"
]
},
"metadata": {},
@@ -313,7 +427,7 @@
}
],
"source": [
- "pm.densityplot(traces, var_names=['alpha', 'sigma']);"
+ "az.plot_density(traces, var_names=['alpha', 'sigma']);"
]
},
{
@@ -325,18 +439,17 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
- "/home/junpenglao/Documents/pymc3/pymc3/stats.py:219: UserWarning: For one or more samples the posterior variance of the\n",
- " log predictive densities exceeds 0.4. This could be indication of\n",
- " WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
- " \n",
- " \"\"\")\n"
+ "/home/osvaldo/proyectos/00_BM/arviz/arviz/stats/stats.py:150: UserWarning: \n",
+ "The scale is now log by default. Use 'scale' argument or 'stats.ic_scale' rcParam if you rely on a specific value.\n",
+ "A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.\n",
+ " \"\\nThe scale is now log by default. Use 'scale' argument or \"\n"
]
},
{
@@ -360,65 +473,78 @@
" \n",
"
\n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 9 seconds.\n",
+ "There were 2 divergences after tuning. Increase `target_accept` or reparameterize.\n"
]
}
],
@@ -122,34 +202,26 @@
"with pm.Model() as hierarchical:\n",
" \n",
" eta = pm.Normal('eta', 0, 1, shape=J)\n",
- " mu = pm.Normal('mu', 0, sigma=1e6)\n",
- " tau = pm.HalfCauchy('tau', 5)\n",
+ " mu = pm.Normal('mu', 0, sigma=10)\n",
+ " tau = pm.HalfNormal('tau', 10)\n",
" \n",
" theta = pm.Deterministic('theta', mu + tau*eta)\n",
" \n",
" obs = pm.Normal('obs', theta, sigma=sigma, observed=y)\n",
" \n",
- " trace_h = pm.sample(1000)"
+ " trace_h = pm.sample(2000, target_accept=0.9, return_inferencedata=True)"
]
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": 8,
"metadata": {},
"outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/home/junpenglao/Documents/pymc3/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
- " warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
- ]
- },
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
- "
"
+ "
"
]
},
"metadata": {},
@@ -157,27 +229,19 @@
}
],
"source": [
- "pm.traceplot(trace_h, varnames=['mu']);"
+ "az.plot_trace(trace_h, var_names='mu');"
]
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 9,
"metadata": {},
"outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/home/junpenglao/Documents/pymc3/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
- " warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
- ]
- },
{
"data": {
- "image/png": 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\n",
+ "image/png": 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"text/plain": [
- "
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+ "
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]
},
"metadata": {},
@@ -185,84 +249,100 @@
}
],
"source": [
- "pm.forestplot(trace_h, varnames=['theta']);"
+ "az.plot_forest(trace_h, var_names='theta');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
+ "### Leave-one-out Cross-validation (LOO)\n",
+ "\n",
+ "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 (without the need for re-fitting the data). This approximation is based on importance sampling. The importance weights are stabilized using a method known as Pareto-smoothed importance sampling (PSIS).\n",
+ "\n",
"### Widely-applicable Information Criterion (WAIC)\n",
"\n",
- "WAIC (Watanabe 2010) is a fully Bayesian criterion for estimating out-of-sample expectation, using the computed log pointwise posterior predictive density (LPPD) and correcting for the effective number of parameters to adjust for overfitting."
+ "WAIC (Watanabe 2010) is a fully Bayesian criterion for estimating out-of-sample expectation, using the computed log pointwise posterior predictive density (LPPD) and correcting for the effective number of parameters to adjust for overfitting.\n",
+ "\n",
+ "By default ArviZ uses LOO, but WAIC is also available."
]
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "61.173190685882204"
+ "-30.541155330185944"
]
},
- "execution_count": 8,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "pooled_waic = pm.waic(trace_p, pooled)\n",
+ "pooled_loo = az.loo(trace_p, pooled)\n",
" \n",
- "pooled_waic.WAIC"
+ "pooled_loo.loo"
]
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 11,
"metadata": {},
"outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/osvaldo/proyectos/00_BM/arviz/arviz/stats/stats.py:682: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
+ " \"Estimated shape parameter of Pareto distribution is greater than 0.7 for \"\n"
+ ]
+ },
{
"data": {
"text/plain": [
- "61.38571263305805"
+ "-30.79701778020852"
]
},
- "execution_count": 9,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "hierarchical_waic = pm.waic(trace_h, hierarchical)\n",
+ "hierarchical_loo = az.loo(trace_h, hierarchical)\n",
" \n",
- "hierarchical_waic.WAIC"
+ "hierarchical_loo.loo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "PyMC3 includes two convenience functions to help compare WAIC for different models. The first of this functions is `compare`, this one computes WAIC (or LOO) from a set of traces and models and returns a DataFrame."
