diff --git a/06_Monte_Carlo_and_MCMC.ipynb b/06_Monte_Carlo_and_MCMC.ipynb new file mode 100644 index 0000000..e727818 --- /dev/null +++ b/06_Monte_Carlo_and_MCMC.ipynb @@ -0,0 +1,470 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Monte Carlo method\n", + "\n", + "The Monte Carlo method is a computational technique that uses **`random sampling`** to estimate complex mathematical outcomes or solve problems that might be **`deterministic`** in nature.\n", + "\n", + "## Monte Carlo integration\n", + "\n", + "Let us consider the example of computing of an integral of a function. This is a deterministic problem, but we will solve it using random sampling.\n", + "\n", + "**Problem to solve:** find value of the integral\n", + "\n", + "$$\\int_a^b f(x)dx. $$\n", + "\n", + "Monte Carlo integration estimates this integral by finding the fraction of random points that fall below $f(x)$.\n", + "\n", + "In the **Bayesian inference** context, we are usually interested in estimating expectations (which are themselves point estimates):\n", + "\n", + "$$ E[h(x)] = \\int h(x)f(x)dx,$$\n", + "\n", + "which can be done with\n", + "\n", + "$$ \\bar{h}_n = \\frac{1}{n} \\sum_i^n h(x_i),$$\n", + "where $x_i ∼ f$ is a draw from the density $f$.\n", + "\n", + "**Exercise:** _Do you see how this is **sampling** to figure out a property?_\n", + "\n", + "The convergence of Monte Carlo integration is $\\mathcal{O}(n^{1/2})$ and is independent of the dimensionality. Hence, Monte Carlo integration **generally** beats numerical intergration for moderate- and high-dimensional integration since numerical integration (quadrature) converges as $0(n^d)$!\n", + "\n", + "### Monte Carlo integration - Example\n", + "\n", + "Estimate the integral $\\int_0^1 e^x dx$ using Monte Carlo integration." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import jax.numpy as jnp\n", + "import numpy as np\n", + "\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.7182817\n", + " 10 1.630969\n", + " 100 1.467872\n", + " 1000 1.712517\n", + " 10000 1.703275\n", + " 100000 1.713088\n", + " 1000000 1.717307\n", + " 10000000 1.718232\n", + " 100000000 1.718354\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(jnp.exp(1) - jnp.exp(0))\n", + "\n", + "plt.figure(figsize=(3, 3))\n", + "\n", + "x = jnp.linspace(0, 1, 100)\n", + "plt.plot(x, jnp.exp(x));\n", + "pts = np.random.uniform(0,1,(100, 2))\n", + "pts[:, 1] *= jnp.e\n", + "\n", + "cols = ['steelblue'] * 100\n", + "for i in range(100):\n", + " if pts[i,1] > jnp.exp(pts[i,0]): # acceptance / rejection step\n", + " cols[i] = 'red'\n", + "\n", + "\n", + "plt.scatter(pts[:, 0], pts[:, 1], c = cols)\n", + "plt.xlim([0,1])\n", + "plt.ylim([0, jnp.e]);\n", + "\n", + "# Monte Carlo approximation\n", + "\n", + "for n in 10**np.array([1, 2, 3, 4, 5, 6, 7, 8]):\n", + " pts = np.random.uniform(0, 1, (n, 2))\n", + " pts[:, 1] *= jnp.e\n", + " count = jnp.sum(pts[:, 1] < jnp.exp(pts[:, 0]))\n", + " volume = jnp.e * 1 # volume of region\n", + " sol = (volume * count)/n\n", + " print('%10d %.6f' % (n, sol))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Monte Carlo method - computing $\\pi$\n", + "\n", + "We can also use Monte Carlo to estimate the value of π!" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "#@title The Monte Carlo method - computing π\n", + "\n", + "def in_circle(x, y, r):\n", + " # is point (x,y) within circle of radius r?\n", + "\n", + " return jnp.sqrt(x **2 + y**2) <= r**2\n", + "\n", + "def approx_pi(r, n):\n", + "\n", + " xs, ys, cols = [], [], []\n", + "\n", + " count = 0\n", + "\n", + " for i in range(n):\n", + " x = np.random.uniform(0,r,1)\n", + " y = np.random.uniform(0,r,1)\n", + " xs.append(x)\n", + " ys.append(y)\n", + "\n", + " if in_circle(x, y, r):\n", + " count += 1\n", + " cols.append(\"red\")\n", + " else:\n", + " cols.append(\"steelblue\")\n", + "\n", + " pi_appr = round(4 * count/n, 3)\n", + "\n", + " plt.figure(figsize=(2, 2))\n", + " plt.scatter(xs, ys, c = cols, s=2)\n", + " plt.title(\"pi (approximately) = \" + str(pi_appr))\n", + " plt.xticks([])\n", + " plt.yticks([])\n", + " plt.show()\n", + "\n", + " return pi_appr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Group task Β14.**\n", + "\n", + "Using the functions above, iterate $n$ through vaules $5*10^1, 5*10^2, 5*10^3$ and run the function approximating $\\pi$. How does the result change?" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r = 1\n", + "\n", + "for n in 5*10**jnp.array([1,2,3]):\n", + " approx_pi(r, n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Markov Chain Monte Carlo (MCMC) \n", + "\n", + "We want to estimate the posterior distribution, but this is often intractable.\n", + "\n", + "MCMC is a computational technique used to approximate complex probability distributions by generating a **`sequence of (correlated) samples`**, where each sample is obtained by iteratively transitioning through a Markov chain with carefully designed transition probabilities.\n", + "\n", + "### How does MCMC work (very rough overview)?\n", + "\n", + "- Draw samples from a (simple) proposal distribution so that each draw depends only on the state of the previous draw (i.e. the samples form a Markov chain).\n", + "- Under certain conditions, the Markov chain will have a unique stationary distribution.\n", + "\n", + "- We set up an acceptance criteria for each draw based on comparing successive states with respect to a target distribution that enusre that the stationary distribution is the posterior distribution we are searching for.\n", + "\n", + "- There is no need to evaluate the potentially intractable marginal likelihood.\n", + "\n", + "- After sufficient number of iterations, the Markov chain of accepted draws will converge to the staionary distribution, and we can use those samples as (correlated) draws from the posterior distribution, and find functions of the posterior distribution.\n", + "\n", + "The next optional section demonstrates an example of **`Matrolopolis-Hastings`** algorithm - this is an example of MCMC.\n", + "\n", + "## Metropolis-Hastings random walk algorithm\n", + "\n", + "- Start with an initial guess for $\\theta$\n", + "\n", + "- Chose a new proposed value as $\\theta_p = \\theta + \\delta_\\theta, \\delta_\\theta \\sim N(0, \\sigma).$\n", + " \n", + " Here we have chosen the proposal distribution to be $N(0, \\sigma).$\n", + " \n", + "- If $g$ is the posterior probability, calculate the ratio $\\rho = \\frac{g(\\theta_p \\mid X)}{g(\\theta \\mid X)}$\n", + "\n", + "- (adjust for symmetry of the proposal distribution)\n", + "\n", + "\n", + "- If $\\rho \\ge 1,$ accept $\\theta = \\theta_p;$ if $\\rho < 1,$ accept $\\theta = \\theta_p$ with probability $p,$ otherwise keep $\\theta = \\theta.$ (This step is done with the help of the standard Uniform distribution)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Portion of accepted steps = 0.1801\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#@title Metropolis-Hastings\n", + "\n", + "def target(likelihood, prior, n, h, theta):\n", + " \"\"\"\n", + " define target distribution\n", + " \"\"\"\n", + " if theta < 0 or theta > 1:\n", + " return 0\n", + " else:\n", + " return likelihood(n, theta).pmf(h)*prior.pdf(theta)\n", + "\n", + "\n", + "# number of experiments\n", + "n = 100\n", + "\n", + "# number of successes\n", + "h = 61\n", + "\n", + "# hyperparameters for the prior\n", + "a = 10\n", + "b = 10\n", + "likelihood = stats.binom\n", + "prior = stats.beta(a, b)\n", + "sigma = 0.3\n", + "\n", + "# initilisation\n", + "naccept = 0\n", + "theta = 0.1\n", + "\n", + "# set the number of MCMC iterations\n", + "niters = 10000\n", + "\n", + "# run MH\n", + "samples = np.zeros(niters+1)\n", + "samples[0] = theta\n", + "\n", + "for i in range(niters):\n", + " theta_p = theta + stats.norm(0, sigma).rvs()\n", + " rho = min(1, target(likelihood, prior, n, h, theta_p)/target(likelihood, prior, n, h, theta ))\n", + " u = np.random.uniform()\n", + " if u < rho:\n", + " naccept += 1\n", + " theta = theta_p\n", + " samples[i+1] = theta\n", + "\n", + "# analyse MH output\n", + "nmcmc = len(samples)//2\n", + "print(\"Portion of accepted steps = \" + str(naccept/niters))\n", + "\n", + "post = stats.beta(h+a, n-h+b)\n", + "thetas = np.linspace(0, 1, 200)\n", + "\n", + "plt.figure(figsize=(4, 4))\n", + "plt.hist(samples[nmcmc:], 20, histtype='step', linewidth=1, label='Distribution of posterior samples', density =True);\n", + "plt.hist(prior.rvs(nmcmc), 40, histtype='step', linewidth=1, label='Distribution of prior samples', density=True);\n", + "plt.plot(thetas, post.pdf(thetas), c='red', linestyle='--', alpha=0.5, label='True posterior')\n", + "plt.xlim([0,1]);\n", + "plt.grid(0.3)\n", + "plt.legend(loc='best');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We run the chain for $N$ iterations and discard the first $B$ samples. This is called **`burn-in`** (or \"warm-up\").