From 363084f4fc8410aa4cdb61e8a39769c27256933b Mon Sep 17 00:00:00 2001 From: aloctavodia Date: Thu, 9 Feb 2017 09:40:30 -0300 Subject: [PATCH 1/3] fix bug in loo and p_loo computation, also return waic and loo results as dataframes --- pymc3/stats.py | 58 +++++++++++++++++++++++---------------- pymc3/tests/test_stats.py | 6 ++-- 2 files changed, 37 insertions(+), 27 deletions(-) diff --git a/pymc3/stats.py b/pymc3/stats.py index 8e2f491693..4203081549 100644 --- a/pymc3/stats.py +++ b/pymc3/stats.py @@ -104,7 +104,7 @@ def log_post_trace(trace, model): return np.vstack([obs.logp_elemwise(pt) for obs in model.observed_RVs] for pt in trace) -def waic(trace, model=None, n_eff=False, pointwise=False): +def waic(trace, model=None, pointwise=False): """ Calculate the widely available information criterion, its standard error and the effective number of parameters of the samples in trace from model. @@ -117,9 +117,6 @@ def waic(trace, model=None, n_eff=False, pointwise=False): trace : result of MCMC run model : PyMC Model Optional model. Default None, taken from context. - n_eff: bool - if True the effective number parameters will be returned. - Default False pointwise: bool if True the pointwise predictive accuracy will be returned. Default False @@ -127,9 +124,11 @@ def waic(trace, model=None, n_eff=False, pointwise=False): Returns ------- + DataFrame with the following columns: waic: widely available information criterion waic_se: standard error of waic - p_waic: effective number parameters, only if n_eff True + p_waic: effective number parameters + waic_i: and array of the pointwise predictive accuracy, only if pointwise True """ model = modelcontext(model) @@ -151,16 +150,18 @@ def waic(trace, model=None, n_eff=False, pointwise=False): p_waic = np.sum(vars_lpd) - - if n_eff: - return waic, waic_se, p_waic - elif pointwise: - return waic, waic_se, waic_i, p_waic + if pointwise: + return pd.DataFrame([[waic, waic_se, p_waic, waic_i]], + columns=['WAIC', 'WAIC_se', 'p_WAIC', 'waic_i'], + index=['model']) else: - return waic, waic_se + return pd.DataFrame([[waic, waic_se, p_waic]], + columns=['WAIC', 'WAIC_se', 'p_WAIC'], + index=['model']) + -def loo(trace, model=None, n_eff=False): +def loo(trace, model=None, pointwise=False): """ Calculates leave-one-out (LOO) cross-validation for out of sample predictive model fit, following Vehtari et al. (2015). Cross-validation is computed using @@ -172,17 +173,20 @@ def loo(trace, model=None, n_eff=False): trace : result of MCMC run model : PyMC Model Optional model. Default None, taken from context. - n_eff: bool - if True the effective number parameters will be computed and returned. + pointwise: bool + if True the pointwise predictive accuracy will be returned. Default False Returns ------- - elpd_loo: log pointwise predictive density calculated via approximated LOO cross-validation - elpd_loo_se: standard error of waic elpd_loo - p_loo: effective number parameters, only if n_eff True + A DataFrame with the following columns: + loo: approximated Leave-one-out cross-validation + loo_se: standard error of loo + p_loo: effective number of parameters + loo_i: and array of the pointwise predictive accuracy, only if pointwise True """ + model = modelcontext(model) log_py = log_post_trace(trace, model) @@ -220,24 +224,30 @@ def loo(trace, model=None, n_eff=False): # Replace importance ratios with order statistics of fitted Pareto r_sorted[q80:] = np.vstack(expvals).T # Unsort ratios (within columns) before using them as weights - r_new = np.array([r[np.argsort(i)] - for r, i in zip(r_sorted, np.argsort(r, axis=0))]) + r_new = np.array([r[np.argsort(i)] + for r, i in zip(r_sorted.T, np.argsort(r.T, axis=1))]).T # Truncate weights to guarantee finite variance w = np.minimum(r_new, r_new.mean(axis=0) * S**0.75) - loo_lppd_i = -2.0 * logsumexp(log_py, axis = 0, b = w / np.sum(w, axis = 0)) + loo_lppd_i = - 2. * logsumexp(log_py, axis=0, b=w/np.sum(w, axis=0)) loo_lppd_se = np.sqrt(len(loo_lppd_i) * np.var(loo_lppd_i)) loo_lppd = np.sum(loo_lppd_i) + + lppd = np.sum(logsumexp(log_py, axis=0, b=1./log_py.shape[0])) + p_loo = lppd + (0.5 * loo_lppd) - if n_eff: - p_loo = np.sum(np.log(np.mean(py, axis=0))) - loo_lppd - return loo_lppd, loo_lppd_se, p_loo + if pointwise: + return pd.DataFrame([[loo_lppd, loo_lppd_se, p_loo, loo_lppd_i]], + columns=['LOO', 'LOO_se', 'p_LOO', 'LOO_i'], + index=['model']) else: - return loo_lppd, loo_lppd_se + return pd.DataFrame([[loo_lppd, loo_lppd_se, p_loo]], + columns=['LOO', 'LOO_se', 'p_LOO'], + index=['model']) def bpic(trace, model=None): diff --git a/pymc3/tests/test_stats.py b/pymc3/tests/test_stats.py index 91538f5635..21f75809c3 100644 --- a/pymc3/tests/test_stats.py +++ b/pymc3/tests/test_stats.py @@ -77,7 +77,7 @@ def test_waic(self): step = pm.Metropolis() trace = pm.sample(100, step) - calculated_waic, calculated_waic_se = pm.waic(trace) + calculated_waic = pm.waic(trace) log_py = st.binom.logpmf(np.atleast_2d(x_obs).T, 5, trace['p']).T @@ -88,8 +88,8 @@ def test_waic(self): actual_waic_se = np.sqrt(len(waic_i) * np.var(waic_i)) actual_waic = np.sum(waic_i) - assert_almost_equal(calculated_waic, actual_waic, decimal=2) - assert_almost_equal(calculated_waic_se, actual_waic_se, decimal=2) + assert_almost_equal(calculated_waic['WAIC'].values, actual_waic, decimal=2) + assert_almost_equal(calculated_waic['WAIC_se'].values, actual_waic_se, decimal=2) def test_hpd(self): """Test HPD calculation""" From 