+ "ArviZ includes two convenience functions to help compare LOO for different models. The first of these functions is `compare`, which computes LOO (or WAIC) from a set of traces and models and returns a DataFrame."
]
},
{
"cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [],
- "source": [
- "hierarchical.name = 'hierarchical'\n",
- "pooled.name = 'pooled'"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
+ "execution_count": 12,
"metadata": {},
"outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/osvaldo/proyectos/00_BM/arviz/arviz/stats/stats.py:150: UserWarning: \n",
+ "The scale is now log by default. Use 'scale' argument or 'stats.ic_scale' rcParam if you rely on a specific value.\n",
+ "A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.\n",
+ " \"\\nThe scale is now log by default. Use 'scale' argument or \"\n",
+ "/home/osvaldo/proyectos/00_BM/arviz/arviz/stats/stats.py:682: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
+ " \"Estimated shape parameter of Pareto distribution is greater than 0.7 for \"\n"
+ ]
+ },
{
"data": {
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"text/plain": [
- " WAIC pWAIC dWAIC weight SE dSE var_warn\n",
- "pooled 61.17 0.69 0 1 2.2 0 0\n",
- "hierarchical 61.39 0.99 0.21 0 2.01 0.31 0"
+ " rank loo p_loo d_loo weight se dse \\\n",
+ "pooled 0 -30.5412 0.661857 0 0.56286 0.986818 0 \n",
+ "hierarchical 1 -30.797 1.14051 0.255862 0.43714 1.02204 0.256169 \n",
+ "\n",
+ " warning loo_scale \n",
+ "pooled False log \n",
+ "hierarchical True log "
]
},
- "execution_count": 11,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "df_comp_WAIC = pm.compare({hierarchical: trace_h, pooled: trace_p})\n",
- "df_comp_WAIC"
+ "df_comp_loo = az.compare({\"hierarchical\": trace_h, \"pooled\": trace_p})\n",
+ "df_comp_loo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "We have many columns so let check one by one the meaning of them:\n",
+ "We have many columns, so let's check out their meaning one by one:\n",
"\n",
"\n",
- "1. The first column clearly contains the values of WAIC. The DataFrame is always sorted from lowest to highest WAIC. The index reflects the order in which the models are passed to this function.\n",
+ "0. The index is the names of the models taken from the keys of the dictionary passed to `compare(.)`.\n",
"\n",
- "2. The second column is the estimated effective number of parameters. In general, models with more parameters will be more flexible to fit data and at the same time could also lead to overfitting. Thus we can interpret pWAIC as a penalization term, intuitively we can also interpret it as measure of how flexible each model is in fitting the data. \n",
+ "1. **rank**, the ranking of the models starting from 0 (best model) to the number of models.\n",
"\n",
- "3. The third column is the relative difference between the value of WAIC for the top-ranked model and the value of WAIC for each model. For this reason we will always get a value of 0 for the first model.\n",
+ "2. **loo**, the values of LOO (or WAIC). The DataFrame is always sorted from best LOO/WAIC to worst. \n",
"\n",
- "4. Sometimes when comparing models, we do not want to select the \"best\" model, instead we want to perform predictions by averaging along all the models (or at least several models). Ideally we would like to perform a weighted average, giving more weight to the model that seems to explain/predict the data better. There are many approaches to perform this task, one of them is to use Akaike weights based on the values of WAIC for each model. These weights can be loosely interpreted as the probability of each model (among the compared models) given the data. One caveat of this approach is that the weights are based on point estimates of WAIC (i.e. the uncertainty is ignored).\n",
+ "3. **p_loo**, the value of the penalization term. We can roughly think of this value as the estimated effective number of parameters (but do not take that too seriously).\n",
"\n",
- "5. The fifth column records the standard error for the WAIC computations. 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.\n",
+ "4. **d_loo**, the relative difference between the value of LOO/WAIC for the top-ranked model and the value of LOO/WAIC for each model. For this reason we will always get a value of 0 for the first model.\n",
"\n",
- "6. In the same way that we can compute the standard error for each value of WAIC, we can compute the standard error of the differences between two values of WAIC. Notice that both quantities are not necessarily the same, the reason is that the uncertainty about WAIC is correlated between models. This quantity is always 0 for the top-ranked model.\n",
+ "5. **weight**, the weights assigned to each model. These weights can be loosely interpreted as the probability of each model being true (among the compared models) given the data.\n",
"\n",