\n", + "\n", + "We can run several parallel versions of the algorithm. Each of them is called a **`chain`**.\n", + "\n", + "Neigbouring samples will contain similar information. We might want to save only every second, or fifth, or tenth. This is called **`thinning`**." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Convergence diagnostics" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#@title Convergence diagnostics\n", + "\n", + "def mh_coin(niters, n, h, theta, likelihood, prior, sigma):\n", + " samples = [theta]\n", + " while len(samples) < niters:\n", + " theta_p = theta + stats.norm(0, sigma).rvs()\n", + " rho = min(1, target(likelihood, prior, n, h, theta_p)/target(likelihood, prior, n, h, theta ))\n", + " u = np.random.uniform()\n", + " if u < rho:\n", + " theta = theta_p\n", + " samples.append(theta)\n", + "\n", + " return samples\n", + "\n", + "n = 100\n", + "h = 61\n", + "lik = stats.binom\n", + "prior = stats.beta(a, b)\n", + "sigma = 0.05\n", + "niters = 100\n", + "\n", + "chains = [mh_coin(niters, n, h, theta, likelihood, prior, sigma) for theta in np.arange(0.1, 1, 0.2)]\n", + "\n", + "# compare multiple chains\n", + "\n", + "plt.figure(figsize=(5, 4))\n", + "\n", + "for chain in chains:\n", + " plt.plot(chain, '-o')\n", + "\n", + "plt.xlim([0, niters])\n", + "plt.ylim([0, 1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Was it very painful to write a sampler by hand?\n", + "\n", + "If not, bare in mind that we only wrote the simplest one possible! Sampling algorithms can get very complicated. 🧠" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Probabilistics programming\n", + "\n", + "[Probabilistic programming](https://en.wikipedia.org/wiki/Probabilistic_programming) is a paradigm in computer programming that enables the creation of models and algorithms capable of handling uncertainty and randomness. It combines principles from probability theory and programming to build systems that can reason about uncertain data and make informed decisions. This approach allows developers to express complex models in a natural and intuitive way, enabling tasks such as Bayesian inference, machine learning, and statistical analysis to be performed more effectively.\n", + "\n", + "In this section we will give an overview of the modern landscape of probabilistic programming languages (PPLs), and demonstrate abilities of one of them (NumPyro).\n", + "\n", + "Familiarity with a PPL will equip participants with a tool allowing them to focus on the scientific problem of interest, while inference is being taken care of by the inference engine. We will show how to use the [NumPyro](https://num.pyro.ai/en/latest/index.html#) library to perform exact Bayesian inference (using Markov Chain Monte Carlo).\n", + "\n", + "## Probabilistic programming languages (PPLs)\n", + "\n", + "Luckily, we do not need to write a sampler by hand every time, because PPLs are there to help.\n", + "\n", + "A PPL allows us to formalize a Bayesian model and perform inference with the help of powerful algorithms. **A user needs to only formulate the model** and maybe chose a sampler." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/07_ICAR.ipynb b/07_ICAR.ipynb new file mode 100644 index 0000000..867f447 --- /dev/null +++ b/07_ICAR.ipynb @@ -0,0 +1,171 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ICAR (Intrinsic Conditional Autoregressive) model is a statistical model commonly used in spatial statistics to analyze and model spatial data. It is specifically used to account for spatial dependencies or autocorrelation in the data, where observations in close proximity tend to be more similar than those farther apart. The ICAR model is a type of conditional autoregressive model that assumes that the value of a location in a spatial dataset depends on the values of its neighboring locations.\n", + "\n", + "Here are the key components of the ICAR model:\n", + "\n", + "- Neighborhood Structure: The ICAR model requires a predefined neighborhood structure. This structure specifies which locations are considered neighbors of each other. Common choices include defining neighbors based on contiguity, distance thresholds, or some other criteria.\n", + "\n", + "- Conditional Autoregressive Structure: In the ICAR model, each location's value is assumed to be conditionally dependent on the values of its neighbors. This conditional dependency is often modeled as a weighted sum of the neighboring values, where the weights are determined by the neighborhood structure. The weights are typically constrained such that they sum to zero, ensuring stationarity of the model.