07402b16498ec09449e217ddf5bf897de340dded Mon Sep 17 00:00:00 2001 From: aloctavodia Date: Thu, 9 Feb 2017 10:33:19 -0300 Subject: [PATCH 2/3] autopep8 --- pymc3/stats.py | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/pymc3/stats.py b/pymc3/stats.py index 4203081549..c43b458b82 100644 --- a/pymc3/stats.py +++ b/pymc3/stats.py @@ -134,7 +134,7 @@ def waic(trace, model=None, pointwise=False): log_py = log_post_trace(trace, model) - lppd_i = logsumexp(log_py, axis = 0, b = 1.0 / log_py.shape[0]) + lppd_i = logsumexp(log_py, axis=0, b=1.0 / log_py.shape[0]) vars_lpd = np.var(log_py, axis=0) if np.any(vars_lpd > 0.4): @@ -160,7 +160,6 @@ def waic(trace, model=None, pointwise=False): index=['model']) - def loo(trace, model=None, pointwise=False): """ Calculates leave-one-out (LOO) cross-validation for out of sample predictive @@ -224,19 +223,19 @@ def loo(trace, model=None, pointwise=False): # Replace importance ratios with order statistics of fitted Pareto r_sorted[q80:] = np.vstack(expvals).T # Unsort ratios (within columns) before using them as weights - r_new = np.array([r[np.argsort(i)] + r_new = np.array([r[np.argsort(i)] for r, i in zip(r_sorted.T, np.argsort(r.T, axis=1))]).T # Truncate weights to guarantee finite variance w = np.minimum(r_new, r_new.mean(axis=0) * S**0.75) - loo_lppd_i = - 2. * logsumexp(log_py, axis=0, b=w/np.sum(w, axis=0)) + loo_lppd_i = - 2. * logsumexp(log_py, axis=0, b=w / np.sum(w, axis=0)) loo_lppd_se = np.sqrt(len(loo_lppd_i) * np.var(loo_lppd_i)) loo_lppd = np.sum(loo_lppd_i) - - lppd = np.sum(logsumexp(log_py, axis=0, b=1./log_py.shape[0])) + + lppd = np.sum(logsumexp(log_py, axis=0, b=1. / log_py.shape[0])) p_loo = lppd + (0.5 * loo_lppd) From 6c23f7763483bf70b049e1294919e294740e9b2f Mon Sep 17 00:00:00 2001 From: aloctavodia Date: Thu, 9 Feb 2017 15:51:35 -0300 Subject: [PATCH 3/3] use namedtuple instead of dataframe, update model comparison example --- docs/source/notebooks/Model Comparison.ipynb | 92 ++++++++++---------- pymc3/stats.py | 25 +++--- pymc3/tests/test_stats.py | 4 +- 3 files changed, 61 insertions(+), 60 deletions(-) diff --git a/docs/source/notebooks/Model Comparison.ipynb b/docs/source/notebooks/Model Comparison.ipynb index 11dbdb5101..15e700313a 100644 --- a/docs/source/notebooks/Model Comparison.ipynb +++ b/docs/source/notebooks/Model Comparison.ipynb @@ -79,9 +79,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "WARNING (theano.tensor.blas): We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n", - "WARNING:theano.tensor.blas:We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n", - "100%|██████████| 2000/2000 [00:00<00:00, 3510.88it/s]\n" + "Average ELBO = -42.09: 100%|██████████| 200000/200000 [00:15<00:00, 12578.89it/s] 8, 10674.33it/s]\n", + "100%|██████████| 2000/2000 [00:00<00:00, 2385.73it/s]\n" ] } ], @@ -99,9 +98,9 @@ "outputs": [ { "data": { - "image/png": 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Dye4Xvt49Ng/KDSq4PAG0dGZu1ePi66auyHMQCNJo6bTFxCH7A0FO1zyr0wel\nTJS1xUyaYbCnuTvyt8XuxVeHOzG+sjAmzi8VDrcfaoUkcp9QoGDsdcPq9MIaZQkpNygTYq6j7xqT\nLbTI4PEFoZL3n2P4eQgXmAZix8nrD2LfMSNUcjEmVvdny/MHaew50o3KUjXnvXEyKo1+uP92kyMm\nviosY7gYMZBaoUrXYyWcTIXNarr3aDcmVuszrvOZi4K9fOF1p/r9/phMfmIx/6rpBMK5xq4DndjT\nbERNuRbfvXhEvsUZMhRqZFhTPwVqhRib/3UUXx/uyrdIhAucU6dO4fXXX8fcuXPx4x//GH/729/Q\n3d2d+sBBIH6SES48GlYE0qXL4kpY+Q5bHlKtyVrsXpzqsIXciYKZ1YEJBGm4PAEcbevF/hMha0G8\n8pdqdVgeNcGM31dAUQnKXsTNKGm7fePMY1Ln9gZw5LQFp5IokGzEW6H8gdjV8+hrmkyKcLKKZJnO\nAkEaXx3uRGt3cstXvGsTX9gsW0fOWBBgsQhE1yGMvwQ9Vg+ropzQX9hN1eVDp9mFls7+sW8+08t6\njM3lQ9NpM46ctqRsny/x5x1WittN3NZXNstLuJno+7fTnGhtoaLuhEjiyzSsJ2FFtMfqwd6jxogV\nc98xI4D+xYZoWQM0jRNnrZGEC5lgdfrQbnLGvGsYhoHV4c2otlz84kPMNo7xsDl9GVuagsH0jnOk\naV1LBi+F6qqrrsIPf/hDbN68GX/5y1+wYsUKXHHFFVkTgkAYKrQbHdj8r2bIpaJQAoYc1/g41ygt\nVGD14imQSYV45b3DaDxuSn0QgZAj9Ho9KIpCdXU1mpubUVJSMmQL0EfHICQj2XTAbI/NVhV2beKc\nfPT93NxqQZfFFWNJYZiQK1X0BDcVYfeksDtOfK9sE8tooled40WmKJbzoNj3ZSPVBKzX4UXjCRN6\nnV5OdyO+HG9L7dLFJo9ElPoeCE+U2+OUuPjJfab1tr45krgQxuWGergl2u2vvz+vP4hj7b1oPDGw\n97/D44c/EERXXza3MOHir2yT3XhlFhiYt6fV6eUcSzY3w7Cc/dZhJrJYkjWh0K+E9fYpMZxKUuos\n/6GfeN4vJ89a0dptj3G5YwA0nbGg6Ywlbl8bPL4A6zuEz+lz3XcMEp95u8uHlk5byvPYd9wY854b\nzBkcrzf8fffdh2XLluHUqVM4c+YMli9fjnvvvTflcQzD4LHHHkN9fT2WL1+O1tbWmO3btm3DwoUL\nUV9fj48lxxLKAAAgAElEQVQ//hgA4Ha7sXbtWtxyyy24+eabceDAgfTPikDIAK8viA1vH4QvQGPF\n98bBkCSz1YVMZakady+cDKGAwkvbD+LQKfbYAgIh19TU1OB///d/8a1vfQsbN27Eyy+/DL9/aNQ5\niYfN4hCeUMRM6AapYKg/QMPeZzXgS7QRyOsPJsgaXxcpnujdGSZ2lZ2iqITJsscXgNcfTDokYUWs\nzZjconPkDD9rB5+JpzeQ2spndbIo9jysaFy1y45GWXMcbj9rnE669wHDxFqhUu2bSkYAkfgwvpxo\nt+FUpy3mPowepej2TnXYsPdo9i3QkTi8KLw+9mscrUglI3wO3RYXuvtiCNkUN2OvO2m8ULwbbKYE\nB1DGIfqZiLZKBmgaJ9qTL8gEgwz8HM+L1cFx7zFMwlgdajGj0+xCb9wxkULLUXT3DmzBJFN4O6eO\nGjUK8+bNw1VXXQWtVovdu3enPGbHjh3w+XzYsmUL1qxZE1MzxGQyYdOmTdi6dSteeeUVrF+/Hn6/\nH6+++ipqa2uxefNmPPnkkzh16lRmZ0YgpAHDMNj0r2Z09Lhw1UXlmD7GkG+RhjRjRujwk5smAwBe\nfGs/mnlOVgiEbPL4449j3rx5GD16NH7yk5+gu7sb69evz7dYAEITruj5c7ybV0unDXuauyPB6eGJ\nSqqJWjrFgi1xE8XoiVG6LjU0w+BQlMVi3zFjSlnDsLk8dZpdkaKx4X18LNaHfceMSWWlwD1ZdHsD\nvNzSsklodZ1hX33nMebxrlxhos8xetzisfNUkICQFexwi5mXtSvZHl5/EPuOGmGxe9FhTs/dLHx9\nXJ4AfP4gjrb2xijW0e1xWRZTie8P0KyWrTAtnfaYeywQpLHvuJGjr9B+fBWUkx22BHfKaCW2y+JK\n6t6ZrRQLXWksnCTIECVEvFUyVZIdsz3kssiGv8+NOFWfyfpjNdDlKS8FLyfcJ554Ajt37kRFRUXk\nN4qi8Prrryc9bu/evZg1axaAUHHEgwcPRrbt378f06dPh0gkgkqlQlVVFY4cOYLPP/8c8+bNw8qV\nK6FWq/Hoo49mcl4EQlr8a3crvjjYiephaiyeMzrf4pwTTKgqxJ0LJuK3fz+A5/+2Hz9dNBljRujy\nLRbhAuLuu+/G97//ffh8Plx55ZW48sor8y1ShFQf9fCKfDg43Or0QS4VpVSY9rO6IbHve6y