- "7. Finally we have the last column named \"warning\". A value of 1 indicates that the computation of WAIC may not be reliable, this warning is based on an empirical determined cutoff value and need to be interpreted with caution. For more details you can read this [paper](https://arxiv.org/abs/1507.04544)."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The second convenience function takes the output of `compare` and produces a summary plot in the style of the one used in the book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath (check also [this port](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3) of the examples in the book to PyMC3)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- "
"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "pm.compareplot(df_comp_WAIC);"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The empty circle represents the values of WAIC and the black error bars associated with them are the values of the standard deviation of WAIC. \n",
+ "6. **se**, the standard error for the LOO/WAIC computations. The standard error can be useful to assess the uncertainty of the LOO/WAIC estimates. By default these errors are computed using stacking.\n",
"\n",
- "The value of the lowest WAIC is also indicated with a vertical dashed grey line to ease comparison with other WAIC values.\n",
+ "7. **dse**, the standard errors of the difference between two values of LOO/WAIC. The same way that we can compute the standard error for each value of LOO/WAIC, we can compute the standard error of the differences between two values of LOO/WAIC. Notice that both quantities are not necessarily the same, the reason is that the uncertainty about LOO/WAIC is correlated between models. This quantity is always 0 for the top-ranked model.\n",
"\n",
- "The filled black dots are the in-sample deviance of each model, which for WAIC is 2 pWAIC from the corresponding WAIC value.\n",
+ "8. **warning**, If `True` the computation of LOO/WAIC may not be reliable.\n",
"\n",
- "For all models except the top-ranked one we also get a triangle indicating the value of the difference of WAIC between that model and the top model and a grey errobar indicating the standard error of the differences between the top-ranked WAIC and WAIC for each model."
+ "9. **loo_scale**, the scale of the reported values. The default is the log scale as previously mentioned. Other options are deviance -- this is the log-score multiplied by -2 (this reverts the order: a lower LOO/WAIC will be better) -- and negative-log -- this is the log-score multiplied by -1 (as with the deviance scale, a lower value is better)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### Leave-one-out Cross-validation (LOO)\n",
- "\n",
- "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 point-wise out-of-sample prediction accuracy."
+ "The second convenience function takes the output of `compare` and produces a summary plot in the style of the one used in the book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath (check also [this port](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3) of the examples in the book to PyMC3)."
]
},
{
@@ -412,153 +466,28 @@
"outputs": [
{
"data": {
+ "image/png": "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\n",
"text/plain": [
- "61.203032352985645"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "pooled_loo = pm.loo(trace_p, pooled)\n",
- " \n",
- "pooled_loo.LOO"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "61.47557753820364"
+ "
"
- ],
- "text/plain": [
- " LOO pLOO dLOO weight SE dSE shape_warn\n",
- "pooled 61.2 0.7 0 1 2.21 0 0\n",
- "hierarchical 61.48 1.03 0.27 0 2.01 0.31 0"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
+ "output_type": "display_data"
}
],
"source": [
- "df_comp_LOO = pm.compare({hierarchical: trace_h, pooled: trace_p}, ic='LOO')\n",
- "df_comp_LOO"
+ "az.plot_compare(df_comp_loo, insample_dev=False);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "The columns return the equivalent values for LOO, notice that in this example we get two warnings. Also notice that the order of the models is not the same as the one for WAIC.\n",
+ "The empty circle represents the values of LOO and the black error bars associated with them are the values of the standard deviation of LOO. \n",
"\n",
- "We can also plot the results"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": "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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "pm.compareplot(df_comp_LOO);"
+ "The value of the highest LOO, i.e the best estimated model, is also indicated with a vertical dashed grey line to ease comparison with other LOO values.\n",
+ "\n",
+ "For all models except the top-ranked one we also get a triangle indicating the value of the difference of WAIC between that model and the top model and a grey errobar indicating the standard error of the differences between the top-ranked WAIC and WAIC for each model."