\n", + "\n", + "- Intrinsic Condition: The \"intrinsic\" part of the ICAR model refers to the fact that the sum of the weights for each location is constrained to be zero. This constraint helps ensure identifiability of the model parameters.\n", + "\n", + "The ICAR model is useful in various spatial applications, such as spatial interpolation, spatial smoothing, and spatial prediction. It is commonly employed in Bayesian spatial modeling, where prior distributions are assigned to the model parameters, and the posterior distribution is obtained through Bayesian inference methods like Markov Chain Monte Carlo (MCMC) sampling.\n", + "\n", + "By accounting for spatial dependencies through the ICAR model, statisticians and researchers can better analyze and model spatial data while considering the inherent spatial correlation that often exists in such datasets." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To implement the ICAR (Intrinsic Conditional Autoregressive) model in NumPyro, you can define a custom NumPyro model using the Pyro probabilistic programming framework, which NumPyro is built on. Here's an example of how you can write the ICAR model in NumPyro:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "sample: 100%|██████████| 2000/2000 [00:02<00:00, 779.69it/s, 3 steps of size 7.13e-08. acc. prob=0.91] \n" + ] + } + ], + "source": [ + "import jax\n", + "import numpy as np\n", + "import numpyro\n", + "import numpyro.distributions as dist\n", + "import jax.numpy as jnp\n", + "from numpyro.infer import MCMC, NUTS\n", + "\n", + "def icar_model(y, neighbors):\n", + " n = len(y)\n", + " alpha = numpyro.sample('alpha', dist.Normal(0, 1))\n", + " sigma = numpyro.sample('sigma', dist.HalfCauchy(1))\n", + " \n", + " # Calculate the precision matrix\n", + " tau = 1.0 / (sigma**2)\n", + " precision_matrix = tau * (jnp.diag(jnp.sum(neighbors, axis=1)) - neighbors)\n", + " \n", + " # Define the conditional autoregressive structure\n", + " with numpyro.plate('data', n):\n", + " mu = alpha + jnp.matmul(precision_matrix, y)\n", + " y = numpyro.sample('y', dist.MultivariateNormal(mu, precision_matrix), obs=y)\n", + "\n", + "# Example usage:\n", + "# Define your spatial data 'y' and neighbor structure 'neighbors'\n", + "y = np.array([1.2, 2.5, 3.8, 4.1, 5.2]) # Replace with your data\n", + "neighbors = np.array([[0, 1, 0, 0, 0],\n", + " [1, 0, 1, 0, 0],\n", + " [0, 1, 0, 1, 0],\n", + " [0, 0, 1, 0, 1],\n", + " [0, 0, 0, 1, 0]]) # Replace with your neighbor structure\n", + "\n", + "# Run MCMC to infer the parameters\n", + "nuts_kernel = NUTS(icar_model)\n", + "mcmc = MCMC(nuts_kernel, num_samples=1000, num_warmup=1000)\n", + "mcmc.run(rng_key=jax.random.PRNGKey(0), y=y, neighbors=neighbors)\n", + "\n", + "# Extract posterior samples\n", + "samples = mcmc.get_samples()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1000, 2)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpyro.distributions as dist\n", + "import jax\n", + "import jax.numpy as jnp\n", + "from numpyro.infer import MCMC, NUTS\n", + "\n", + "# Define the mean and covariance matrix for the multivariate normal distribution\n", + "mean = jnp.array([0.0, 0.0]) # Mean vector\n", + "cov_matrix = jnp.array([[1.0, 0.5], [0.5, 2.0]]) # Covariance matrix\n", + "\n", + "# Create a MultivariateNormal distribution\n", + "mvn = dist.MultivariateNormal(mean, cov_matrix)\n", + "\n", + "# Sample from the distribution\n", + "samples = mvn.sample(key=jax.random.PRNGKey(0), sample_shape=(1000,))\n", + "\n", + "samples.shape\n", + "\n", + "# Now, 'samples' contains 1000 samples from the multivariate normal distribution\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this code:\n", + "\n", + "- We define the ICAR model as a Python function icar_model that takes y (the spatial data) and neighbors (the neighbor structure) as arguments.\n", + "\n", + "- Inside the model, we sample the parameters alpha (the intercept) and sigma (the spatial correlation parameter).\n", + "\n", + "- We use a plate to handle multiple data points if needed. The core of the model is the calculation of mu, which represents the conditional expectation based on the ICAR structure.\n", + "\n", + "- Finally, we sample y from a Normal distribution with mean mu and observation noise of 1.\n", + "\n", + "- We provide example usage of the model, where you should replace the y and neighbors arrays with your actual data and neighbor structure.\n", + "\n", + "- We run MCMC using the NUTS sampler to infer the posterior distribution of the model parameters.\n", + "\n", + "- After running MCMC, you can extract posterior samples from the mcmc object.\n", + "\n", + "Make sure to adapt this code to your specific dataset and spatial structure as needed." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/07_intro_to_Numpyro.ipynb b/07_intro_to_Numpyro.ipynb new file mode 100644 index 0000000..208f1fe --- /dev/null +++ b/07_intro_to_Numpyro.ipynb @@ -0,0 +1,711 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "J1LV5w4eFSzA" + }, + "source": [ + "## Introduction to NumPyro: Probabilistic Programming\n", + "\n", + "Probabilistic programming is a powerful approach to modeling and inference in machine learning and statistics. It allows us to build models that incorporate uncertainty and make probabilistic predictions. NumPyro is a probabilistic programming library that combines the flexibility of NumPy with the probabilistic modeling capabilities of Pyro, making it an excellent choice for researchers and data scientists. In this introductory tutorial, we'll explore the basics of NumPyro and how to get started with probabilistic programming.\n", + "\n", + "## Prerequisites" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "hVzA5-UuFU9Z", + "outputId": "17a25d31-0465-4219-d91d-b9987eb593ed" + }, + "outputs": [], + "source": [ + "# uncomment this line on Colab\n", + "# !pip install numpyro" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "mhhWCsnWNO7Q" + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "\n", + "import numpyro\n", + "import numpyro.distributions as dist\n", + "from numpyro.infer import MCMC, NUTS\n", + "import jax\n", + "import jax.numpy as jnp\n", + "\n", + "import arviz as az" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "EfFD5kPmHSog" + }, + "source": [ + "## Getting Started\n", + "\n", + "Now that you have the required packages installed, let's start with a simple example of a probabilistic model in NumPyro.\n", + "\n", + "In this code:\n", + "\n", + "- We define a simple probabilistic model with two parameters: mean and scale.\n", + "- We specify priors for these parameters.\n", + "- The likelihood of the data is assumed to be normally distributed with the specified mean and scale.\n", + "- In this example, the likelihood is specified within the `numpyro.sample` statement inside the model function. NumPyro automatically evaluates the likelihood for the observed data points `(obs=data)` when performing MCMC inference.\n", + "- We use the No-U-Turn Sampler (NUTS) to perform Markov Chain Monte Carlo (MCMC) inference.\n", + "- Finally, we visualize the posterior distributions of the parameters.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 635 + }, + "id": "VBBPGHrmGvj6", + "outputId": "8df2a881-62bf-4d30-c3a2-7cba91fd0cf1" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: All log messages before absl::InitializeLog() is called are written to STDERR\n", + "I0000 00:00:1705865525.515832 1 tfrt_cpu_pjrt_client.cc:349] TfrtCpuClient created.\n", + "sample: 100%|██████████| 2000/2000 [00:02<00:00, 945.66it/s, 3 steps of size 6.52e-01. acc. prob=0.92] \n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " mean std median 5.0% 95.0% n_eff r_hat\n", + " mean 1.17 0.67 1.21 0.03 2.21 465.31 1.00\n", + " scale 1.85 0.62 1.75 0.87 2.63 490.01 1.00\n", + "\n", + "Number of divergences: 0\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[,\n", + " ],\n", + " [,\n", + " ]], dtype=object)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "# Define a simple probabilistic model\n", + "def model(data):\n", + " # Define priors\n", + " mean = numpyro.sample(\"mean\", dist.Normal(0, 1))\n", + " scale = numpyro.sample(\"scale\", dist.Exponential(1))\n", + "\n", + " # Likelihood\n", + " with numpyro.plate(\"data_plate\", len(data)):\n", + " numpyro.sample(\"obs\", dist.Normal(mean, scale), obs=data)\n", + "\n", + "# Simulated data\n", + "data = jnp.array([2.3, 3.9, 1.7, -0.8, 2.5])\n", + "\n", + "# Initialize the NUTS sampler\n", + "nuts_kernel = NUTS(model)\n", + "\n", + "# Perform Markov Chain Monte Carlo (MCMC) inference\n", + "mcmc = MCMC(nuts_kernel, num_samples=1000, num_warmup=1000)\n", + "mcmc.run(jax.random.PRNGKey(0), data)\n", + "\n", + "# Get the posterior samples\n", + "posterior_samples = mcmc.get_samples()\n", + "\n", + "# Print summary statistics of posterior\n", + "mcmc.print_summary()\n", + "\n", + "# Plot posterior distributions\n", + "az.plot_trace(mcmc)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-fNL2gt-HxCF" + }, + "source": [ + "## Conclusion\n", + "\n", + "NumPyro is a versatile library for probabilistic programming that combines the power of NumPy and Pyro. In this introductory tutorial, we've covered the basics of defining a probabilistic model, performing MCMC inference, and visualizing the results. As you delve deeper into probabilistic programming with NumPyro, you'll be able to build more complex and customized models for your specific applications. Happy modeling!