9Fyo5\n++JQupMOrz9x4pS2RSTq3/HKHgUKDMPhApSkH4qiOCe34ckfW1FTvsVK0+VUhw1t3U5WJSXdeZ7Z\n5kGhJrG2DjcMa4KRbJxntMIR3Vy7yYl2owM0w0SKyKaDUCgAAkEYrW4YrX2p5+2JhViTwaZERidw\nSWXV8gWCsNi9kbFmdeHrIzwMqZ5Trq3+AB3nShl6F1SValj7jb6NkskVDZurJJeizodkzx9bNkG+\nhCzadtSNik1xzyB2YSlaibK5fLHeQyy3ttsbQJCmebtZZwteve3atQsffvghNm3aFPkvlTIFAA6H\nI1IQEQBEIhHoPk09fptCoYDD4YDFYoHdbserr76Kyy+/HE8//XS650QgpMXuI93Y+tFxFKgk+H83\nTLqgU6SnS93oItxxw0QEgjR+/bdGNLUQ9z/C4HHTTTfh3//+N+bOnYuHH34Y33zzTVbabWxsxLJl\nywAAZ86cwdKlS3HLLbfgiSeeyEr7XARpmnM1NwxXenMuAnGxEJF/p6kNBZKs8PMlus/4CWnGc34q\n5DYVT3QAPWuKcY7msrG67Q8G0077zMbRNvakDVzkcmU+EGRwutOGQJCOUdBau+0Zx3NlCyHLN5vV\n5TIJ0Up5MmtW+FxTWoo5NvuSuIsePJn4/Yx+ZpwsShHFM0ooMBCXvwzsZOkckTDeTOy9HJ2dMR62\n87e5fNh9pJvT1TBX8Jo5VlRUZJRxQ6VSwensN9fSNA1Bn8aoUqngcPSbOZ1OJzQaDXQ6XSThxRVX\nXIFDhw6l3S+BwJejrb3447uHIZUI8dNFddBr01kNJADAtFoD7rxxEmiawfNv7sfBZPVCCIQsMmfO\nHDz33HP417/+hZkzZ+KXv/wl5syZM6A2X3nlFTz88MORWKx169Zh9erV2Lx5M2iaxo4dO/g1lOST\nyeWW5WOxAqUD2yQ+ZroRJVO62a3YssDxTbUddrmKnkawycqdWyP5/MPjTZw4RQfQs7lU5aVeDY8u\nuaxJfBTOdOLh0uVMlx0tZ22hmKYsDl2yjId8YRub5lYL3N4AzLb0rF1AcsU07HaYyuWP657lshR1\nWVwxGTgjsVpRzZissecSb+VNKs8A7vdMDo0vG5GMnrhrxIA76UqCApWkG6vTx+u5yda7gJdCpdVq\nce2112LNmjV44IEHIv+lYtq0afjkk08AAA0NDaitrY1smzx5Mvbu3Qufzwe73Y6TJ0+ipqYGU6dO\njRzzzTffYPRo4n5FyA2nOmx48a39YBgGdy6YmHYdEEI/U0YX4e6FoZiq37y1H3ubk6+yEwjZ4vjx\n4/j973+PF154AQUFBbjnnnsG1F5lZSVeeumlyN+HDh3CRRddBACYPXs2vvzyS17tMGBYJyJSsZAz\nrmcg33V/gMbuI904lsSqMZBpA5sVyGTlLtgbTY/Ng71Hu2My1bFNSLnk67VzWxv8fjohA178BIlN\ngc1UeRsIfFqOl51vjSsAkeQH8ZhtHlidPrgGkCI6nKTB4wvmdIwygauwrNnuRZuRX0xX9LybzwQ7\nnVhGPsdxpfKPViziXSHDSiMvBnDJMlE4pGL+nj6ssXEcXdIMd5KLeLKRWTUdeMVQzZo1KxILlQ5z\n587Frl27UF9fDyC00rdx40ZUVlZizpw5WLZsGZYuXQqGYbB69WpIJBKsWrUKDz/8MOrr6yEWi4nL\nHyEnHG3txfN/a4TXH8TKa8fFFMgjZMbEkXr89KbJ+M1bB7Dh7QO4dd44zJw8LN9iEc5j5s+fD6FQ\niO9///t47bXXUFxcPOA2586di/b29sjf0ZMJpVIJu52fVYZrDiIWCZJ86DP9tDMRV8D41V5eQuWB\n+BVohi1Xch/h9PBsBIJ0QhwHP8WFx05ZJhM3QJfXD4VMBK1SGom3426f/aRsLh9spwfmjs1E/j90\n7qFUCAUUbwuY1x+E2xuAXCqC3ZX8mKOtvSktvFz3V6pMmFEtAMhcccsmJ86mV7cN6E99nwkMw3Aq\ncSarO2YhJ5kBqtPsAq/KN1kaYl4K1YIFC9DW1objx49j5syZ6OjoiElQwQVFUQk+59XV1ZF/L1q0\nCIsWLYrZrtVq8eKLL/IRi0DIiIOnevDbtw4gSDO4/fsTMGNcSb5FOm8YV1WI+5ZMxa+3NeBP7zfB\n7Q1g7sWp3xUEQiY899xzGDNmTE77EEQpP2HXdD4UFCig16ugMSWuvnbZvNCoY8sy6HQKFKik0BjT\nd9tSysUoNqjR2pM44dYXqSNt6vUqaCzpu0ANBu4gA5snmDAufIg/pqhIDY26fxKoUoghEMdOd+RK\nKXQaGRxuP1Ty/tTLtFAIjS03tcxcfiYiq8Gghkbdn/rcYAh5SNi8QTh8/YqXvlAFQ6ECDj8NX/7n\n1hCIRDC7Ahldp8HGz1C85bR6grB6nJgxoRTOVmvS4wJIvOfiKSpSQSQUZDxODj8Dp9sPL526Lz6w\nPQNh5Eppyj4k0sT05MkQiwSQZhh3qdMpoVVJeL2rCtRSQMieWp4BoNFIEaSSW6r0RapMxEyAl0L1\n/vvv43e/+x08Hg+2bNmC+vp63H///bj++uuzIgSBMFh81ngWr/+zGRRF4c4bJ2HK6KLUBxHSYuRw\nDdb+YBrWb23AG/85BqfHj+tnVuckoxbhwibXyhQAjB8/Hrt378bFF1+MTz/9FJdccgmv47qMdgR9\nftjs/NzizGYRAl7++0cT8PnR0yNhPXb/kU7Y+lyFTD2OjNofDDKVS6OWJxzbfMIY85vP609I5vH5\nvlaMLtPieLsV5UUqlBeHJlU9ve5BGSOj0R7Tj9EYslxYLK6Y33vMDlDBIMxmZ96vXXis8y0HXzKR\n86OvW7KSZONAc/eA6iHZ7G6YsngvBv0BTtfI46fNafejkIqTWv8EFJXxOJrFAvg9Pl4yUcFg0lpq\nbG2oZOIYC6PRaMewUm1GskbDy8Hwj3/8I9544w0olUro9Xps374dL7/88oA7JxAGC5pmsO2j4/jz\nB0cgkwixenEdUaZySLlBhQdumQ5DgQzv7GrBX3ccy3smKAIhE9auXYvf/OY3qK+vRyAQwDXXXMPr\nOKfHn4Z7Twi2OCU+JPMki3YBvFAewRNnY4veBjlq5dicoUlVp9mVsp7OYOBw+znrOF0o1y7fZOs7\nla/ispkgEaWf2TiVK+VAx5Hv4Zks1MZnhczWs8XLQiUQCKBS9ZvEiouLY9wgCIShjNsbwB/fPYyG\n4yaUFipwz02TUVKoyLdY5z3FBXL87AfT8attDfjP3ja4PAGsuHbsoNeGIBDSpaysDFu2bAEAVFVV\nYdOmTTnv0+7yp11/J4zHH0C7ibs46IWOn0NZ6u1LrR6gaexp7kb1MM2gWdLZkk+wFezt7HGhSDv0\n3esIQ5tkMU1nTekVY841oYQ+/LScXif/TIdhhHGBVdlKr85rZlNTU4PNmzcjEAigqakJjzzyCMaO\nHZsVAQiEXNJlceGpTXvRcNyE8VU6PLR8OlGmBhGdWoq1S6dh5HANvjzUiT+8c3hIrAQTzg/a29tx\n66234uqrr0Z3dzeWL1+Otra2fIuVEclq3/AhaTKKPmxp1uY534mvCdTa5cAZnqngB0r8dLGJI2lE\nuunt4yk3ZCc+hHBuUaCUxvydLCHKQIrz5opczhIKNbFjw1YsPRN4KVSPPvoourq6IJVK8eCDD0Kl\nUuGxxx7LigAEQq443GLGz1/bg7MmJ666qBz3Lq6DUpZeYCVh4KjkYqy5eQpqy7XYc6Qbv3v74IAn\njwQCEPo2rVy5EkqlEgaDAddddx3Wrl2bb7EyYxAMI1zuZIOJVMweQD4UCNA0a72tXOCIyyTHZUUL\nk2l2PTEpVM9JkSY7lj+hQIDhemVW2uJCq5CktX90opVsIxEJMbps4DFHXDBMbuvEiXL0TPBqVaFQ\nYM2aNXjrrbewfft2rF27NsYFkEAYany+vwO/3tYIjy+IW+eNxdKraomrWR6RS0W4d/EUjKvUYd8x\nE17afoAoVYQBY7FYMHPmTDAMA4qisHjx4piC8ecSXMV+zze8/uy415zrpOPeGaTpjOI8ZBLRoCjq\n5yriDGKH2BBQVEJcTrbxpln0m+KVLzx9ZGIRptUaQvdWFolXAHMZM5irR4LXHTB27FiMGzcu5r/Z\ns2fnSCQCIXMYhsE7n5/Cn95vgkwixP/UT8GsuuH5FosAQCoR4p6bJmPiyELsP9GD3//jIHH/IwwI\nmUyGzs7OSNzLnj17IJGkt5JLIOQDsYi/pa6tOzPL4shBjAk7F9GqsvOuEFC511uT1WJjIz5OaKgT\nXQu0y+LiTCSTFXL0TPBSMY8cORL5t9/vx44dO9DQ0JATgQiETKEZBpv/2YyPG85Cr5Hh3sV1GF6U\nWzM8IT0kYiHuWjAJL7y5H/uOmfDyO4dw+/UTiPWQkBE/+9nPcPvtt+PMmTO4/vrrYbVa8fzzz+db\nrPMOtVwCu/vCsKANFkwaBVt7Hd6M4lwkYgF856lFUCUTo1SvwPF2a+qdOShQSTFcr8TZHm6FdfRw\nLY6fTd4HJaByNUfPmHNFnxJQFKbWGBJ+bzXmztMgV0OTts1OLBZj3rx5+P3vf58LeQiEjKBpBn9+\nvwm7DnZiRLEK9y6ug1YlTX0gYdCRiIW4e+Fk/HpbA/Y0GyH6vyb8+LrxEAy1LxJhyDN58mS8+eab\naGlpQTAYxMiRI3NmoVqwYAHU6lDx1fLycvziF7/IST98kEtEgxpIPq5KB6vDh+ZWy6D1eb6TTlrp\nTK81BSqnFqriAkXe0oP7AjQKNTIgSqHKpPaRWiEBWBSqmrIC+AJB6LWylAoVX+WlRKdAl2VwxitX\n39NwLF+2mpdJhFlzveRNjh4JXgrV22+/Hfk3wzA4duwYRKLs+k8SCJkSpGm8+l4Tvjrchephaqy+\neQpJPjHEkUqEuGdRHX61tQFfHeqCSibGkqtqiHsKgRcPPPBA0u3r1q3Lan8+nw8UReH111/ParuZ\nUlGswtG23kHrT0BR0KkvzAUqQ4E84/pgbIwdocORM5bBqctH5cy7CQCy4rJdU1YAlzcAm9OXlhXU\nFwgmKA2ZKFRc97VMKoReK+PVBkXxU1wlg5iQRZBjExVX6+MrC3GYI2Nlei3ljrxaqL7++uuYv3U6\nHS+3CoZh8Pjjj6O5uRkSiQRPPfUUKioqItu3bduGrVu3QiwWY9WqVbj88ssj23bv3o377rsPH3/8\nMb8zIVyQ0DSDV95rwteHuzC6TIufLqqDQkaU/XMBuVSEexbV4em//Bc79rZBrRBj/mXV+RaLcA4w\nY8aMQe3vyJEjcLlcWLlyJYLBIO69917U1dUNqgzJqC7V4FSnbUBtDCtUZj0LoFohySjZxsjhWpxM\nYRUYDGrLC1CokWVVoQpPdAcjmSCFzAqfDiZ6rQx6AKc77QN2KxUIqIzybbPdp+mMmoCieO0vS6JQ\nSUTChDT+tSN02HModO9NGqnHgTTSe+dMoUqhr6ZrbcrH7ZmrZ4LXzDPT1b4dO3bA5/Nhy5YtaGxs\nxLp167BhwwYAgMlkwqZNm7B9+3Z4PB4sWbIEl112GcRiMTo7O/HnP/8ZgcDQy41PGDowDIPX/3kk\nokzdu7gOcilRps4lVHIxVt88Bb/YtBfbPzsFtUKCy6eW5VsswhBnwYIFkX83NTXhq6++glAoxGWX\nXYZRo0ZlvT+ZTIaVK1di0aJFaGlpwW233YZ//vOfGRe4L1TLoFVJcKpjYEpQmGxk9CrVK1gVqkI1\nv1V6NlQycdoKVaFaxpoiurJEjdNdmdeIokCBAQOZWJR2gH+6iIUCVJaqIRELcbgldrVeFFaoBsFC\nReXYQpVN0pWT7b7M1M1NyHoc/7b4disRc78v9BpZzPOn18hilCKlTAypSAgvzyK0uXehZ28/3W5F\nUec4boQOTWfOXbdiXrPPK664glWjC6eq/c9//sN63N69ezFr1iwAQF1dHQ4ePBjZtn//fkyfPh0i\nkQgqlQpVVVVobm5GbW0tHn/8cTz55JO48cYbMzknwgUAwzDY+tFxfNrYgRElKvx0EVGmzlV0ain+\np34KfrF5Lzb9qxlapQRTaxODVAmEeP70pz9hy5YtuPLKKxEMBnHHHXfg9ttvx8KFC7PaT1VVFSor\nKyP/LigogNFoRElJCecxGjV3jZuCAjkKNTL0ODIr2lpUpEKn1dv/t14Fkz09xaVymAanoxQ6g0EN\nTWdiIPglU8oiGcM0av5Wo5FlWsgkIjj70j2PLNPiZIoEAiWFCoytKoTHF4CmKyTL9HEloAAo5WJY\nXOyKULKxDlM7Qge5VASPL4Dm0/wmbYWFKhh08rTOW62QYNrY4sjfbT2x1q3iYg00Rhd8dHK5hxUp\n0WEamMXQYFBD7vZDY+Gfoj0ZF48vwamzNpj6LHZarQyBATpQGQyhuESrNwiHj7956Vt1wyESCmKu\njVIuhtPN/5mK9O0Jgo5LgmAwqKDoCx1Idf11GikKC+TocSbvW69XQdPDbu0sH66NPCtA6B0hoKjI\nPWIwqKHtcsDj46dQFRer0WZObVkdUapOq5i1VCKEwaCGw+WDxph4fxYVqaHpSn3fSsRCSCVCjCrT\nRuLdDQY1Sks02Hukm7c8KoUYQgEFq4P/+89QpILGlP1YNl4z0Pnz50MsFmPx4sUQiUR49913ceDA\nAdx7771Jj3M4HJEgXgAQiUSgaRoCgSBhm0KhgN1ux5NPPokVK1aguLiYrUkCAQDw3hct+NfuVgzT\nK7D65inEze8cp6RQgZ8uqsPTf/0v/vDOIfzPkqk5LRxIOD/YunUr/v73v0fqIt55551YsmRJ1hWq\nt956C0ePHsVjjz2Grq4uOJ1OGAzJlX6bnXsyI6EABAJJ90lGT48TJRopjrWH4qh6Lc6026L18phj\nTEY7axsmoz2yUp5OHw6bBBKNDCqJAIUaGRx2d8rji1RiGI12eP3ByL5uR0gZcDk8rMdr1PKE32vL\nC9DR44pxIXPYZRAxUvRa2dthw2x2xFwnlUwMhyf5pJkOBGA09k9Q4/uymB28+h9foYWuIlQMPdNi\nwyaTA4Egzdlfuq6VCpkYKrEAJ/vaE9A0bM6QYp8qWx4X4bEKev28r4tKJoalz5oTfYxOIUJHXBuF\nahlnza9w3729roS+TSZHZJE2lVxChoaQ5h7nMGYz93MqCGpitkkoYGxlISQUYNDJYTTa4ff6YXN4\nWY+Px2Tid59ZpMK0nmuJSAij0Q6Hm/16mUzs75F49BoZKkpV8Ll9MMa5eqYjj0YmRJlehdYO/vex\nkefYpAsvf4XPPvsMd911F4qLi1FYWIgf/vCHOHnyJMrKylBWxu2eo1Kp4HT2P2BhZSq8LboAo9Pp\nhFgsxt69e/Hb3/4Wy5YtQ29vL9asWZPpuRHOUz7e147tn52CXiPD/9RPhSbNCuKEoUn1MA3+3w0T\nEQgy+M2b+9GRwceZcGGh1WpjEiTJ5XIoldkvlXDTTTfBbrdj6dKlWLNmDX7xi1/wcverMKjYN4SC\nWzKWh6IQEzBPp5GCO1mb2UYgoDCiRJ1QtDO65kw0hoLUliY+UBQFkTD2hPienijJdQ2PskQkRGWJ\nmnUfrTJ58o5cF4CNRxJV70os7P+3WiFhdXUbX1WIIi33dVDIRAnXExh4woVkcS3yuCKyYyt1rPvp\n1NKIu2iRVo66UUUo4plYIlGedPYduG8lRVGhjIORH0LPz+hyLbTK0O9VpRrO42vKCmLeN0Ge7wQm\nQ9fTgb5z0nVJrC0vYP2drRVdnjI8817W/+KLL3DppZcCAHbu3MnrozVt2jTs3LkT11xzDRoaGlBb\nWxvZNnnyZDz//PPw+Xzwer04efIkJk+ejA8++CCyz8yZM7F+/fp0zodwnrO3uRub/tUMlVyMNfVT\nLtjMU+crk0cV4YfXjMGfPziCX29rxEPLL4p8TAiEeCoqKnDzzTfj2muvhUgkwr///W+oVCr89re/\nBQDcddddWelHLBbjueeeS/u4MoOKtZ4KlaIQaDjeh3t7LKkmT0VaOUzWDFdks6VoRYmo4HDPDk+q\ncxL9EW47ReNhpa7T7EpwIw9PPlVyMYbplQkxXbXlBShI8U1KdyKZLNZKIRWhprwAjSdMnH1xdTeh\nqhBmW6LlRiRInWAhvEe0ZBQFjKnQoaPHCVsGiUiShQGKRAKgr8mRw7UQcSilFEVhdHkBui0ulBQq\nIBIK4PZmnnKeL3yTUqTuMzlSCbfSKhRSKDOo0Ov0gaYZaBTZzXSskovhiHKnjF+wCJNMP4u2YpYU\nKtLqnzPJRtwNLhIIoFNLYeFpycsmvBSqJ598EmvXroXJFHpoR44ciaeffjrlcXPnzsWuXbtQX18P\nIJTcYuPGjaisrMScOXOwbNkyLF26FAzDYPXq1aTCPSEpzWcs+MM7hyERCXHv4jqUpvlAEs4NZtUN\nh9nuxT8+P4UX/taItUunJf2QEC5cqqurUV1dDZ/PB5/Ph8suuyzfIvGCAgVZkntaJRcnz3gWN4lQ\n9lkMuFJ8Vw9TsypU4TTT1cM0yHTBmW+yiLAFQybOjXt2tBLKMEzCxI7vhJcBg6pSDcqLlQkFx8Nt\ncikpGqUkK8kAqqMsEVwT1MkjiyCXCkH1FUY92W6FNV6RoWItP/GiRSviYqEQaoUYMqmIdbDKiqKs\nreHtDIOJ1Xp0ml0waOUQCCgEaZpToVLKxHByuUzGCTemQsda90yv4VZYKYSyzJVxWYb7mDK6KGZc\nWRcv0rFQCZCVAsoyiSgydpneRROqCgcsBxsKaaxCpZCJMXKYBifTSKwT/c5js3Img8sixjZOqV5l\nmVrlUsHrzTZx4kT83//9H8xmM2QyGRQKfhNZiqLwxBNPxPxWXd2fFnnRokVYtGgR5/Gff/45r34I\n5z+nO+144c39YBgGd904GdXDuE3fhHOf719WhR6bB5/v78Dv/nEQP1k4KWFyQyBkywI12FAUYt17\n4kiVtC9+s0ImwrQaA8QiAatCRVEUxo3QwWz3xhQWnVBdiC6zG4YCOQIB/nE60fV+uFy14qcsGqUE\nteUFUCvEKWeLmegkFJV8dZxvnG04EQHb+ybcfHbsEdxEr97Hn5dCKoJWKY05H6lYiFK9MkGhSiVl\ndL3GYp0cFcWqvuMSjyw39HslRfQphCbG0fGubAqlXiODSChARbEKe5rZEw6Io6xOM8aWwMuhoKSb\n8prNwieTpL4X0k2bHgjym6QXKKXodbJbT0aUqAa1UDIFKmLtS1XDKzzs0bsUFcjTUqgGkq5cyaGA\nxTdJUUitUeUIXjOU9vZ23Hrrraivr4fT6cTy5cvR1taWa9kIBABAl8WFX29rgNcXxG3zx2NCdW5W\nYAhDB4qisPy7YzCxuhD7T/Rg0z+P5mxViXDu8tprr2HGjBkYN24cxo0bh7Fjx2LcuHH5Fisl4UnA\nsEIO1/k0Jx4UQhYgrgkLBUCrksYsRDEITahHDtdAQFGQiIWoLtVgRDF7bFA0Y0awx7B8axx31kMA\nKNTIIBYJc17Kk2ZibQ4XjSnmdBOLR5xkv8g7qO8E4pWHZJdNrZBguD51qESy+A+1QoLJo4pQWZp4\njdiU8FQT2GilTBjVAJubdXRbccMQQ9jyUFqoiMRsiYQCVA/TJL0GCpkI1cM0mDyyCAIBxakcp20B\njGuHb3xNejFUsYobW9r/8H61FQUYPZw94VLM+HD0zxVnmOnnsVgnx3C9EmMq+mOUksVqRcN1LcLn\nP6ZCl1HZBbZ4KSHP0hAlOkVqC1XaEvGD1xvm0UcfxcqVK6FQKFBUVITrrrsOa9euzZFIBEI/FrsX\n67Bfx2YAACAASURBVLc0wOby45arazEjxQebcP4gEgpwxw0TMaJYhU8bz+LdL1ryLRJhiPHaa6/h\n7bffRlNTE5qamnDkyBE0NTXlW6yUcFk4hhUqMWV0EZ8GYv/kmNhMrzVg8siimO3hSRCb4lBSqMDw\nIiXqRvXLwNaylKOeDt8VaLb9xnEoaXyJaZNBxjPMZKcQ7/IXfx7JLFcjh2kwgiORRZjptQbUVLAH\n34sEAtSWJ8l8ymPs2XYpLghZwwqiFA29VhaTzCKesAu2mkXxkoiFmDGuBFWlmoiSxzeBQYlOEVHy\n+E6gUxFtd51YrUcNR3KDRNKoQ4VYBTA68Ui8Ei0QUNAlcVsMjzvXvTRquDZp4pR0oKjQd3ZEiTpi\nmQUApUzEWxGqYFmAGTNCh0kj9dCppRE3PwoUb7dfdRrxX/HPYJlBybn4KhIIUKCUpu1uyBdeV8Vi\nsWDmzJkAQsIvXrw4JkMfgZALbE4fntuyDyarBzfMrMacaeX5FokwyMilIvx0cR30Ghne/uwUPtt/\nNt8iEYYQI0eORFERDwVkgDAMg8ceewz19fVYvnw5WltbB9Qe19xXIhZAJhHxSArAD7FImODqVje6\nCLXlBUnr9qWq6Rc9iQlbM8qLksetpELLw3IwPkl8SPSY0IhdheayjExnqXeXTCkMz9PCSmnCnkku\nTHRQPVeci1gk5Fz112tD1j0u+NwTbEpK1TA1ptcaEu6TYh13pr+qUjVGDtOgrIjd4hY+h7Bba7J4\nQS74xs1OGtmfMZKrXmoYlVzMndwgjuimorNSTq0xQBqX0VAgoFAW5RIZ7oMChfLixOdiIK5vADCl\npgiTR2b3vRetoyUfo1hlpaxIiak1/c+RWCSAQEBF3EmjFyG0SglqygowoTrV4kli/1wyxf9KUdzW\nzbGVOoyt1EFAUTFxitmCl1OxTCZDZ2dn5CbYs2cPSSBByCkOtx/rtzago8eF786owPzLqvItEiFP\nFKikWH1zHX6xaS9e+6AZGoUEdXxW8QnnPcuXL8f8+fNRV1cHYVRK6HXr1mW1nx07dsDn82HLli1o\nbGzEunXrsGHDhozb86WIV0o13wp/i0cN1yZkMTNo5TAmyegnFQsTJoTpEi2eXCrCjHElWUnGkIpk\nJTLGjCjAoRYzgJD1LZxwIZmLF1sKc7azqC0vAM0waOlInnwj2QhEj49aIeGdzIM3PIaf7RoJKAoC\nFkUtWXMioQDFutSx9FXD1NCoJCjSZJa6XKuQROLCKorV8AcS46qUMjEmjdTD7QlALGKJe8uCf1e0\nRYNNKaUoxDxT4XFmwMSMORW1XSEVw+VNTNChU0vRZXFBlcRKIxIKeLmwjhuhQ6/Dhw5z6hIksXLG\nnuPEaj1rbGYYqViIGWNL4AsEOeUKt6/nkcae7VUioChMGV0Er59G02lz1M6h/1WWqCNW9+hLXqJT\nwOcPoraiIEaRZbtXBgovheqBBx7A7bffjjNnzuD666+H1WrFCy+8kHVhCAQAcHkC+PW2BrR2OzBn\nahkWzxk94BUdwrnNML0S99xUh2e37MPv3j6I/6mfitHJ3F8IFwRPPfUU5s+fn7QeYjbYu3cvZs2a\nBQCoq6vDwYMHUx4zuW/lXCwUwB+MVaCCQXaFKl2lhC2eQq2UJFWo0iX63VthUMHlDYTSWEcxGMpU\nKtQKCabWGNDr8EKnluJ0Z0hZSZbMhq/UhX0KQVihCp/vmBEFOHHWBo8vpNSyfadGFKthdfoS62Kl\nGyeXZqIS1n3ScaPLwjUVCQUoTlJbjDOGkAUuaxgQUqqiE2xEEz5lPvdodKbI+N3HVOjgdPtZFYb4\na8nHI2/SyEJ097pxKi6pQ2WpGkVaWdpuaWxublqVFFqVNKJQiQSCmCLRsRkg+/9NM0xE4Qi7yIUV\nKs7YNgHFmuwjfB58FKlUyCQiyOLWVMJSD4t2rYwSkiuBWS5CsnkpVD09PXjzzTfR0tKCYDCIkSNH\nEgsVISc4PX78amsDTnXYcdnEUvzg6lqiTBEAAKPLtbjjhon47VsH8PzfGvGzW6ahPEV6XML5jUQi\nGZRMfw6HA2p1f6yASCSKKVTPRjgmYWqNAd8c6YrZFuCKKeGIzakpK4BISKHpjKVvO7esmbhX8SWc\njjrXCWLSbT4cpyIVC1HSZzkZVqTAqQ5bUtc19r65O9eppTBa3VDKQ1MntUKCCVWF2HuUPXMdAAwv\nUmI4izIQfwm5anP175/8O8jnO6lRSOBw+SPZ/JL3lxumjjaAAcPbyjJQirRyOD0BlKR5H8SPt04t\n5ax7Ga+ncl0rWdQ1pqh+BST62gviC/zyJJ1j1HIJ7G4fRsTdB6PLtDD1eqCQiVBRrIKAojBMr+iT\nN22RAIQUKalEzzvLZtqwuXnmpqeU8DrDZ599FpdffjlqampyLQ/hAsbu8mH9lgac6XbgskmluHXe\nuCGx8kkYOkwZXYRbvzcWr/5fE361tQEP3DKdM+sR4fzn0ksvxS9/+UvMnj0bYnH/iu7FF1+c1X5U\nKhWczn63mVTK1HCDEgZDvwJ2qUyMI6ctKFBJYep1o6hADoNBDQ8NOP39K8b6QhUMRUp0230IgIJC\nJkJdjQESsRC9di80llAh1qIiNecKtgGARCZBgVqa0cQsjEZtDbVnYE+koGmzsW4PH1dYqIQhSVa7\n8H5hotvx+oPQdDqSth9m5pQyVjcsg0GNcaOLE7ZRYhE01lDa6uJiTeQ8wugKldBr2d8phXoVHC5f\nTLyXP0BD02e54horNgKUAD3OkMvXtLHFkEtFrAqGpt0Gmmag0ymSti9z+aAxxabcDu8fuZZFKkyb\nMIyXfB4a6HX3u5OG20rnHAeKK8CgpcOGEaXqAfVbUpI8XsbqCcLlZ2JShxsMas64HW2XAx5fv/th\nkV4Fg0EVGeeiIlXkuTYY1JHfS4pj5TAYgIICBbQqCWd8XLLzDrd70bgSzrTi0fsNK1Kiw+TEuOpC\nGArkCUp4fF/DSvu9QMJjJBIJ0r4WiZGKyQnSDDRnY91ho/uMfgfoWd4zzgADmyeYcFw0jEgIjS27\nxX95KVQVFRV44IEHUFdXB5ms32x3ww03ZFUYwoVLr8OL9Vsb0G504jtThmPZd8cQZYrAymWThsHh\n9mPrR8fx7Bv78LMfTIu45BAuLA4fPgwAOHToUOQ3iqLw+uuvZ7WfadOmYefOnbjmmmvQ0NCA2tra\npPvXVOhgNMZOCGqHqUEzDII+P3RyIYxGOyRgoJEJ0WYMKQ8WiwQihobd5obN7obXI4S1ry6NxxeA\nzR5yu+kxOeBOsuIrEwAepxcejno3fAj3FX8eqbaHfzebJRDS3LFi4f3CRLfj8wdTth9GKKA4ZWTt\n1+WLaTu+PYvFBdoXYDu0X9aoosuBIJ1yrNgwW1yR45JdK5vNDZph0CsRwCjltj66PH7OMe2/JiLI\neBqFLBZnTHtGox0GgzqtcxwoMiFQViiHQpTeNU4XS2/oXKMVKpPJzmn1s9rcMXWyLBYxxGAi4yUZ\npgKCQZQZVDAa7agZpgZFcd8fvRb2+y3VeEfeBz0OuJJYOGuGqcAwgEgkgLhIASoQhMmUXmK58BiJ\nBIKc3wM0wyR9P0Rvs7C8Z8zmkKwUuO8bhmZABYMQiQTosXmyIndShaqrqwslJSXQ6UIZORobG2O2\nE4WKkA06zS78amsDTFYPrpxWjqVza4ibHyEp350xAm5vAO/sasFzWxqw9gfTWGunEM5vNm3aNCj9\nzJ07F7t27UJ9fT2AzJNehFxoYrOBlRtUEYWKivodAKLnCdHxCefC63Egbjfh80+1qMZV7ycZarkY\nhgI5CpSx7luTRuphsXmhSSNl82CS2g0yuzfFUPgGCyhqUN/rfApWsxG/r1AoiMlImYsECOkQbf3K\nNGV4rotZp0NFsRqt3SFFKT6eE+h32012CQUCCuOqCtFj9QyOQrVq1Sps374d69atw5/+9CesWLEi\nK50SCGFOnLXihb/th8Ptxw2zqjH/0qoh8SInDH2un1kNX4DGh1+fwfot+3DfkqkDcnEinHvs2bMH\nr776KlwuFxiGAU3TOHv2LD766KOs9kNRFJ544omstslGODNdWJGgcxyrNBQoLlCgtDA2Y5xIKMCk\nkXpIkkxERw3XZuTuS1EURrEUVk2W2CAZmXpSZPvKhiftYqEQ/mBiNrx0+7yQvsLD9Uo4PQFUFKtw\nuMWc+oA44uPuBtu7ZjC6YwYxMun/t3fvQVGddx/Av2f37I1dlouAcpNFLooXeAVjmmCoNtBIUxOt\nZDRGWjOmihPf12q1ak0jSUSaGNt0gmba6kRj2lSDk87rjDHRvFEr0WgwYhAhGgTlInfZC7Cw7PP+\ngayICHuDs7v8PjOOsGfZ/Z3nnD3P/s55zu+xZdqIgT6zthw2fVTWTbhtjUHT5r47yZEjR2x+8aHm\n7jh06BAWLlyIxYsX4+TJkwCA2tpavPjii8jMzERmZiYqKipsfl/iHgrL6rHjo29h6OjCsvRJeCY5\nkpIpYjWO4/Dc7Cj8JDEUVQ0GvPXPb9Fq6Bz6D4nHeOWVV5Camoru7m688MILiIiIQGpqqtBh2a23\nGmDvWVf+IfdwWDuXjjuYEKIe8IZ1pVwy6LxLzpr41dVZ2ydK+J4kNCF6zNBPtsLDCjB4IqlEjCka\nf3hbefWm/9Wa0fC9pf+k1sOpf3v2L9jSd7FY/PCArElseyc2doZBE6q+K2VPVZ++c3f89re/vW+Y\nRGNjIw4cOICDBw9iz5492LlzJ7q6uvCXv/wFmZmZOHDgAFauXImdO3fa/L7EtTHG8L8FN7Drk2Jw\n4PDfv4hHSkKI0GERN8RxHF5Ii8WTSWGobjTgzX9cRIvOuTeaEtcll8uxcOFCzJw5E2q1Gtu2bcOF\nCxeEDstm/N0CF93dPf1ssL8Xxvp5YVLEwBNg0v2lwg+jsnChTaGUS5xWOU8qEY+6Kqr2JkbKuycE\nVHZc4XQ/I7/Dx4b7PnTZQMfC3odG+sST1XUM7dnRBpu74/Lly0hKSgLP81CpVNBoNCgrK8OmTZss\n5WlNJhNkstFzlmQ06Og04f2jpbhQWo8xajn+JyPeqhKuhDwMx3FYkhoDiViEY+dv4s1/XMTaRQmW\n8snEc8lkMty5cweRkZEoKirCY489hra2tqH/0MXEafxQUatDSEDPPisScQ+dPwVw7aszkcFqVN7W\nwU81+PDbGROD7DrbHRvmixa90e57QfoLD1RB5kCpeXu3hFiApNh19xr30rvp/L3lCAlQWqZImBLp\nL1jJ7uE2kleo+kqKDXzgSvVQ+UjwGCU6OrsRFuicoXzWGjShunbtGp588kkAPQUqen9mjIHjOHzx\nxReDvvhgc3f0X+bl5QWdTgdf355MtLy8HDt27MCuXbvsWzPicqoa9Hjv38WobWpDTJgPXl4wDWoq\nJECcgOM4PDcnChJehCNfVSDng0KsyYhHVChN/uvJli1bhrVr1+Ldd9/Fc889hyNHjmDq1KlCh2Uz\npVyCKZH+Qz/xLlce8jfWz8uqkxn2XknxV8udWtUzVKCrMCO5DSdr/FHdYLB5Ti6PzQ4cFBPmg8o6\nPTTjvCGV3Puyz3GuVLrBuSwTHo/ge8ok4gGH/Q710ZHwokGvag2XQROqzz77zKEXH2zuDpVKBb3+\nXtlGg8EAtbrnjNy5c+fwxhtvYMeOHdBoNA7FQITHGEPBd7fx4edl6DSZ8dTMcCz8cdSITOpHRg+O\n47AgZQL8vGU48HkZ3vroW6yYNxlJE4OEDo0Mk/T0dMydOxccx+Hw4cOoqKjApEmThA5r2PipZNC3\ndwkdBumD4zjEjfe774u1NRR37wsZqlKhRCxCt9mMLtPDS9D3lxQbiL5ffdVeUqgjbD952ZtPeW6a\nYB8vuQRxDxmOK4QR2T73doYR8cikoIcObXbVE0qDJlShoaEOvfhgc3fEx8fjnXfeQWdnJ4xGI8rL\nyxETE4Nz585h+/bt2LNnD4KDrZuAjrgubVsnPjhWhovfN0Ah47H6mSlIjLV1mjdCrDd7eij81TK8\n9+8r2PVJMdJ/NB6/SJkA8SATsRL38+WXXyI6Ohrh4eE4ceIE8vPzERcXh5iYmEEn3bVHSkqK5eTe\n9OnTsXbtWqe+vrUmjnedL3GhAapBq/CNJn0n+rWWQsYjISpgyOGGE8f74la9HqE2DF8arJgH8UAj\nmk+NTDIzWH/tqn251fdQ2WOguTv27duHiIgIzJkzB5mZmViyZAkYY1i3bh2kUilyc3NhMpmwceNG\nMMYwYcKEESlXS5yLMYaL3zfgg8/KoGvrQmy4L156Og4BdpS5JcRW8VEB