From 9dd1f7a0378ad4525f2c97bc37e7efd60badc850 Mon Sep 17 00:00:00 2001 From: Martin Kilbinger Date: Thu, 8 Sep 2022 13:31:59 +0200 Subject: [PATCH 1/5] Added importance sampling nb --- README.md | 145 +++--------- docs/docker | 1 - docs/presentation_tips | 1 - docs/tensorflow-introduction | 1 - importance_sampling.ipynb | 440 +++++++++++++++++++++++++++++++++++ maintenance_recipes.md | 17 -- requirements.txt | 5 + 7 files changed, 474 insertions(+), 136 deletions(-) delete mode 160000 docs/docker delete mode 160000 docs/presentation_tips delete mode 160000 docs/tensorflow-introduction create mode 100644 importance_sampling.ipynb delete mode 100644 maintenance_recipes.md create mode 100644 requirements.txt diff --git a/README.md b/README.md index ef77e8e..7bb1832 100644 --- a/README.md +++ b/README.md @@ -1,132 +1,45 @@ - - -[![All Contributors](https://img.shields.io/badge/all_contributors-9-orange.svg?style=flat-square)](#contributors-) - - -# CosmoStat Tutorials +## Importance sampling --- -CosmoStat is committed to the philosophy of reproducible research, endeavouring -to provide source code and data for all publications. In this spirit, we have -additionally put significant effort into providing useful educational -materials. The aim being to provide other researchers with an in-depth -understanding of the various tools we use in our work. - -We always welcome new tutorial requests, just click [here](https://github.com/CosmoStat/Tutorials/issues/new?assignees=&labels=tutorial+request&template=tutorial-request.md&title=%5BTutorial%5D+Your+idea+for+a+tutorial). - -## Contents - -1. [Career Development](#Career-Development) -1. [Cosmology](#Cosmology) -1. [Data Science](#Data-Science) -1. [Software Carpentries](#Software-Carpentries) - -### Career Development - -1. **[Presentation Tips](https://cosmostat.github.io/Tutorials/presentation_tips/presentation_tips/index.html)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/presentations) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/playlist?list=PLquvp9RIoLGCmfAZTOKJz7qDO0NqCnMAV) - *Authors:* [@pettorin](https://github.com/pettorin) - This tutorial provides tips on how to adapt presentations for different goals. The tutorial is mainly meant for scientists, but several tips can be useful for other types of talks. - -### Cosmology - -1. **[Cosmology with Python wrappers for Einstein-Boltzmann Codes](https://github.com/CosmoStat/Tutorials/tree/boltzmann)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/boltzmann) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=EMpCxUvF3lc) - *Authors:* [@santiagocasas](https://github.com/santiagocasas) - This tutorial is comprised of a series of Jupyter notebooks with simple demonstrations and exercises on how to use `CAMB` and `CLASS` using python wrappers. The code is designed for non-experts in the field, therefore it includes relatively simple explanations of cosmological concepts. It intends to show a general overview of the things that are possible with Einstein-Boltzmann codes and python. - -2. **[Power Spectrum](http://github.com/CosmoStat/Tutorials/tree/power-spectrum)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](http://github.com/CosmoStat/Tutorials/tree/power-spectrum) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/CosmoStat/Tutorials/blob/power-spectrum/WL_power_spectrum.ipynb) - *Authors:* [@b-remy](https://github.com/b-remy), [@dlanzieri](https://github.com/dlanzieri), [@EiffL](https://github.com/EiffL) - This tutorial presents how to compute a power spectrum from a lensing map (in the flat sky approximation) and how to compute the corresponding theory spectrum using a cosmology code. - -### Data Science - -1. **[Introduction to Python](https://github.com/CosmoStat/Tutorials/tree/python)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/python) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=cbekcGxm70Q&list=PLquvp9RIoLGBFfsz8dqzPtLeaEngHYybM) [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/CosmoStat/Tutorials/python) - *Authors:* [@sfarrens](https://github.com/sfarrens), [@santiagocasas](https://github.com/santiagocasas) - * [Tutorial 1: Beginner Topics](https://github.com/CosmoStat/Tutorials/tree/python#tutorial-1-beginner-topics) - The objective of this tutorial