diff --git a/examples/pymc3_howto/sampling_compound_step.ipynb b/examples/pymc3_howto/sampling_compound_step.ipynb
index 45119eed8..137e703f1 100644
--- a/examples/pymc3_howto/sampling_compound_step.ipynb
+++ b/examples/pymc3_howto/sampling_compound_step.ipynb
@@ -12,10 +12,11 @@
"# Compound Steps in Sampling\n",
"This notebook explains how the compound steps work in `pymc3.sample` function when sampling multiple random variables. We are going to answer the following questions associated with compound steps:\n",
"\n",
- "- How does compound steps work?\n",
- "- What will happen when PyMC3 assign step methods by default?\n",
+ "- How do compound steps work?\n",
+ "- What happens when PyMC3 assigns step methods by default?\n",
"- How to specify the step methods? What is the order to apply the step methods at each iteration? Is there a way to specify the order of the step methods? \n",
- "- What are the issues with mixing discrete and continuous samplers, especially with HMC/NUTS?"
+ "- What are the issues with mixing discrete and continuous samplers, especially with HMC/NUTS?\n",
+ "- What happens to sample statistics that occur in multiple step methods? "
]
},
{
@@ -29,9 +30,20 @@
},
"outputs": [],
"source": [
+ "import arviz as az\n",
"import numpy as np\n",
"import pymc3 as pm\n",
- "import theano"
+ "import theano\n",
+ "import xarray"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "az.style.use(\"arviz-darkgrid\")"
]
},
{
@@ -45,7 +57,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "When sampling a model with multiple free random variables, the compound steps will be needed in the `pm.sample` function. When the compound steps are involved, the function takes a list of `step` to generate a list of `methods` for different random variables. So for example in the following code,\n",
+ "When sampling a model with multiple free random variables, compound steps are needed in the `pm.sample` function. When compound steps are involved, the function takes a list of `step` to generate a list of `methods` for different random variables. For example in the following code:\n",
"```python\n",
"with pm.Model() as m:\n",
" rv1 = ... # random variable 1 (continuous)\n",
@@ -56,7 +68,7 @@
" step2 = pm.CategoricalGibbsMetropolis([rv3])\n",
" trace = pm.sample(..., step=[step1, step2]...)\n",
"```\n",
- "the compound step is now contain a list of `methods`. And at each sampling step, it iterates each method, which takes a `point` as input, and generates a new `point` as output. The new `point` is proposed within each step via a stochastic kernel, and if the proposal was rejected by the Metropolis-Hastings criteria it just outputs the original input `point`."
+ "The compound step now contains a list of `methods`. At each sampling step, it iterates over these methods, taking a `point` as input. In each step a new `point` is proposed as an output, if rejected by the Metropolis-Hastings criteria the original input `point` sticks around as the output. "
]
},
{
@@ -64,12 +76,18 @@
"metadata": {},
"source": [
"## Compound steps by default\n",
- "When we call `pm.sample()`, `PyMC3` assigns the best step method to each of the free random variables. Take the following example:"
+ "To conduct Markov chain Monte Carlo (MCMC) sampling to generate posterior samples in PyMC3, we specify a step method object that corresponds to a particular MCMC algorithm, such as Metropolis, Slice sampling, or the No-U-Turn Sampler (NUTS). PyMC3’s step_methods can be assigned manually, or assigned automatically by PyMC3. Auto-assignment is based on the attributes of each variable in the model. In general:\n",
+ "\n",
+ "- Binary variables will be assigned to BinaryMetropolis\n",
+ "- Discrete variables will be assigned to Metropolis\n",
+ "- Continuous variables will be assigned to NUTS\n",
+ "\n",
+ "When we call `pm.sample()`, `PyMC3` assigns the best step method to each of the free random variables. Take the following example"
]
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2018-07-28T21:54:23.727052Z",
@@ -104,8 +122,8 @@
" background: #F44336;\n",
" }\n",
" \n",
- " \n",
- " 100.00% [8000/8000 00:06<00:00 Sampling 4 chains, 0 divergences]\n",
+ " \n",
+ " 100.00% [44000/44000 00:19<00:00 Sampling 4 chains, 0 divergences]\n",
" \n",
" "
],
@@ -120,7 +138,7 @@
"name": "stderr",
"output_type": "stream",
"text": [
- "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 8 seconds.\n"
+ "Sampling 4 chains for 1_000 tune and 10_000 draw iterations (4_000 + 40_000 draws total) took 33 seconds.\n"
]
}
],
@@ -130,7 +148,7 @@
" p = pm.Beta(\"p\", 1.0, 1.0)\n",
" ni = pm.Bernoulli(\"ni\", 0.5)\n",
" k = pm.Binomial(\"k\", p=p, n=n_[ni], observed=4)\n",
- " trace = pm.sample()"
+ " trace = pm.sample(10000, return_inferencedata=True)"
]
},
{
@@ -142,7 +160,7 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2018-07-28T21:56:05.311321Z",
@@ -153,10 +171,10 @@
{
"data": {
"text/plain": [
- "[p_logodds__, ni]"
+ "[p_logodds__ ~ TransformedDistribution, ni ~ Bernoulli]"
]
},
- "execution_count": 3,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -177,35 +195,80 @@
"metadata": {},
"source": [
"## Specify compound steps\n",
- "But we can also specify the steps manually:"
+ "Auto-assignment can be overriden for any subset of variables by specifying them manually prior to sampling:"
]
},
{
"cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "ExecuteTime": {
- "end_time": "2018-07-28T21:56:07.867622Z",
- "start_time": "2018-07-28T21:56:07.051095Z"
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Multiprocess sampling (4 chains in 4 jobs)\n",
+ "CompoundStep\n",
+ ">Metropolis: [p]\n",
+ ">BinaryMetropolis: [ni]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "