notebooks/tutorials/0 - Getting started.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import hmclab\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting started"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, you will see all the essentials of using `hmclab`. We will cover the following topics:\n",
    "\n",
    "1. Creating and sampling from a distribution;\n",
    "2. Investigating your samples;\n",
    "3. Accessing the raw samples and misfits;\n",
    "3. Interrupting sampling;\n",
    "4. Using Bayes' rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To start, we will sample one of the most common distributions in statistics, the standard normal distribution. To sample anything in this framework, we need an instance of the distribution class we wish to sample. Here is how we create a standard normal distribution in 1 dimension:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution = hmclab.Distributions.StandardNormal1D()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every distribution object should have a few essential methods and attributes, which will be covered in the tutorial on implementing your own inverse problem. However, maybe the most important attribute of any distribution is its dimensionality, indicating the dimensions of the model space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distribution.dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issubclass(\n",
    "    type(distribution),\n",
    "    hmclab.Distributions._AbstractDistribution,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the 1 dimensional standard normal distribution has 1 dimension. Great!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling for the first time\n",
    "\n",
    "To generate samples of the distribution, one can use the methods contained in the submodule `hmclab.Samplers`. As of yet, it only has the vanilla HMC algorithm. \n",
    "\n",
    "Running the associated `sample()` method requires you to **minimally** pass the **distribution** and the **filename** of the h5 file you wish to write to. This h5 file will be created if it does not exist. If it does exist, the program will prompt you with options on how to continue.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Note:** .h5 files\n",
    "    \n",
    "The sample files with extension .h5 are a special kind of files that are designed to hold a lot of data.  They were specifically chosen for hmclab because MCMC generates large amounts of data. \n",
    "    \n",
    "The samplers in this package buffer samples to RAM, and flush them intermittently to the hard drive. This is to allow for sample sizes bigger than RAM (by writing to disk) as well as avoiding continuous writes to disk which might slow down sampling (by buffering).\n",
    "    \n",
    "However, these files are not the easiest to work with. They require either an API to access them (in Python `h5py`) or a specialized program (e.g. `HDFCompass`). There are no easy ways to 'have a peek' in the file if you're not a little experienced with the file format.\n",
    "    \n",
    "In this package, we provide a class (`hmclab.Post.Samples`) that allows us to work in an easy way with the samples. However, they should **ALWAYS** be used in a Python context manager, as shown in the section `Investigating your samples`.\n",
    "\n",
    "We now also provide saving to .npy files, which avoids some of the troubles with broken files, but might be less stable for very large inferences.\n",
    "\n",
    "</div>\n",
    "\n",
    "\n",
    "Any other setting has defaults for all samplers, such that *you* can get started quickly. \n",
    "\n",
    "For the Hamiltonian Monte Carlo algorithm, important settings you could change include:\n",
    "1. Mass matrix;\n",
    "2. Amount of integration steps;\n",
    "3. Integration time step.\n",
    "4. ...\n",
    "\n",
    "You can find detailed descriptions of all the parameters in the API reference. `Tutorial 1` explains all the essential tuning parameters of HMC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
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       "model_id": "3073d53de0c2436491fc56bf66cc05bd",
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       "version_minor": 0
      },
      "text/plain": [
       "Tot. acc rate: 0.00. Progress:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/plain": [
       "Tab(children=(HBox(children=(VBox(children=(Label(value='local start time (not timezone aware)'), Label(value=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<hmclab.Samplers.HMC at 0x134ae79a0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# filename = \"bin_samples/tutorial_0_standard_normal.h5\"\n",
    "filename = \"bin_samples/tutorial_0_standard_normal.npy\"\n",
    "\n",
    "sampler = hmclab.Samplers.HMC()\n",
    "\n",
    "sampler.sample(\n",
    "    filename,\n",
    "    distribution,\n",
    "    proposals=100,\n",
    "    online_thinning=1,\n",
    "    overwrite_existing_file=True,\n",