]
},
{
@@ -567,7 +496,7 @@
"source": [
"### Interpretation\n",
"\n",
- "Though we might expect the hierarchical model to outperform a complete pooling model, there is little to choose between the models in this case, giving that both models gives very similar values of the information criteria. This is more clearly appreciated when we take into account the uncertainty (in terms of standard errors) of WAIC and LOO.\n",
+ "Though we might expect the hierarchical model to outperform a complete pooling model, there is little to choose between the models in this case, given that both models gives very similar values of the information criteria. This is more clearly appreciated when we take into account the uncertainty (in terms of standard errors) of LOO and WAIC.\n",
"\n",
"## Reference\n",
"\n",
@@ -578,26 +507,27 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "pymc3 3.8\n",
- "arviz 0.8.3\n",
- "numpy 1.17.5\n",
- "last updated: Thu Jun 11 2020 \n",
+ "autopep8 1.5\n",
+ "pymc3 3.9.3\n",
+ "arviz 0.9.0\n",
+ "numpy 1.18.5\n",
+ "json 2.0.9\n",
+ "last updated: Thu Aug 13 2020 \n",
"\n",
- "CPython 3.8.2\n",
- "IPython 7.11.0\n",
+ "CPython 3.7.6\n",
+ "IPython 7.17.0\n",
"watermark 2.0.2\n"
]
}
],
"source": [
- "%load_ext watermark\n",
"%watermark -n -u -v -iv -w"
]
}
@@ -618,7 +548,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.2"
+ "version": "3.7.6"
}
},
"nbformat": 4,
diff --git a/pymc3/sampling.py b/pymc3/sampling.py
index 8f0fecb3c0..240ebbf6d7 100644
--- a/pymc3/sampling.py
+++ b/pymc3/sampling.py
@@ -226,9 +226,7 @@ def _print_step_hierarchy(s, level=0):
else:
varnames = ", ".join(
[
- get_untransformed_name(v.name)
- if is_transformed_name(v.name)
- else v.name
+ get_untransformed_name(v.name) if is_transformed_name(v.name) else v.name
for v in s.vars
]
)
@@ -491,10 +489,7 @@ def sample(
start = start_
except (AttributeError, NotImplementedError, tg.NullTypeGradError):
# gradient computation failed
- _log.info(
- "Initializing NUTS failed. "
- "Falling back to elementwise auto-assignment."
- )
+ _log.info("Initializing NUTS failed. " "Falling back to elementwise auto-assignment.")
_log.debug("Exception in init nuts", exec_info=True)
step = assign_step_methods(model, step, step_kwargs=kwargs)
else:
@@ -559,9 +554,7 @@ def sample(
has_demcmc = np.any(
[
isinstance(m, DEMetropolis)
- for m in (
- step.methods if isinstance(step, CompoundStep) else [step]
- )
+ for m in (step.methods if isinstance(step, CompoundStep) else [step])
]
)
_log.info("Population sampling ({} chains)".format(chains))
@@ -625,9 +618,7 @@ def sample(
if compute_convergence_checks:
if draws - tune < 100:
- warnings.warn(
- "The number of samples is too small to check convergence reliably."
- )
+ warnings.warn("The number of samples is too small to check convergence reliably.")
else:
trace.report._run_convergence_checks(idata, model)
trace.report._log_summary()
@@ -664,14 +655,7 @@ def _check_start_shape(model, start):
def _sample_many(
- draws,
- chain: int,
- chains: int,
- start: list,
- random_seed: list,
- step,
- callback=None,
- **kwargs,
+ draws, chain: int, chains: int, start: list, random_seed: list, step, callback=None, **kwargs,
):
"""Samples all chains sequentially.
@@ -833,9 +817,7 @@ def _sample(
"""
skip_first = kwargs.get("skip_first", 0)
- sampling = _iter_sample(
- draws, step, start, trace, chain, tune, model, random_seed, callback
- )
+ sampling = _iter_sample(draws, step, start, trace, chain, tune, model, random_seed, callback)
_pbar_data = {"chain": chain, "divergences": 0}
_desc = "Sampling chain {chain:d}, {divergences:,d} divergences"
if progressbar:
@@ -909,9 +891,7 @@ def iter_sample(
for trace in iter_sample(500, step):
...