is to provide a first look at Python for beginners. The level is aimed at individuals with little or no experience whatsoever with Python. Experienced users are unlikely to benefit from this tutorial. - * [Tutorial 2: Intermediate and Advanced Topics](https://github.com/CosmoStat/Tutorials/tree/python#tutorial-2-intermediate-and-advanced-topics) - The objective of this tutorial is to provide a more in-depth look at object-oriented and pythonic coding. The level is aimed at individuals with some experience with Python and good knowledge of basic object types. This tutorial will likely benefit all except the most advanced users. - -2. **[Python Optimisation and Memory Management](https://github.com/CosmoStat/Tutorials/tree/profiling)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/profiling) - *Authors:* [@sfarrens](https://github.com/sfarrens) - This tutorial introduces some techniques for determinisitic and memory profiling of Python scripts, followed by some tips on how to implement some basic optimisation. - -3. **[C++](https://github.com/CosmoStat/Tutorials/tree/CPlusPlus)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/CPlusPlus) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=47Ldg6i2B8Y&list=PLquvp9RIoLGD5yDykupoCueNp2EHEjuZB) - *Authors:* [@kansal9](https://github.com/kansal9) - This tutorial aims to help newcomers learn C++ and solve their programming problems. It is assumed that readers are already familiar with C, or at least that they do not have any difficulty reading C code. In other words, those who have experience in C and peo·ple who desire to quickly understand the features of modern C++ in a short period of time are well suited to follow this tutorial. - -4. **[Sparsity](https://github.com/CosmoStat/Tutorials/tree/ada)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/ada) [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/CosmoStat/Tutorials/ada) - *Authors:* [@sfarrens](https://github.com/sfarrens) - This tutorial is comprised of a series of Jupyter notebooks that demonstrate how the tools implemented in sparsity work as well as showing the applicability of these tools to various simple problems. - -5. **[Low-Rank](https://github.com/CosmoStat/Tutorials/tree/low-rank)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/low-rank) [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/CosmoStat/Tutorials/low-rank) - *Authors:* [@sfarrens](https://github.com/sfarrens) - The objective is to provide a beginner level introduction to the concept of low-rank approximation, in particular as a regularisation method for solving linear inverse problems. - -6. **[TensorFlow](https://github.com/CosmoStat/Tutorials/tree/tensorflow-tutorial)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/tensorflow-tutorial) - *Authors:* [@zaccharieramzi](https://github.com/zaccharieramzi), [@EiffL](https://github.com/EiffL) - * *First Steps with TensorFlow*: [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=kawHQpxytLo) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/CosmoStat/Tutorials/blob/tensorflow-tutorial/TensorFlowFirstSteps.ipynb) - A short introduction to the basic concepts underpinning TensorFlow, in particular automatic differentation. - * *MRI reconstruction with TensorFlow*: [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=HqNm5fowdTU) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/CosmoStat/Tutorials/blob/tensorflow-tutorial/MRIReconstructionWithTensorflow.ipynb) - An illustration of how to use TensorFlow to solve a toy MRI reconstruction problem using classical iterative reconstructions, and a deep learning approach. - -7. **[Blind Source Separation](https://github.com/RCarloniGertosio/bss_tutorial)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/RCarloniGertosio/bss_tutorial) [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/RCarloniGertosio/bss_tutorial/master) - *Authors:* [@RCarloniGertosio](https://github.com/RCarloniGertosio) - The goal of this tutorial is to present Blind Source Separation (BSS) problems and the main methods to solve them. This tutorial does not provide in-depth mathematical explanations for every methods; the emphasis is rather on illustrations and intuition. +> Author: [Martin Kilbinger](http://www.cosmostat.org/people/kilbinger) +> Year: 