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FNUc0rUuLmPB" + }, + "source": [ + "## Numpyro distributions\n", + "\n", + "The statement `import numpyro.distributions` as dist is used to import the `distributions` module from the NumPyro library and give it an alias or nickname `dist`. This alias makes it easier to access and use the various probability distributions provided by NumPyro throughout your code.\n", + "\n", + "\n", + "In probabilistic programming, you often need to specify probability distributions for the prior and likelihood in your models. NumPyro provides a variety of probability distributions that you can use, such as normal distributions, exponential distributions, categorical distributions, and many others. These distributions are organized within the `distributions` module.\n", + "\n", + "\n", + "By using the `import numpyro.distributions as dist` statement, you create a shorthand reference to the `distributions` module, so instead of typing `numpyro.distributions` every time you want to use a distribution, you can simply use `dist`. This simplifies your code and makes it more concise and readable.\n", + "\n", + "\n", + "For example, if you want to create a normal distribution in your code, you can now use `dist.Normal(...)` instead of `numpyro.distributions.Normal(...)`, thanks to the `dist` alias. It's a common practice in NumPyro code to use this alias to improve code clarity and reduce typing effort when working with probability distributions.\n", + "\n", + "\n", + "These examples below demonstrate how to create various probability distributions using the `dist` alias and sample from them. You can then use these distributions as components of your probabilistic models when defining priors or likelihoods in a Bayesian context or when generating random data for simulation and analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "M8QkvptfNSlU" + }, + "source": [ + "### Normal distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "x_bxwE5yLn7F", + "outputId": "a334a158-6273-4fac-938f-479454e549ab" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.20584226\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Normal distribution\n", + "\n", + "# Create a normal distribution with mean=0 and standard deviation=1\n", + "normal_dist = dist.Normal(0, 1)\n", + "\n", + "# Sample from the normal distribution, once\n", + "sample = normal_dist.sample(jax.random.PRNGKey(0))\n", + "\n", + "print(sample)\n", + "\n", + "# Sample from the normal distribution, many times\n", + "samples = normal_dist.sample(jax.random.PRNGKey(0), (1000,))\n", + "\n", + "# Plot a histogram of the samples\n", + "sns.histplot(samples, kde=True)\n", + "plt.title(\"Samples from Normal Distribution\")\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "h3ayvTT4O5Nj" + }, + "source": [ + "### Exponential distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "u77Wfb1-MdOZ", + "outputId": "65e64034-f40d-49e2-b276-42997f9abf4f" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.2710352\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# exponential distribution\n", + "\n", + "# Create an exponential distribution with rate parameter 2.0\n", + "exponential_dist = dist.Exponential(2.0)\n", + "\n", + "# Sample from the exponential distribution, once\n", + "sample = exponential_dist.sample(jax.random.PRNGKey(0))\n", + "\n", + "print(sample)\n", + "\n", + "# Sample from the exponential distribution, many\n", + "samples = exponential_dist.sample(jax.random.PRNGKey(0), (1000,))\n", + "\n", + "# Plot a histogram of the samples\n", + "sns.histplot(samples, kde=True)\n", + "plt.title(\"Samples from Exponential Distribution\")\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vZCIb_T_PGam" + }, + "source": [ + "### Categorical" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "kd76OYdLMm8w", + "outputId": "79c1499d-0241-4543-d5ff-b4c8f3ce5cc2" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# categorical\n", + "\n", + "# Define probabilities for three categories\n", + "probabilities = jnp.array([0.3, 0.4, 0.3])\n", + "\n", + "# Create a categorical distribution\n", + "categorical_dist = dist.Categorical(probabilities)\n", + "\n", + "# Sample from the categorical distribution, once\n", + "sample = categorical_dist.sample(jax.random.PRNGKey(0))\n", + "\n", + "print(sample)\n", + "\n", + "# Sample from the categorical distribution, many\n", + "samples = categorical_dist.sample(jax.random.PRNGKey(0), (1000,))\n", + "\n", + "# Plot a bar chart of the samples\n", + "plt.hist(samples, bins=[0, 1, 2, 3], align='left', rwidth=0.8)\n", + "plt.xticks([0, 1, 2], labels=[\"Category 0\", \"Category 1\", \"Category 2\"])\n", + "plt.title(\"Samples from Categorical Distribution\")\n", + "plt.xlabel(\"Category\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6_bngSJYPQte" + }, + "source": [ + "### Beta" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "mcIkgrXhMrL3", + "outputId": "0da5f725-9292-41b0-8ddb-b8d808e9a8a1" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.41446027\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# beta\n", + "\n", + "# Create a beta distribution with alpha=2 and beta=3\n", + "beta_dist = dist.Beta(2, 3)\n", + "\n", + "# Sample from the beta distribution\n", + "sample = beta_dist.sample(jax.random.PRNGKey(0))\n", + "print(sample)\n", + "\n", + "# Sample from the beta distribution, many\n", + "samples = beta_dist.sample(jax.random.PRNGKey(0), (1000,))\n", + "\n", + "# Plot a histogram of the samples\n", + "sns.histplot(samples, kde=True)\n", + "plt.title(\"Samples from Beta Distribution\")\n", + "plt.xlabel(\"Value\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3It0QjQZPbgX" + }, + "source": [ + "### Multivariate Normal\n", + "\n", + "Mean `mu` and covariance `K`.\n", + "\n", + "```{margin}\n", + "We will use this distribution a lot when dealing with spatial data.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "lkCeMN5lMw7A", + "outputId": "df522f91-a3cf-4ff2-820c-585d02ebbdb7" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.78476596 1.740587 ]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# MVN\n", + "\n", + "# Create a multivariate normal distribution with mean vector and covariance matrix\n", + "mean = jnp.array([0.0, 1.0])\n", + "cov_matrix = jnp.array([[1.0, 0.5], [0.5, 2.0]])\n", + "multivariate_normal_dist = dist.MultivariateNormal(mean, cov_matrix)\n", + "\n", + "# Sample from the multivariate normal distribution\n", + "sample = multivariate_normal_dist.sample(jax.random.PRNGKey(0))\n", + "print(sample)\n", + "\n", + "# Sample from the multivariate normal distribution, many\n", + "samples = multivariate_normal_dist.sample(jax.random.PRNGKey(0), (1000,))\n", + "\n", + "# Plot a scatter plot of the samples\n", + "sns.scatterplot(x=samples[:, 0], y=samples[:, 1])\n", + "plt.title(\"Samples from Multivariate Normal Distribution\")\n", + "plt.xlabel(\"X\")\n", + "plt.ylabel(\"Y\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Vb4ILFuduHfK" + }, + "source": [ + "In a NumPyro program, you define a probabilistic model that consists of various elements. Let's break down the key elements of a typical NumPyro program:\n", + "\n", + "1. Importing Libraries:\n", + "\n", + "At the beginning of your NumPyro program, you import the necessary libraries, including NumPyro and other required dependencies like JAX and Pyro if applicable. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "id": "NZ7-DnBcuM_7" + }, + "outputs": [], + "source": [ + "import numpyro\n", + "import numpyro.distributions as dist\n", + "import jax\n", + "import jax.numpy as jnp\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "25oL3ubXuWZg" + }, + "source": [ + "2. Defining the Model Function:\n", + "\n", + "In NumPyro, you define your probabilistic model as a Python function. This function encapsulates the entire model, including both the prior distributions and the likelihood. Typically, the model function takes one or more arguments, such as data or model parameters, and returns a set of latent variables and observations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "z_AsEI8SuSAu" + }, + "outputs": [], + "source": [ + "def model(data):\n", + " # Define prior distributions for model parameters\n", + " mean = numpyro.sample(\"mean\", dist.Normal(0, 