    "    autotuning=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! We just generated 100 samples from the distribution. The total acceptance rate was 1.00, and the acceptance rate of the last 100 samples (coincidentally the total amount of samples) is also 1.00. These numbers are rounded, so at a high amount of samples there might still be some rejected samples if you see 1.00."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next cell, we try to write to the same samples file again, so the sampler also asks us for permission to overwrite the previous file.\n",
    "\n",
    "This package allows you to run the `sample()` method on either the instance, or directly on the class. What this means is that the previous and the following code snippets do the same thing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
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       "model_id": "b4d23599044d44c2908b760e6409c72f",
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       "version_minor": 0
      },
      "text/plain": [
       "Tot. acc rate: 0.00. Progress:   0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "af3baf6fb6e64e4c80f094c70a98e7a4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tab(children=(HBox(children=(VBox(children=(Label(value='local start time (not timezone aware)'), Label(value=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<hmclab.Samplers.HMC at 0x134ae7700>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hmc_instance = hmclab.Samplers.HMC()\n",
    "\n",
    "hmc_instance.sample(\n",
    "    \"bin_samples/tutorial_0_standard_normal.h5\",\n",
    "    distribution,\n",
    "    proposals=10000,\n",
    "    overwrite_existing_file=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sneakily, I've now also passed an extra argument: proposals. This controls how many proposals the algorithm makes. How many of those are accepted still depends on other settings! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Investigating your samples\n",
    "\n",
    "Now that we have some samples generated on disk, we should do something useful with them! \n",
    "\n",
    "As a first step, we should verify the generated samples. The samples are stored in H5 files. This allows us to not instantly load everything into memory, which might be helpful if our results are really big.\n",
    "\n",
    "Let's see how we can access the samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Object type <class 'hmclab.Samples.Samples'>\n",
      "[ 0.61118422  0.20236144 -0.4033621 ]\n",
      "[0.18677307 0.02047508 0.08135049]\n",
      "Shape of the samples: (2, 10000)\n"
     ]
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\") as samples:\n",
    "\n",
    "    # Show the object type\n",
    "    print(f\"Object type {type(samples)}\")\n",
    "\n",
    "    # Load the first model parameter, samples 0 through 3\n",
    "    print(samples[0, 0:3])\n",
    "\n",
    "    # Load misfits 0 through 3\n",
    "    print(samples[1, 0:3])\n",
    "\n",
    "    # Load everything into a numpy object\n",
    "    # (this might take a lot of memory for high dimensional results)\n",
    "    samples_numpy = samples.numpy\n",
    "    print(f\"Shape of the samples: {samples_numpy.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes you know that your results easily fit into memory. You can easily get the results directly into a numpy object in one of two ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_numpy_method_1 = hmc_instance.load_results()\n",
    "\n",
    "samples = hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\")\n",
    "samples_numpy_method_2 = samples.numpy\n",
    "# NOTE: The samples object is closed after getting .numpy,\n",
    "# as the HDF5 should be closed after usage. To use it more than\n",
    "# once, use a context manager.\n",
    "\n",
    "assert numpy.allclose(samples_numpy_method_1, samples_numpy_method_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might wish to visualize the resulting distribution. Luckily, there is a visualization module, `hmclab.Post.Visualization`.\n",
    "\n",
    "This module contains multiple helpful functions to start with. One of them is `marginal`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This works with both `Samples` objects and numpy arrays.\n",
    "with hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\") as samples:\n",
    "    hmclab.Visualization.marginal(\n",
    "        samples, dimension=0, bins=25  # Note that dimensions are zero indexed\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing the raw samples and misfits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes you want more control over your samples. Luckily, we got your back. You can access the samples both as a NumPy array as well as the actual HDF5 dataset object. \n",
    "\n",
    "If you know how to work with it, accessing via HDF is faster, as it doesn't necessarily load all samples into RAM before slicing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type:  <class 'numpy.ndarray'>\n",
      "Shape: (2, 10000)\n",
      "\n",
      "Type:  <class 'h5py._hl.dataset.Dataset'>\n",
      "Shape: (2, 10000)\n"
     ]
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\") as samples:\n",