2022 +> Email: [martin.killbinger@cea.fr](mailto:martin.killbinger@cea.fr) -7. **[Introduction to MCMC and Bayesian inference](https://colab.research.google.com/drive/1EUF7-CwamhAT6wedntStdb4x3dDbihoo?usp=sharing)** | [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=EfWEGBHeA3k) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/drive/1EUF7-CwamhAT6wedntStdb4x3dDbihoo?usp=sharing) - *Authors:* [@EiffL](https://github.com/EiffL) - This tutorial is a practical introduction to Bayesian inference using emcee and - touching on questions related to measurement errors and covariance. +[notebook](./importance_sampling.ipynb) -### Software Carpentries +This is a very brief tutorial about how importance sampling for Bayesian parameter inference. +Specifically, it describes the case where an existing sample (e.g. a Monte-Carlo Markov chain) can be importance-sampled +to obtain samples under a joint posterior distribution. -1. **[Git Tutorial](https://github.com/zaccharieramzi/git-tuto)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/zaccharieramzi/git-tuto) [![slides](https://img.shields.io/badge/slides-google-yellow)](https://docs.google.com/presentation/d/1vfsG__2-T7xJYGKFs9HfPKmaoMN1Je0V0h7gLyiY1AU/edit?usp=sharing) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=S1A2qSA0TWo) - *Authors:* [@zaccharieramzi](https://github.com/zaccharieramzi) - This tutorial will help you practice the basics of the GitHub flow and how to work on open source projects. +For a more general tutorial of Bayesian paremeter inference see the Introduction to MCMC and Bayesian inference linked from CosmoStat Tutorial site. -2. **[Jekyll Tutorial](https://github.com/sfarrens/jekyll_tutorial)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/sfarrens/jekyll_tutorial) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=qRxbbSaVW7M) - *Authors:* [@sfarrens](https://github.com/sfarrens) - The objective of this tutorial is to introduce Jekyll and show you how to build a website that you can host on GitHub for free. +This tutorial contains a single Jupyter notebook with description and executable code. -3. **[Make and CMake Tutorial](https://github.com/sfarrens/make-tutorial)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/sfarrens/make-tutorial) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=K27-uncFZgM) - *Authors:* [@sfarrens](https://github.com/sfarrens) - This tutorial is designed to provide a first look at using Make and CMake to build C/C++ projects. +### Requirements -4. **[Introduction to Docker for Data Scientists](https://cosmostat.github.io/Tutorials/docker/docker-introduction)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/docker) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=N7cYFfIWjdw) - *Authors:* [@EiffL](https://github.com/EiffL) - This tutorial demonstrates how to create a Docker container to distribute a complete Jupyter notebook environment. +In order to run the tutorial notebooks tutees will need to have the following installed: -5. **[Bash and Scripting Tutorial for Researchers](https://github.com/CosmoStat/Tutorials/tree/bash_tutorial/README.md)** | [![github](https://badgen.net/badge/icon/github?icon=github&label)](https://github.com/CosmoStat/Tutorials/tree/bash_tutorial) [![youtube](https://img.shields.io/badge/-youtube-red?logo=youtube&labelColor=grey)](https://www.youtube.com/watch?v=NU8dYd3RM-E&t=37s) [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/CosmoStat/Tutorials/bash_tutorial?filepath=intro.ipynb) +* Python (require >=3.5) +* NumPy (recommend >=1.16.2) +* SciPy (recommend >=1.2.1) +* Astropy (recommend >=3.1.2) +* Matplotlib (recommend >=3.0.3) +* Jupyter (recommend >=1.0.0) - *Authors:* [@fadinammour](https://github.com/fadinammour), [@JulienNGirard](https://github.com/JulienNGirard)(screen segment) - This tutorial gives the key concepts of bash and its scripts to help researchers manage and process their data with more ease. +All of the packages listed above can easily be installed using either `pip` or Anaconda. -## Contributors ✨ +*e.g.* -Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)): +```bash +$ pip install numpy scipy astropy matplotlib jupyter +``` - - - - - - - - - - - - - - - - - -

Samuel Farrens
🖋 🤔 🚧
Santiago Casas
🖋 🤔
Zaccharie Ramzi
🖋 🤔
Francois Lanusse
🤔 🚧 🖋
Vanshika Kansal
🖋
pettorin
🤔 🖋
fadinammour
🤔 🖋

Julien N Girard
🖋
RCarloniGertosio
🖋
+or - - +```bash +$ conda install numpy scipy astropy matplotlib jupyter +``` - +### Notebooks -This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome! +1. [Introduction to Low-Rank Approximation](https://mybinder.org/v2/gh/CosmoStat/Tutorials/master?filepath=%2Flow-rank%2Flow-rank.ipynb) diff --git a/docs/docker b/docs/docker deleted file mode 160000 index d8f223d..0000000 --- a/docs/docker +++ /dev/null @@ -1 +0,0 @@ -Subproject commit d8f223d4381c2603b39681bdcd044050bda63cb5 diff --git a/docs/presentation_tips b/docs/presentation_tips deleted file mode 160000 index 2700adc..0000000 --- a/docs/presentation_tips +++ /dev/null @@ -1 +0,0 @@ -Subproject commit 2700adc9882714e371ede3a22ba6d6033996482c diff --git a/docs/tensorflow-introduction b/docs/tensorflow-introduction deleted file mode 160000 index 1592869..0000000 --- a/docs/tensorflow-introduction +++ /dev/null @@ -1 +0,0 @@ -Subproject commit 15928695d2b6a1bbc4cab31529bd9399ae4f949d diff --git a/importance_sampling.ipynb b/importance_sampling.ipynb new file mode 100644 index 0000000..9b1521b --- /dev/null +++ b/importance_sampling.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3814beb8", + "metadata": {}, + "source": [ + "# Importance sampling" + ] + }, + { + "cell_type": "markdown", + "id": "b74e2ebc", + "metadata": {}, + "source": [ + "A Monte-Carlo chain of points $\\{x \\}_{i=1}^N$ represents, when converged, a sample under a posterior function $p(x) = \\pi(x) L(x)$, with $\\pi$ the prior and $L$ the likelihood function. We write\n", + "\n", + "$$x \\sim p.$$" + ] + }, + { + "cell_type": "markdown", + "id": "75142390", + "metadata": {}, + "source": [ + "This allows us to estimate (high-dimensional) integrals of the form\n", + "\n", + "$$\\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, \\pi(x) L(x) f(x).$$" + ] + }, + { + "cell_type": "markdown", + "id": "84ec49e5", + "metadata": {}, + "source": [ + "The (unbiased) estimator is\n", + "\n", + "$$ \\int {\\rm d} x \\, p(x) f(x) \\approx \\frac 1 N \\sum_{i=1}^N f(x_i),$$\n", + "\n", + "which is just the normalised sum over the function $f$ evaluated at all chain points." + ] + }, + { + "cell_type": "markdown", + "id": "f4e53939-134f-483b-b7c9-47d5ff468468", + "metadata": {}, + "source": [ + "For example, for the mean of a parameter we set $f(x) = x$. The mean estimated by MCMC is simply\n", + "\n", + "$$\\bar x \\approx \\frac 1 N \\sum_{i=1}^N x_i.$$" + ] + }, + { + "cell_type": "markdown", + "id": "5ab283bf", + "metadata": {}, + "source": [ + "Importance sampling is based on the following identity\n", + "\n", + "$$\\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x),$$\n", + "\n", + "which holds if the support of the proposal distribution $q$ is contained in the support of $p$." + ] + }, + { + "cell_type": "markdown", + "id": "22736e7b", + "metadata": {}, + "source": [ + "This integral can be estimated with samples under $q$ instead of $p$,\n", + "\n", + "$$y \\sim q,$$\n", + "\n", + "if the samples are multiplied by the importance weights\n", + "\n", + "$$w_i = \\frac{p(x_i)}{q(x_i)}.$$\n", + "\n", + "Proof:\n", + "\n", + "$$ \\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x) \\approx \\frac 1 N \\sum_{i=1}^N w_i f(y_i),$$\n", + "\n", + "\n", + "Importance sampling can be useful if sampling under $p$ is very time-consuming of difficult, but evaluating $p$ at points $x_i$ is not. One then choses a simple proposal function $q$, e.g. a (multi-variate) normal.\n", + "\n", + "Importance sampling permits to separate sampling (fast; under $q$) and evaluating the original posterior (potentiall slow, but can now be done in parallel using the already sampled points $y_i$)." + ] + }, + { + "cell_type": "markdown", + "id": "01e3f214", + "metadata": {}, + "source": [ + "Our case is the following. We have already run an MCMC and obtained samples $x \\sim p$ under the posterior $p(x) = L(x) \\pi(x)$.\n", + "\n", + "However, we would like to get samples under a new, combined, posterior $p_{\\rm comb}(x) = L(x) L_2(x) \\pi(x)$. For example, $L$ is the CMB likelihood, $L_2$ is the one for weak lensing. We want to get the combined weak-lensing + CMB constraints.