"""
- sampling = _iter_sample(
- draws, step, start, trace, chain, tune, model, random_seed, callback
- )
+ sampling = _iter_sample(draws, step, start, trace, chain, tune, model, random_seed, callback)
for i, (strace, _) in enumerate(sampling):
yield MultiTrace([strace[: i + 1]])
@@ -1012,8 +992,7 @@ def _iter_sample(
if callback is not None:
warns = getattr(step, "warnings", None)
callback(
- trace=strace,
- draw=Draw(chain, i == draws, i, i < tune, stats, point, warns),
+ trace=strace, draw=Draw(chain, i == draws, i, i < tune, stats, point, warns),
)
yield strace, diverging
@@ -1067,9 +1046,7 @@ def __init__(self, steppers, parallelize, progressbar=True):
import multiprocessing
for c, stepper in (
- enumerate(progress_bar(steppers))
- if progressbar
- else enumerate(steppers)
+ enumerate(progress_bar(steppers)) if progressbar else enumerate(steppers)
):
secondary_end, primary_end = multiprocessing.Pipe()
stepper_dumps = pickle.dumps(stepper, protocol=4)
@@ -1136,9 +1113,7 @@ def _run_secondary(c, stepper_dumps, secondary_end):
# but rather a CompoundStep. PopulationArrayStepShared.population
# has to be updated, therefore we identify the substeppers first.
population_steppers = []
- for sm in (
- stepper.methods if isinstance(stepper, CompoundStep) else [stepper]
- ):
+ for sm in stepper.methods if isinstance(stepper, CompoundStep) else [stepper]:
if isinstance(sm, arraystep.PopulationArrayStepShared):
population_steppers.append(sm)
while True:
@@ -1682,13 +1657,9 @@ def sample_posterior_predictive(
nchain = 1
if keep_size and samples is not None:
- raise IncorrectArgumentsError(
- "Should not specify both keep_size and samples arguments"
- )
+ raise IncorrectArgumentsError("Should not specify both keep_size and samples arguments")
if keep_size and size is not None:
- raise IncorrectArgumentsError(
- "Should not specify both keep_size and size arguments"
- )
+ raise IncorrectArgumentsError("Should not specify both keep_size and size arguments")
if samples is None:
if isinstance(_trace, MultiTrace):
@@ -1714,15 +1685,11 @@ def sample_posterior_predictive(
if var_names is not None:
if vars is not None:
- raise IncorrectArgumentsError(
- "Should not specify both vars and var_names arguments."
- )
+ raise IncorrectArgumentsError("Should not specify both vars and var_names arguments.")
else:
vars = [model[x] for x in var_names]
elif vars is not None: # var_names is None, and vars is not.
- warnings.warn(
- "vars argument is deprecated in favor of var_names.", DeprecationWarning
- )
+ warnings.warn("vars argument is deprecated in favor of var_names.", DeprecationWarning)
if vars is None:
vars = model.observed_RVs
@@ -1741,11 +1708,7 @@ def sample_posterior_predictive(
# the trace object will either be a MultiTrace (and have _straces)...
if hasattr(_trace, "_straces"):
chain_idx, point_idx = np.divmod(idx, len_trace)
- param = (
- cast(MultiTrace, _trace)
- ._straces[chain_idx % nchain]
- .point(point_idx)
- )
+ param = cast(MultiTrace, _trace)._straces[chain_idx % nchain].point(point_idx)
# ... or a PointList
else:
param = cast(PointList, _trace)[idx % len_trace]
@@ -1783,9 +1746,9 @@ def sample_posterior_predictive_w(
Parameters
----------
traces : list or list of lists
- List of traces generated from MCMC sampling, or a list of list
- containing dicts from find_MAP() or points. The number of traces should
- be equal to the number of weights.
+ List of traces generated from MCMC sampling (xarray.Dataset, arviz.InferenceData, or
+ MultiTrace), or a list of list containing dicts from find_MAP() or points. The number of
+ traces should be equal to the number of weights.
samples : int, optional
Number of posterior predictive samples to generate. Defaults to the
length of the shorter trace in traces.
