print(model.summary())









    



mu:
 
	Mean             SD               MC Error        95% HPD interval
	------------------------------------------------------------------
	2.031            1.002            0.029            [ 0.271  3.931]
	
	
	Posterior quantiles:
	
	2.5             25              50              75             97.5
	 |---------------|===============|===============|---------------|
	0.559            1.295           1.904          2.601         4.463
	
None



In [7]:

    
pymc.Matplot.plot(model)









    



Plotting mu

This does not match the example very well. The example is centered around 0.9

Using a conjugate prior (gamma)



In [8]:

    
mu = pymc.Gamma('mu', 3.0, 5.0)
deaths = pymc.Poisson('deaths', mu = 2.0*mu, observed=True, value=[3])
model = pymc.MCMC((mu, deaths))
model.sample(10000, burn=100, burn_till_tuned=True)
print(model.summary())
pymc.Matplot.plot(model)









    



 [-----------------100%-----------------] 14900 of 14900 complete in 0.7 sec
mu:
 
	Mean             SD               MC Error        95% HPD interval
	------------------------------------------------------------------
	0.854            0.355            0.009            [ 0.271  1.571]
	
	
	Posterior quantiles:
	
	2.5             25              50              75             97.5
	 |---------------|===============|===============|---------------|
	0.321            0.598           0.806          1.054         1.697
	
None
Plotting mu

This matches the example quite well, figure 2.5, page 46.



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