\n", + "\n", + "Now, instead of re-running a new chain sampling from $p_2$, we can see that the integral\n", + "\n", + "$$\\int {\\rm d} x p_{\\rm comb} f(x) = \\int {\\rm d} x L(x) \\pi(x) L_2(x) f(x)$$\n", + "\n", + "has a form similar to the modified one above, if we identify\n", + "\n", + "$$q(x) = L(x) \\quad \\mbox{and} \\quad L_2(x) = \\frac{p(x)}{q(x)}.$$" + ] + }, + { + "cell_type": "markdown", + "id": "678f6d9b", + "metadata": {}, + "source": [ + "So we can use the existing chain points $x$ and multiply each data point $x_i$ with the \"importance weight\" $L_2(x_i)$, and can thus obtain estimators of integrals with the combined posterior $p_{\\rm comb}$!" + ] + }, + { + "cell_type": "markdown", + "id": "825765c7", + "metadata": {}, + "source": [ + "Let's test this." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d23712d6", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import matplotlib.pylab as plt\n", + "#from scipy.stats import norm\n", + "import numpy as np\n", + "import emcee" + ] + }, + { + "cell_type": "markdown", + "id": "02225b65-2c7d-4fc3-a752-ff8159be3520", + "metadata": {}, + "source": [ + "First, we sample a one distribution with emcee to see whether this works." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "26860f9e", + "metadata": {}, + "outputs": [], + "source": [ + "# Define simple log of a 1D normal distribution with mean μ and width σ\n", + "def log_prob(x, μ, σ):\n", + " diff = x - μ\n", + " return -0.5 * (diff / σ)**2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4e7a619b", + "metadata": {}, + "outputs": [], + "source": [ + "# Input values\n", + "μ = 0\n", + "σ = 3" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "45f3f7d9", + "metadata": {}, + "outputs": [], + "source": [ + "# Set x array for plotting\n", + "n = 5\n", + "x = np.linspace(-σ*n, σ*n, 1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5da74549", + "metadata": {}, + "outputs": [], + "source": [ + "# Set up MCMC\n", + "ndim = 1\n", + "nwalkers = 5\n", + "\n", + "# Random starting points\n", + "p0 = np.random.rand(nwalkers, ndim)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4dcffc21-a30c-48d5-b014-db396b6a900f", + "metadata": {}, + "outputs": [], + "source": [ + "# Initialise emcee samples\n", + "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_prob, args=[μ, σ])\n", + "n_burn = 100\n", + "n_chain = 5000" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "37e1b0a8-ae4d-4e0b-a768-e896f7f27c64", + "metadata": {}, + "outputs": [], + "source": [ + "# Run burn-in phase and remove points from chain\n", + "state = sampler.run_mcmc(p0, n_burn)\n", + "sampler.reset()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "6803b569-df99-42da-a7ec-b554ecf75453", + "metadata": {}, + "outputs": [], + "source": [ + "# Run rest of the chain\n", + "sampler.run_mcmc(state, n_chain);" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "15bbb805", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Get pdf = exponential of log distribution\n", + "# Use input values for mean and scale\n", + "pdf = np.exp(log_prob(x, μ, σ))\n", + "\n", + "# Normalise to unit area (because with MCMC it's tricky anyway to estimate the normalisation)\n", + "pdf = pdf / sum(pdf) / (x[1] - x[0])\n", + "\n", + "# Plot\n", + "plt.plot(x, pdf)\n", + "\n", + "# Get chain points\n", + "samples = sampler.get_chain(flat=True)\n", + "\n", + "# Plot estimated pdf which is proprtional to chain points density\n", + "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True)\n", + "plt.xlabel('x')\n", + "_ = plt.ylabel('probability')" + ] + }, + { + "cell_type": "markdown", + "id": "24eac54e-1c09-4c09-9e56-7c8d4f8d572c", + "metadata": {}, + "source": [ + "Now we introduce a second non-normaal distribution, and compare sampling under the combined\n", + "pdf versus the importance-sampling trick." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "c8a39416", + "metadata": {}, + "outputs": [], + "source": [ + "# Add another distribution.