    "\n",
    "    # Access samples as a numpy array\n",
    "    print(f\"Type:  {type(samples.numpy)}\")\n",
    "    print(f\"Shape: {samples.numpy.shape}\")\n",
    "    print()\n",
    "\n",
    "    # Access samples as a HDF dataset\n",
    "    print(f\"Type:  {type(samples._hdf5_dataset)}\")\n",
    "    print(f\"Shape: {samples._hdf5_dataset.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might notice the the `raw_samples_hdf` attribute has one extra dimension. That is because the samples file also records the misfits of each sample. We can easily access these as a NumPy array in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type:  <class 'numpy.ndarray'>\n",
      "Shape: (10000, 1)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\") as samples:\n",
    "\n",
    "    # Access misfits as a numpy array\n",
    "    print(f\"Type:  {type(samples.misfits)}\")\n",
    "    print(f\"Shape: {samples.misfits.shape}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accessing the data directly might be handy when you need to compute some properties of a parameter, or wish to visualize some behaviour of the Monte Carlo sampler. \n",
    "\n",
    "Here is an example where we plot the evolution of parameter 1 and the misfit during the Markov chain, as well as printing statistics on parameter 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "emperical mean: 0.11\n",
      "emperical standard deviation: 0.09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "with hmclab.Samples(\"bin_samples/tutorial_0_standard_normal.h5\") as samples:\n",
    "\n",
    "    plt.figure(figsize=(8, 8))\n",
    "\n",
    "    plt.subplot(211)\n",
    "    plt.plot(samples[0, :])\n",
    "    plt.xlabel(\"sample index\")\n",
    "    plt.ylabel(\"parameter 1 value\")\n",
    "\n",
    "    plt.subplot(212)\n",
    "    plt.plot(samples.misfits)\n",
    "    plt.xlabel(\"sample index\")\n",
    "    plt.ylabel(\"misfit\")\n",
    "\n",
    "    print(f\"emperical mean: {samples[:,1].mean():.2f}\")\n",
    "    print(f\"emperical standard deviation: {samples[:,1].std():.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interrupting sampling: no big deal\n",
    "\n",
    "Sometimes you think you have the perfect settings for your 'run', and then after half an hour realize sampling is going to take longer than expected. At least, we experienced this a lot during our work with HMC.\n",
    "\n",
    "Luckily, we've added some nice functionality in this specific case. When a sampler is busy doing his thing, and you want it to wrap up, simply interrupt the process. What this means is you either **once** press `CTRL + C` when you're running from a terminal, or press the stop button (■) at the top if you're in a Jupyter Notebook. This ensures that the algorithm gracefully wraps up, leaving your dear samples intact.\n",
    "\n",
    "Try this out with the next cell. Let it progress to some percentage, and interrupt the kernel. After 3 seconds, it is automatically interrupted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e5b546eaeda64b099e6f590d4a310ae0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tot. acc rate: 0.00. Progress:   0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b91d01a586df4de8a2def621863420c2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tab(children=(HBox(children=(VBox(children=(Label(value='local start time (not timezone aware)'), Label(value=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<hmclab.Samplers.HMC at 0x134f1eb50>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hmclab.Samplers.HMC().sample(\n",
    "    \"bin_samples/tutorial_0_standard_normal.h5\",\n",
    "    distribution,\n",
    "    proposals=100000,\n",
    "    online_thinning=100,\n",
    "    overwrite_existing_file=True,\n",
    "    max_time=3.0,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we now inspect the resulting samples, we see that because we interrupted the kernel, the `samples written` is less than we would expect after dividing requested proposals by `online thinning` (i.e. the number we would expect if the sampler finished)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting multidimensional results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = numpy.array([-40.2, 4])\n",
    "std = numpy.array([1.0, 4.5])\n",
    "variance = std**2\n",
    "\n",
    "normal_2d = hmclab.Distributions.Normal(mean, variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "25cc651a94d843c580d84806a9a9ff65",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tot. acc rate: 0.00. Progress:   0%|          | 0/25000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a0081f40914049878c176622479ad78d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tab(children=(HBox(children=(VBox(children=(Label(value='local start time (not timezone aware)'), Label(value=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<hmclab.Samplers.HMC at 0x134fb1550>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hmclab.Samplers.HMC().sample(\n",
    "    \"bin_samples/tutorial_0_mvn.h5\",\n",
    "    normal_2d,\n",
    "    stepsize=1.5,\n",