@@ -1811,6 +1774,17 @@ def sample_posterior_predictive_w(
"""
np.random.seed(random_seed)
+ if isinstance(traces[0], InferenceData):
+ n_samples = [
+ trace.posterior.sizes["chain"] * trace.posterior.sizes["draw"] for trace in traces
+ ]
+ traces = [dataset_to_point_dict(trace.posterior) for trace in traces]
+ elif isinstance(traces[0], xarray.Dataset):
+ n_samples = [trace.sizes["chain"] * trace.sizes["draw"] for trace in traces]
+ traces = [dataset_to_point_dict(trace) for trace in traces]
+ else:
+ n_samples = [len(i) * i.nchains for i in traces]
+
if models is None:
models = [modelcontext(models)] * len(traces)
@@ -1830,7 +1804,7 @@ def sample_posterior_predictive_w(
weights = np.asarray(weights)
p = weights / np.sum(weights)
- min_tr = min([len(i) * i.nchains for i in traces])
+ min_tr = min(n_samples)
n = (min_tr * p).astype("int")
# ensure n sum up to min_tr
@@ -1933,8 +1907,7 @@ def sample_prior_predictive(
if vars is None and var_names is None:
prior_pred_vars = model.observed_RVs
prior_vars = (
- get_default_varnames(model.unobserved_RVs, include_transformed=True)
- + model.potentials
+ get_default_varnames(model.unobserved_RVs, include_transformed=True) + model.potentials
)
vars_ = [var.name for var in prior_vars + prior_pred_vars]
vars = set(vars_)
@@ -1942,9 +1915,7 @@ def sample_prior_predictive(
vars = var_names
vars_ = vars
elif vars is not None:
- warnings.warn(
- "vars argument is deprecated in favor of var_names.", DeprecationWarning
- )
+ warnings.warn("vars argument is deprecated in favor of var_names.", DeprecationWarning)
vars_ = vars
else:
raise ValueError("Cannot supply both vars and var_names arguments.")
@@ -1974,13 +1945,7 @@ def sample_prior_predictive(
def init_nuts(
- init="auto",
- chains=1,
- n_init=500000,
- model=None,
- random_seed=None,
- progressbar=True,
- **kwargs,
+ init="auto", chains=1, n_init=500000, model=None, random_seed=None, progressbar=True, **kwargs,
):
"""Set up the mass matrix initialization for NUTS.
@@ -2036,9 +2001,7 @@ def init_nuts(
if set(vars) != set(model.vars):
raise ValueError("Must use init_nuts on all variables of a model.")
if not all_continuous(vars):
- raise ValueError(
- "init_nuts can only be used for models with only " "continuous variables."
- )
+ raise ValueError("init_nuts can only be used for models with only " "continuous variables.")
if not isinstance(init, str):
raise TypeError("init must be a string.")
@@ -2092,9 +2055,7 @@ def init_nuts(
mean = approx.bij.rmap(approx.mean.get_value())
mean = model.dict_to_array(mean)
weight = 50
- potential = quadpotential.QuadPotentialDiagAdaptGrad(
- model.ndim, mean, cov, weight
- )
+ potential = quadpotential.QuadPotentialDiagAdaptGrad(model.ndim, mean, cov, weight)
elif init == "advi+adapt_diag":
approx = pm.fit(
random_seed=random_seed,
diff --git a/pymc3/tests/test_sampling.py b/pymc3/tests/test_sampling.py
index 91ce994862..6c6baf5779 100644
--- a/pymc3/tests/test_sampling.py
+++ b/pymc3/tests/test_sampling.py
@@ -718,22 +718,24 @@ def test_sample_posterior_predictive_w(self):
mu = pm.Normal("mu", mu=0, sigma=1)
y = pm.Normal("y", mu=mu, sigma=1, observed=data0)
trace_0 = pm.sample()
+ idata_0 = az.from_pymc3(trace_0)
with pm.Model() as model_1:
mu = pm.Normal("mu", mu=0, sigma=1, shape=len(data0))
y = pm.Normal("y", mu=mu, sigma=1, observed=data0)
trace_1 = pm.sample()
-
- traces = [trace_0, trace_0]
- models = [model_0, model_0]
- ppc = pm.sample_posterior_predictive_w(traces, 100, models)
- assert ppc["y"].shape == (100, 500)
+ idata_1 = az.from_pymc3(trace_1)
traces = [trace_0, trace_1]
+ idatas = [idata_0, idata_1]
models = [model_0, model_1]
+
ppc = pm.sample_posterior_predictive_w(traces, 100, models)
assert ppc["y"].shape == (100, 500)
+ ppc = pm.sample_posterior_predictive_w(idatas, 100, models)
+ assert ppc["y"].shape == (100, 500)
+
@pytest.mark.parametrize(
"method",