2Lw0Ebv/XYxPz93E9apW\nZD07dVRVrvJke/fuxdGjR/Hmm2+itLQU69evx5YtW3D9+nW89dZb2LJli9Pe6+bNm5gyZQree+89\np72mOwgP8kbHIBPc0r2vjlMMMhlr3+cIMXwJsG4+HyKc2DBftBo6IbPx6qhdRvgK1WB6q/6pXWya\nFI7ZU77PxYzkzN1kaPV32vHP49/j8g9N4MUiLPzxBKQ9Ek6VqciIa+swYd+nV/FNWQOUch7PzYnG\nrPhg2hcFFBjoeInaZ555BgcPHoRCocDbb7+Nmpoa/OlPfwJjDD/72c/w6aefOiHSHkePHsWePXug\nUqmgUCiwadMmREZGDvl31C+NjMBAb2rrYXKzToeaJgNEHIeZcWNHRVufK7kNAPjR5HECR+Ja+7a+\nvQvFN5owMdzPJU5MGju7IZGInNaXO6NfGtYrVGR0aesw4bPzN3Hs/E10mcyIi/DD0p/GIthJk6YR\nYisvOY9V86fi5LfVOHTyB+z7tBQF39Ui86mJo64ksCfhOA4KRc/V7q+//hpLliyxPO6I/Px87N+/\n/77Htm7dipUrV+Kpp55CYWEhNmzYgPz8fIfehxBC3IlKIXGJJLOXI5U5hwslVMRhxq5u/N/FKhw9\nWwlDhwk+KikW/yQGM+OCRsWEd8S1cRyHOYlhSIgOwD9PXMPF7xuwde95PBIXhHnJkQgNoITf3YjF\nYmi1WrS1teHq1atITk4GAFRXV4Pn7e/WMjIykJGRcd9jHR0dEIt7Ou+kpCTU19db9VrOOONJrENt\nPTy0xm7oO80QiThLG3t6W6u9WwG4znq6ShxkaJRQEbs1azvwfxercepSNQwdJnjJeCz88QSkJoW7\n5NkDMrr5q+VY/YtpKLreiE/+U47zV+tx4Wo9/ismACkJIZg6wd9lb3Yl91uxYgXmz58Pk8mEjIwM\nBAUF4ejRo/jzn/+Ml19+2anvlZeXB19fX7z00ksoLS1FSIh1k5C7ylAdT+dKw6I8TUtLG7S6dohF\nIjQ06EZFW2t17QBc4/M7GtrbVTgjcaV7qIhNjJ3duHS9EV+X1OHyD00wMwaVQoKfJIbip4+EWya4\nI8SVMcZw6XojjhRUoOJ2z/HDz1uGmXFBSIwNRFSIj8uWZnV3zjrjWldXh5aWFkuZ9FOnTkEul+PR\nRx91yuv30mq12LBhA9ra2sDzPF599VW6h8qF0JfO4VN5W4faZgN4kQgzJgWNirame6hGJ0qo7qId\nbng13mlH8Y1mfFfehJKKFhi7ugEA48eq8GRSGH40eSyVaSVuq/K2DqeLanCu5DbajT37tlopxbRI\nf0yO9MdkjT98aAJqpxktQ1ioXxoZ9KVz+FTc1uJ2cxslVAIZDe3tKqgoBXG6LpMZVQ163KjV4npV\nK65V3UGT1mhZPtZPgUfixuLRyWPp3hPiESLGeSNz3EQsfjIaJRUt+PZaAy5da0RB8W0UFPd0rqGB\nSsSN90NchB8mjvelK7GEEI8nl/Z8RVQpRs/xLppGJxA7UUI1ipm6zbhVr0flbR0q63SouK1DVb0e\n3eZ7Fy1VCgmmxwRgSqQ/pkb6I8jPS8CICRk+El6MhOgAJEQHwDyX4VadHiUVzbhS0YzrVa2objDg\nRGEVOA7QjFNjssYPkzX+iA71gYQmOCWEeJggPwVEIg7+LlAme6TQXJnEXjTkb5QwM4a65jaU12hR\nXqPFjVotqhr0MHXf2/y8mEN4kDc0wd7QjPNGdKgPxvl7UaU+Mup1mcwor2nF1coWlFS24EaN1nLi\nQSoRYdJ4P0zR+GPqBH/6zAyBhvwRZ6JhUSOH2npkUXuPHBryRx7K2NWNGzVaXKtuxQ93/xk67s16\n35M8qaAZp4ZmnDcixnkjJEAJXkxn2gnpT8KLMHG8HyaO98P8J4B2ownf37qDKxXNuHKjGZd/aMLl\nH5qAL4Axahkma3ruvYrT+LncbO6EEEIIcS5KqDzEHb0R16tacb26FdeqWnGzTnff0L0gXwWmRY1B\nVIgPJoSoER6kouSJEDspZLxleCDQM4VA8Y1mFN9oxtWKZvznci3+c7kWABASoERsuC9iwnwQGazu\nGUZDV7AIIYQQjzGsCRVjDNnZ2SgrK4NUKkVOTg7Cw8Mtyw8dOoSDBw9CIpEgKysLs2fPRktLC9av\nXw+j0YigoCDk5uZCJhs943et0W404ebde556h/A1aTssy8UirmfIXpgPokN9ER3mQ1XKCBlG/mo5\nUhJCkJIQArOZobJOh5KKZpRWtuB6tRYnG6tx8ttqAIBCJkZYoArBY5QIGeOFID8v+Ktl8FfLoZTz\nNFxQYMePH8exY8ewc+dOAEBRURFycnLA8zwef/xxrF69WuAICSGEuJphTahOnDiBzs5O/Otf/0JR\nURFyc3Oxe/duAEBjYyMOHDiATz75BB0dHXj++eeRnJyMXbt2Yd68eZg/fz7+9re/4aOPPsKyZcuG\nM0yXxBiD1tCJhtYONNxpR02jAbVNbahq0KO+pf2+56oUEsRHjUFMmA+iQ32gCVZDJqEy5oQIQSTi\nEBmsRmSwGk8/poGp24zKOh3Kq7WouK3FjVqd5Upyf7yYg0ohgbeXFEo5D4WMh5es53+5TAyFlIdc\nxkMhE8NLxsNLLoGXjIevSgYvOQ04cFROTg4KCgoQFxdneWzr1q3Iy8tDWFgYVqxYgatXr963nBBC\nCBnWHriwsBBPPPEEACAhIQHFxcWWZZcvX0ZSUhJ4nodKpYJGo0FpaSkuXryIVatWAQBSUlLwzjvv\nuHxCVdtkwKXrjTCbH17fg+M49Nb/YAzoNjOYus0wdZth7OxGe2c32o0m6No6oTV0otXQBVO3+YHX\nUcp5xEX4IWKsN8aPU2FCiA8CfeR0VpsQF8WLRYgK8UFUiI/lsS5TN+qa21HTZEBTaweatB1o1hrR\nauiErq0T9XfaYezstuk9tq94FAE+VKHKEYmJiUhLS8PBgwcBAHq9Hl1dXQgLCwMAzJo1C2fPnqWE\nihBCyH2GNaHS6/Xw9r5XOYPneZjNZohEogeWKZVK6PV6GAwGy+NKpRI6netXODl6ttIyX42jeLEI\nPkoJwoOUGKOWI8BHgQBfOYL9vRASoIRaKaXkiRA3J+HFCAtSISxI9dDndJvNaDd2o81oQofRhI7O\nez+3G01ou/uvvcMEnhfBR0lDo62Vn5+P/fv33/dYbm4u0tPTcf78ectjBoMBKtW9baRUKlFVVTVi\ncRJCCHEPw5pQqVQqGAwGy++9yVTvMr1eb1mm1+uhVqstiZW/v/99ydVghC7Du+nFRwV9f0IIIdbL\nyMhARkbGkM/r7Y96GQwGqNVqq95D6H5pNKG2HjnU1iOL2tt9DGuZt8TERJw6dQoAcOnSJcTGxlqW\nxcfHo7CwEJ2dndDpdCgvL0dMTMx9f3P69GnMmDFjOEMkhBBCBqRSqSCVSnHr1i0wxnDmzBkkJSUJ\nHRYhhBAXM6xXqNLS0lBQUIDFixcD6BlSsW/fPkRERGDOnDnIzMzEkiVLwBjDunXrIJVKsWrVKmzc\nuBEff/wx/Pz8LJWWCCGEkJH22muvYf369TCbzUhOTkZ8fLzQIRFCCHExHOutlEAIIYQQQgghxCY0\nsyshhBBCCCGE2IkSKkIIIYQQQgixEyVUhBBCCCGEEGKnYS1KMRKOHz+OY8eOWYpXFBUVIScnBzzP\n4/HHH8fq1asFjtA+KSkp0Gg0AIDp06dj7dq1wgZkI8YYsrOzUVZWBqlUipycHISHhwsdlsMWLFhg\nKeUfFhaG7du3CxyRfYqKivD222/jwIEDuHnzJjZt2gSRSISYmBhs3bpV6PBs1nd9SkpKkJWVZfn8\nPP/880hPTxc2QCuZTCb8/ve/R3V1Nbq6upCVlYXo6Gi33T4Drc+4cePcdvsMxVOPe0Lrf9xdtGjR\nA/08tb1jrOkT8vLycOrUKfA8j82bNyM+Pt4j+g8hWNNnUXs7xpb+1CltzdzYtm3bWHp6Olu3bp3l\nsWeffZbdunWLMcbYr3/9a1ZSUiJUeHarrKxkWVlZQofhkM8//5xt2rSJMcbYpUuX2KpVqwSOyHFG\no5EtWLBA6DAc9ve//539/Oc/Z4sWLWKMMZaVlcUuXLjAGGPs1VdfZcePHxcyPJv1X59Dhw6x999/\nX9ig7HT48GG2fft2xhhjd+7cYbNnz3br7dN3fVpaWtjs2bPZxx9/7LbbZyieeNwT2kDH3YH6eWp7\n+1nTJ1y5coX96le/YowxVlNTwxYuXPjQ55LBWdNnUXs7ztr+1Flt7dZD/hITE5GdnW35Xa/Xo6ur\nC2FhYQCAWbNm4ezZswJFZ7/i4mLU1dXhl7/8JVauXIkbN24IHZLNCgsL8cQTTwAAEhISUFxcLHBE\njistLUVbWxuWL1+OZcuWoaioSOiQ7BIREYFdu3ZZfr9y5YplvreUlBS3+8wMtD4nT57E0qVLsWXL\nFrS1tQkYnW3S09OxZs0aAD0ToYvFYpSUlLjt9um7Powx8DyPK1eu4Msvv3TL7TMUTzzuCa3/cfeb\nb755oJ//6quvqO0dMFSf0Nu+ycnJAIDg4GCYzWY0Nze7ff8hhMH6rFdeeQUGg4Ha2wms6U+duW+7\nRUKVn5+PefPm3fevuLj4gWEiBoMBKpXK8rtSqYROpxvpcG0y0LoFBQVh5cqV+OCDD7BixQpsks3c\nhgAAA7dJREFU2LBB6DBtptfrLUM0AIDneZjNZgEjcpxcLsfy5cuxd+9eZGdnW+amcTdpaWkQi8WW\n31mfmRPc4TPTX//1SUhIwO9+9zt8+OGHCA8Px7vvvitgdLZRKBTw8vKCXq/HmjVrsHbtWrfePv3X\n5ze/+Q3i4+OxceNGt9w+Q/HE457Q+h93N2/eDLlcblne+5kwGAzU9naypk/o375KpRJ6vf6+13G3\n45NQhuqz8vLyqL2dwNr+1Flt7Rb3UGVkZCAjI2PI5/VvBIPBALVaPZyhOWygdevo6LB82JKSklBf\nXy9EaA5RqVQwGAyW381mM0Qit8jfH0qj0SAiIsLys6+vLxoaGjB27FiBI3NM3+3iDp+ZoaSmploO\njmlpadi2bZvAEdmmtrYWq1evxtKlS/H0009jx44dlmXuuH36r49Op3Pr7TMYTzzuCa3/cdfb2xut\nra2W5QaDAT4+PjAajdT2TtK/T/Dx8YFKpXrg+5W3t7fH9R9C6Ntnpaam4o033kBqaiq1txMM1Z86\nc9/2qKONSqWCVCrFrVu3wBjDmTNnkJSUJHRYNsvLy8P+/fsB9Ax3CAkJETgi2yUmJuLUqVMAgEuX\nLiE2NlbgiBx3+PBh/PGPfwQA1NXVwWAwIDAwUOCoHDd58mRcuHABAHD69Gm3/Mz0tXz5cnz33XcA\