1))\n", + " scale = numpyro.sample(\"scale\", dist.Exponential(1))\n", + "\n", + " # Define likelihood\n", + " with numpyro.plate(\"data_plate\", len(data)):\n", + " numpyro.sample(\"obs\", dist.Normal(mean, scale), obs=data)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-LqThfWVudNN" + }, + "source": [ + "3. Prior Distributions:\n", + "\n", + "- Inside the model function, you define prior distributions for the model parameters. These prior distributions represent your beliefs about the parameters before observing any data. You use the `numpyro.sample` function to specify these priors. In the example above, `mean` and `scale` are defined as random variables sampled from specific prior distributions.\n", + "\n", + "\n", + "4. Likelihood:\n", + "\n", + "- After specifying the prior distributions, you define the likelihood of your observed data. The likelihood represents the probability distribution of your observed data given the model parameters. It describes how likely it is to observe the data under different parameter values. In the example, the numpyro.sample function is used to define the likelihood of the data points given the mean and scale parameters.\n", + "\n", + "5. Plate for Repetition:\n", + "- In Bayesian modeling, you often work with multiple data points that share the same statistical structure. The `numpyro.plate` context manager allows you to create a plate, which represents a repeated structure for data. It's used to efficiently handle repeated observations. In the example, `numpyro.plate` is used to specify that the likelihood applies to multiple data points.\n", + "\n", + "6. Inference Algorithm:\n", + "\n", + "- After defining your model, you need to choose an inference algorithm to estimate the posterior distribution of model parameters. NumPyro supports various inference algorithms, including NUTS (No-U-Turn Sampler) and SVI (Stochastic Variational Inference). You initialize and configure the chosen inference algorithm according to your requirements.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "Qz6nkjdGua0c" + }, + "outputs": [], + "source": [ + "nuts_kernel = NUTS(model)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8C2V-_BdvEwc" + }, + "source": [ + "8. Performing Inference:\n", + "\n", + "- You use the configured inference algorithm to perform Bayesian inference. In the example, MCMC (Markov Chain Monte Carlo) inference is performed using the `MCMC` class. The `run` method of the `MCMC` object is called to run the inference process." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "xAlfnkP6vCV2", + "outputId": "213c669e-9d36-4398-c4a5-c5b389afcfb8" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "sample: 100%|██████████| 2000/2000 [00:04<00:00, 419.40it/s, 3 steps of size 6.52e-01. acc. prob=0.92] \n" + ] + } + ], + "source": [ + "mcmc = MCMC(nuts_kernel, num_samples=1000, num_warmup=1000)\n", + "mcmc.run(jax.random.PRNGKey(0), data)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2DXdboTTvSNu" + }, + "source": [ + "9. Posterior Analysis:\n", + "\n", + "- After running the inference, you can retrieve posterior samples of the model parameters. These samples represent the estimated posterior distribution of the parameters given the observed data. You can then analyze these samples to make inferences about your model." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "wL3YlwkovP6C" + }, + "outputs": [], + "source": [ + "posterior_samples = mcmc.get_samples()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-n-z22VnvbRV" + }, + "source": [ + "10. Visualization and Inference:\n", + "\n", + "- Finally, you can perform various tasks such as visualizing the posterior distributions, computing summary statistics, and making predictions or inferences based on the posterior samples." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "igd5fC_9voTw" + }, + "source": [ + "These elements together form a typical NumPyro program for Bayesian probabilistic modeling. The key steps involve defining the model, specifying prior distributions and likelihood, selecting an inference algorithm, running the inference, and analyzing the posterior samples to draw conclusions about the model parameters." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "kFedhUATvXGz" + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..aade051 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,4 @@ +jupyter-book +matplotlib +numpy +ghp-import \ No newline at end of file