# some early portion of the chain must be removed. This is referred to as # the 'burn-in' period. This period allows the chain to both find the high # density areas, and adjust the proposal widths to their optimal values. # The plot_diagnostics() method can help us decide what size of burn-in to use: chain.plot_diagnostics(filename='gibbs_diagnostics.png') # Occasionally samples are also 'thinned' by a factor of n (where only every # n'th sample is used) in order to reduce the size of the data set for # storage, or to produce uncorrelated samples. # based on the diagnostics we can choose to manually set a global burn and # thin value, which is used (unless otherwise specified) by all methods which # access the samples chain.burn = 10000 chain.thin = 10 # the burn-in and thinning can also be set automatically as follows: # chain.autoselect_burn_and_thin() # After discarding burn-in, what we have left should be a representative # sample drawn from the posterior. Repeating the previous plot as a # scatter-plot shows the sample: p = chain.get_probabilities() # color the points by their probability value plt.scatter(chain.get_parameter(0), chain.get_parameter(1), c=exp(p - max(p)), marker='.') plt.xlabel('parameter 1') plt.ylabel('parameter 2') plt.grid()
# some early portion of the chain must be removed. This is referred to as # the 'burn-in' period. This period allows the chain to both find the high # density areas, and adjust the proposal widths to their optimal values. # The plot_diagnostics() method can help us decide what size of burn-in to use: chain.plot_diagnostics() # Occasionally samples are also 'thinned' by a factor of n (where only every # n'th sample is used) in order to reduce the size of the data set for # storage, or to produce uncorrelated samples. # based on the diagnostics we can choose to manually set a global burn and # thin value, which is used (unless otherwise specified) by all methods which # access the samples chain.burn = 2000 chain.thin = 5 # the burn-in and thinning can also be set automatically as follows: chain.autoselect_burn_and_thin() # After discarding burn-in, what we have left should be a representative # sample drawn from the posterior. Repeating the previous plot as a # scatter-plot shows the sample: p = chain.get_probabilities() # color the points by their probability value plt.scatter(chain.get_parameter(0), chain.get_parameter(1), c=exp(p - max(p)), marker='.') plt.xlabel('parameter 1') plt.ylabel('parameter 2') plt.grid()
def rosenbrock(t): x, y = t x2 = x**2 b = 15. # correlation strength parameter v = 3. # variance of the gaussian term return -x2 - b * (y - x2)**2 - 0.5 * (x2 + y**2) / v # create the chain object from inference.mcmc import GibbsChain gibbs = GibbsChain(posterior=rosenbrock, start=array([2., -4.])) gibbs.advance(150000) gibbs.burn = 10000 gibbs.thin = 70 p = gibbs.get_probabilities() # color the points by their probability value fig = plt.figure(figsize=(5, 4)) ax1 = fig.add_subplot(111) ax1.scatter(gibbs.get_parameter(0), gibbs.get_parameter(1), c=exp(p - max(p)), marker='.') ax1.set_ylim([None, 2.8]) ax1.set_xlim([-1.8, 1.8]) ax1.set_xticks([]) ax1.set_yticks([]) # ax1.set_title('Gibbs sampling') plt.tight_layout() plt.savefig('gallery_gibbs_sampling.png')