    "    proposals=25000,\n",
    "    autotuning=True,\n",
    "    overwrite_existing_file=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the most interesting things to investigate when sampling from multidimensional distributions is the trade-off between different parameters. We can visualize these (second order) trade-offs by inspecting the 2D marginals. We supply a function that can create a set of 2D marginals from a samples object, by specifying which dimensions should be investigated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_mvn.h5\") as samples:\n",
    "    hmclab.Visualization.marginal_grid(\n",
    "        samples, [0, 1], bins=25  # Note that dimensions are zero indexed\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to investigate sampler behaviour, it is often beneficial to look at a trace plot of the Markov chain. In the next cell, we visualize the evolution of parameter 2 (dimension 1, due to zero based index). We give this function only the first 250 samples.\n",
    "\n",
    "Additionally, the used function creates the 2D marginal with another dimension and plots the autocorrelation function of these two parameters during the supplied samples.\n",
    "\n",
    "These types of plots can help us identify problems with sampling and assess convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x576 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_mvn.h5\") as samples:\n",
    "    hmclab.Visualization.visualize_2_dimensions(\n",
    "        samples[:, :100], dim1=1, dim2=0\n",
    "    )  # Note that we only pass the first 250 samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Bayes' rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the main operations users of Bayesian inference do is applying Bayes' rule to two distributions. Bayes' rule combines two distributions (typically a likelihood and a prior) to a combined state of information, the posterior. We provide a simple interface to combine two or more distributions using Bayes' rule in the following way.\n",
    "\n",
    "First we create two distributions we wish to combine. The first distribution is a 2D uniform distribution bounded between $[0, 1]$ for both parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_bounds = numpy.zeros((2, 1))\n",
    "upper_bounds = numpy.ones((2, 1))\n",
    "\n",
    "distribution_1 = hmclab.Distributions.Uniform(\n",
    "    lower_bounds=lower_bounds, upper_bounds=upper_bounds\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next distribution is a mutlivariate (uncorrelated) normal distribution with varying means and standard deviations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = numpy.array([[-0.1], [0.75]])\n",
    "std = numpy.array([[0.1], [0.25]])\n",
    "variance = std**2\n",
    "\n",
    "distribution_2 = hmclab.Distributions.Normal(mean, variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hmclab package additionally warns us that it assumed the passed variance object was the diagonal of a covariance matrix. This is fine, as we don't want to define any correlations in this distribution.\n",
    "\n",
    "We can use Bayes' rule by passing a list of distributions to the method `hmclab.Distributions.BayesRule`. The returned distribution will contain the originally passed distributions completely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "posterior = hmclab.Distributions.BayesRule([distribution_1, distribution_2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The generated distribution can then be investigated using the samplers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9b78c35d52da46fe801d765ff08e71a4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tot. acc rate: 0.00. Progress:   0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "395e0990df8440a9bb9411f64f18a0fe",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Tab(children=(HBox(children=(VBox(children=(Label(value='local start time (not timezone aware)'), Label(value=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<hmclab.Samplers.HMC at 0x134f02730>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hmclab.Samplers.HMC().sample(\n",
    "    \"bin_samples/tutorial_0_posterior.h5\",\n",
    "    posterior,\n",
    "    proposals=10000,\n",
    "    overwrite_existing_file=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Upon visualization we see the influence of both the uniform distributions (truncating the posterior at their limits) as well as the multivariate normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with hmclab.Samples(\"bin_samples/tutorial_0_posterior.h5\") as samples:\n",
    "\n",
    "    hmclab.Visualization.marginal_grid(samples, [0, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that these distributions are not Gaussian anymore (after applying Bayes' rule), and therefore the fitted Gaussians (blue lines) don't match the posterior well. This illustrates that a mean and standard deviation are not always ideal to describe a distribution."
   ]
  }
 ],
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "vscode": {
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