ngLNnz2LKlCkCR2S9xsZGLF++HBs2bMCCBQsAAHFxcW67fQZaH3fePkPxxOOe0Pofd9vb26FQKB7o\n56dPn05t7yQD9QnTp09HQUEBGGOoqamB2WyGn5+fWx+fXEX/Y+LUqVORmJiIM2fOUHs7wNr+1Fn7\ntltcobLFa6+9ZhmKlZycjPj4eKFDslnvML/eiiO5ublCh2SztLQ0FBQUYPHixQDgluvQX0ZGBjZv\n3owlS5ZAJBJh+/btHnEGdOPGjfjDH/6Arq4uREVFYe7cuUKH5JDs7Gy8/vrrkEqlCAwMxOuvvy50\nSFb761//Cq1Wi927d2PXrl3gOA5btmzBtm3b3HL7DLQ+mzdvRk5Ojltun6F44nFPaP2Pu7m5uRCJ\nRA/089OmTaO2d5KB+gSO45CUlIRFixaBMWapeOZp/YcQBuqzlEolZsyYQe3tAGv7U2ft2xzrO6CQ\nEEIIIYQQQojV3P/0OiGEEEIIIYQIhBIqQgghhBBCCLETJVSEEEIIIYQ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Vn7ia2A6O3dGbBMOAs1Ey/CFjGUAdfdYgw8lHYKENriFWiXip2KraxQor9f3c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\n19cTGRmJwWAgNjaWI0eO6BewE5SWllJRUcGcOXNYsGABv/3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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -149,7 +148,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 2000/2000 [00:02<00:00, 679.76it/s]\n" + "Average ELBO = -43.175: 100%|██████████| 200000/200000 [00:21<00:00, 9379.18it/s]6, 7465.47it/s]\n", + "100%|██████████| 2000/2000 [00:02<00:00, 706.05it/s]\n" ] } ], @@ -167,9 +167,9 @@ "outputs": [ { "data": { - "image/png": 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xu9/9DgCg0WiwZMkSbN++PWy7mpoaTJkyBYDLbaK2ttaz7ejRo5gwYQK4XC6k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\nZcoUx8kxJycHGzZsCHCJPFNbW4tly5Zh3rx5eP7557Fp0ybHsmDcP87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hJGmq6zpQe94/JvrSKROrUER+lhI/vX0uinNU2P9VO36x80v0DfFlRy4eeXl5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\nyjQxivoTrlydApN0cuTo5JBJ6GuBEELikZ0hh93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AQygPAADAEMoDTFVZWaW9e/daHQMA0A6UBwAAYAjlAaby+ZjzAABOR3mAqUpKilRYWGh1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\nTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -221,7 +221,7 @@ { "data": { "text/plain": [ - "90.928576354546024" + "90.925442023139937" ] }, "execution_count": 10, @@ -246,7 +246,7 @@ { "data": { "text/plain": [ - "124.78826230698768" + "124.4586578158235" ] }, "execution_count": 11, @@ -280,7 +280,7 @@ { "data": { "text/plain": [ - "(61.19519094778147, 2.1980669582811139)" + "61.207200231982306" ] }, "execution_count": 12, @@ -290,9 +290,9 @@ ], "source": [ "with pooled:\n", - " pooled_waic, pooled_waic_se = waic(trace_p)\n", + " pooled_waic = waic(trace_p)\n", " \n", - "pooled_waic, pooled_waic_se" + "pooled_waic.WAIC" ] }, { @@ -305,7 +305,7 @@ { "data": { "text/plain": [ - "(61.503344897536387, 2.0280476219107615)" + "61.343846074554747" ] }, "execution_count": 13, @@ -315,16 +315,16 @@ ], "source": [ "with hierarchical:\n", - " hierarchical_waic, hierarchical_waic_se = waic(trace_h)\n", + " hierarchical_waic = waic(trace_h)\n", " \n", - "hierarchical_waic, hierarchical_waic_se" + "hierarchical_waic.WAIC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "For WAIC PyMC3 reports a point estimate together its standard error. The standard error can be useful to assess the uncertainty of the WAIC estimates. Nevertheless, caution need to be taken because the estimation of the standard error assumes normality and hence could be problematic when the sample size is low." + "For WAIC PyMC3 reports a point estimate together with its standard error. The standard error can be useful to assess the uncertainty of the WAIC estimates. Nevertheless, caution need to be taken because the estimation of the standard error assumes normality and hence could be problematic when the sample size is low." ] }, { @@ -336,9 +336,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -346,8 +346,8 @@ } ], "source": [ - "plt.errorbar(pooled_waic, 0, xerr=pooled_waic_se, fmt='o')\n", - "plt.errorbar(hierarchical_waic, 1, xerr=hierarchical_waic_se, fmt='o')\n", + "plt.errorbar(pooled_waic.WAIC, 0, xerr=pooled_waic.WAIC_se, fmt='o')\n", + "plt.errorbar(hierarchical_waic.WAIC, 1, xerr=hierarchical_waic.WAIC_se, fmt='o')\n", "plt.title('WAIC')\n", "plt.yticks(np.arange(0, 2), ('pooled', 'hierarchical'))\n", "plt.ylim(-1, 2);" @@ -359,7 +359,7 @@ "source": [ "### Leave-one-out Cross-validation (LOO)\n", "\n", - "LOO cross-validation is a estimate of out-of-sample predictive fit. In cross-validation, the data are repeatedly partitioned into training and holdout sets, iteratively fitting the model with the former and evaluating the fit with the holdout data. Vehtari et al. (2016) introduced an efficient computation of LOO from MCMC samples, which are corrected using Pareto-smoothed importance sampling (PSIS) to provide an estimate of pointwise out-of-sample prediction accuracy." + "LOO cross-validation is an estimate of the out-of-sample predictive fit. In cross-validation, the data are repeatedly partitioned into training and holdout sets, iteratively fitting the model with the former and evaluating the fit with the holdout data. Vehtari et al. (2016) introduced an efficient computation of LOO from MCMC samples, which are corrected using Pareto-smoothed importance sampling (PSIS) to provide an estimate of pointwise out-of-sample prediction accuracy." ] }, { @@ -373,17 +373,19 @@ "name": "stderr", "output_type": "stream", "text": [ - "/home/osvaldo/anaconda3/lib/python3.5/site-packages/pymc3/stats.py:192: UserWarning: Estimated shape parameter of Pareto distribution\n", - " is for one or more samples is greater than 0.5. This may indicate\n", - " that the variance of the Pareto smoothed importance sampling estimate\n", - " is very large.\n", - " is very large.\"\"\")\n" + "/home/osvaldo/anaconda3/lib/python3.5/site-packages/pymc3/stats.py:208: UserWarning: Estimated shape parameter of Pareto distribution is\n", + " greater than 0.7 for one or more samples.\n", + " You should consider using a more robust model, this is\n", + " because importance sampling is less likely to work well if the marginal\n", + " posterior and LOO posterior are very different. This is more likely to\n", + " happen with a non-robust model and highly influential observations.\n", + " happen with a non-robust model and highly influential observations.\"\"\")\n" ] }, { "data": { "text/plain": [ - "(59.796215810927023, 2.0067514127136565)" + "61.53782737562031" ] }, "execution_count": 15, @@ -393,9 +395,9 @@ ], "source": [ "with pooled:\n", - " pooled_loo, pooled_loo_se = loo(trace_p)\n", + " pooled_loo= loo(trace_p)\n", " \n", - "pooled_loo, pooled_loo_se" + "pooled_loo.LOO" ] }, { @@ -409,17 +411,19 @@ "name": "stderr", "output_type": "stream", "text": [ - "/home/osvaldo/anaconda3/lib/python3.5/site-packages/pymc3/stats.py:192: UserWarning: Estimated shape parameter of Pareto distribution\n", - " is for one or more samples is greater than 0.5. This may indicate\n", - " that the variance of the Pareto smoothed importance sampling estimate\n", - " is very large.\n", - " is very large.\"\"\")\n" + "/home/osvaldo/anaconda3/lib/python3.5/site-packages/pymc3/stats.py:208: UserWarning: Estimated shape parameter of Pareto distribution is\n", + " greater than 0.7 for one or more samples.\n", + " You should consider using a more robust model, this is\n", + " because importance sampling is less likely to work well if the marginal\n", + " posterior and LOO posterior are very different. This is more likely to\n", + " happen with a non-robust model and highly influential observations.\n", + " happen with a non-robust model and highly influential observations.\"\"\")\n" ] }, { "data": { "text/plain": [ - "(59.411244130649877, 1.8240316214171435)" + "61.385652284361953" ] }, "execution_count": 16, @@ -429,9 +433,9 @@ ], "source": [ "with hierarchical:\n", - " hierarchical_loo, hierarchical_loo_se = loo(trace_h)\n", + " hierarchical_loo = loo(trace_h)\n", " \n", - "hierarchical_loo, hierarchical_loo_se" + "hierarchical_loo.LOO" ] }, { @@ -450,9 +454,9 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -460,8 +464,8 @@ } ], "source": [ - "plt.errorbar(pooled_loo, 0, xerr=pooled_loo_se, fmt='o')\n", - "plt.errorbar(hierarchical_loo, 1, xerr=hierarchical_loo_se, fmt='o')\n", + "plt.errorbar(pooled_loo.LOO, 0, xerr=pooled_loo.LOO_se, fmt='o')\n", + "plt.errorbar(hierarchical_loo.LOO, 1, xerr=hierarchical_loo.LOO_se, fmt='o')\n", "plt.title('LOO')\n", "plt.yticks(np.arange(0, 2), ('pooled', 'hierarchical'))\n", "plt.ylim(-1, 2);" diff --git a/pymc3/stats.py b/pymc3/stats.py index c43b458b82..50474e6af5 100644 --- a/pymc3/stats.py +++ b/pymc3/stats.py @@ -5,6 +5,7 @@ import itertools import sys import warnings +from collections import namedtuple from .model import modelcontext from scipy.misc import logsumexp @@ -124,7 +125,7 @@ def waic(trace, model=None, pointwise=False): Returns ------- - DataFrame with the following columns: + namedtuple with the following elements: waic: widely available information criterion waic_se: standard error of waic p_waic: effective number parameters @@ -151,13 +152,11 @@ def waic(trace, model=None, pointwise=False): p_waic = np.sum(vars_lpd) if pointwise: - return pd.DataFrame([[waic, waic_se, p_waic, waic_i]], - columns=['WAIC', 'WAIC_se', 'p_WAIC', 'waic_i'], - index=['model']) + WAIC_r = namedtuple('WAIC_r', 'WAIC, WAIC_se, p_WAIC, WAIC_i') + return WAIC_r(waic, waic_se, p_waic, waic_i) else: - return pd.DataFrame([[waic, waic_se, p_waic]], - columns=['WAIC', 'WAIC_se', 'p_WAIC'], - index=['model']) + WAIC_r = namedtuple('WAIC_r', 'WAIC, WAIC_se, p_WAIC') + return WAIC_r(waic, waic_se, p_waic) def loo(trace, model=None, pointwise=False): @@ -179,7 +178,7 @@ def loo(trace, model=None, pointwise=False): Returns ------- - A DataFrame with the following columns: + namedtuple with the following elements: loo: approximated Leave-one-out cross-validation loo_se: standard error of loo p_loo: effective number of parameters @@ -240,13 +239,11 @@ def loo(trace, model=None, pointwise=False): p_loo = lppd + (0.5 * loo_lppd) if pointwise: - return pd.DataFrame([[loo_lppd, loo_lppd_se, p_loo, loo_lppd_i]], - columns=['LOO', 'LOO_se', 'p_LOO', 'LOO_i'], - index=['model']) + LOO_r = namedtuple('LOO_r', 'LOO, LOO_se, p_LOO, LOO_i') + return LOO_r(loo_lppd, loo_lppd_se, p_loo, loo_lppd_i) else: - return pd.DataFrame([[loo_lppd, loo_lppd_se, p_loo]], - columns=['LOO', 'LOO_se', 'p_LOO'], - index=['model']) + LOO_r = namedtuple('LOO_r', 'LOO, LOO_se, p_LOO') + return LOO_r(loo_lppd, loo_lppd_se, p_loo) def bpic(trace, model=None): diff --git a/pymc3/tests/test_stats.py b/pymc3/tests/test_stats.py index 21f75809c3..42a3879b56 100644 --- a/pymc3/tests/test_stats.py +++ b/pymc3/tests/test_stats.py @@ -88,8 +88,8 @@ def test_waic(self): actual_waic_se = np.sqrt(len(waic_i) * np.var(waic_i)) actual_waic = np.sum(waic_i) - assert_almost_equal(calculated_waic['WAIC'].values, actual_waic, decimal=2) - assert_almost_equal(calculated_waic['WAIC_se'].values, actual_waic_se, decimal=2) + assert_almost_equal(calculated_waic.WAIC, actual_waic, decimal=2) + assert_almost_equal(calculated_waic.WAIC_se, actual_waic_se, decimal=2) def test_hpd(self): """Test HPD calculation"""