\n", + "# Set input values\n", + "μ2 = 3\n", + "σ2 = 2" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0f0126ec-956d-4075-834f-7829ddf362d0", + "metadata": {}, + "outputs": [], + "source": [ + "# Define second log pdf, this time not a normal distribution\n", + "def log_prob2(x, μ, σ):\n", + " diff = x - μ\n", + " return -0.5 * np.abs(diff/ σ)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "58907336-05d6-45d8-acf4-9c81db1087ef", + "metadata": {}, + "outputs": [], + "source": [ + "# Combined log pdf = sum of individual log pdf's\n", + "def log_prob_comb(x, μ, σ, μ2, σ2):\n", + " return log_prob(x, μ, σ) + log_prob2(x, μ2, σ2)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "dcc9999e", + "metadata": {}, + "outputs": [], + "source": [ + "# Set up MCMC to sample under combined pdf\n", + "sampler_comb = emcee.EnsembleSampler(nwalkers, ndim, log_prob_comb, args=[μ, σ, μ2, σ2])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "60d5ba22-66af-4c3a-bb18-4556722030fb", + "metadata": {}, + "outputs": [], + "source": [ + "# Burn-in phase\n", + "state_comb = sampler_comb.run_mcmc(p0, n_burn)\n", + "sampler_comb.reset()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "7988743f-4707-4fe1-b1ed-7e7e35e01a2c", + "metadata": {}, + "outputs": [], + "source": [ + "# Run MCMC\n", + "sampler_comb.run_mcmc(state, n_chain);" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "8cd91081-3c99-4fa0-be4c-e4fbc5cb3c70", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Get combined pdf with input values\n", + "pdf_comb = np.exp(log_prob_comb(x, μ, σ, μ2, σ2))\n", + "\n", + "# Normalise to unit area\n", + "pdf_comb = pdf_comb / sum(pdf_comb) / (x[1] - x[0])\n", + "\n", + "_ = plt.plot(x, pdf_comb)\n", + "\n", + "# Get sample points under combined pdf and plot\n", + "samples_comb = sampler_comb.get_chain(flat=True)\n", + "_ = plt.hist(samples_comb[:, 0], 100, histtype=\"step\", density=True)\n", + "\n", + "# Importance sampling: Get weights = pdf2 evaluated at sample points\n", + "weights = np.exp(log_prob2(samples[:, 0], μ2, σ2))\n", + "\n", + "# Plot importance-sampled points by adding those weights to histogram\n", + "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True, weights=weights)\n", + "plt.xlabel('$x$')\n", + "_ = plt.ylabel('probability')" + ] + }, + { + "cell_type": "markdown", + "id": "b0641e72-81e2-4b38-b4f0-c72d2d05d6e2", + "metadata": {}, + "source": [ + "Both chain do a good job to estimate the overall density!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e5bdcea1-ef02-4c72-8578-54ba8fce569a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ebbe4318-7548-4472-81f6-c93d4d57f13e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "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": 5 +} diff --git a/maintenance_recipes.md b/maintenance_recipes.md deleted file mode 100644 index ea17dda..0000000 --- a/maintenance_recipes.md +++ /dev/null @@ -1,17 +0,0 @@ -# Recipes for maintenance tasks on this repo - -This file serves as a collection of git magic recipes that were used to build -this repo. - -## Hosting a new tutorial website on github pages - -Only the master/docs folder is served on gh-pages, so we use submodules to link -to docs that can be hosted on other branches. - -Here is an example of how we did it for the tensorflow tutorial using submodules: - -``` -$ git checkout master -$ cd docs -$ git submodule add -b tensorflow-tutorial https://github.com/CosmoStat/Tutorials.git tensorflow-introduction -``` diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..508fa51 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,5 @@ +jupyter +numpy +matplotlib +emcee + From c21c55d2e4933158e8a8350cef56391b36e69b59 Mon Sep 17 00:00:00 2001 From: Martin Kilbinger Date: Thu, 8 Sep 2022 13:41:31 +0200 Subject: [PATCH 2/5] Update README.md --- README.md | 23 ++--------------------- 1 file changed, 2 insertions(+), 21 deletions(-) diff --git a/README.md b/README.md index 7bb1832..4b9afc4 100644 --- a/README.md +++ b/README.md @@ -5,8 +5,6 @@ > Year: 2022 > Email: [martin.killbinger@cea.fr](mailto:martin.killbinger@cea.fr) -[notebook](./importance_sampling.ipynb) - This is a very brief tutorial about how importance sampling for Bayesian parameter inference. Specifically, it describes the case where an existing sample (e.g. a Monte-Carlo Markov chain) can be importance-sampled to obtain samples under a joint posterior distribution. @@ -21,25 +19,8 @@ In order to run the tutorial notebooks tutees will need to have the following in * Python (require >=3.5) * NumPy (recommend >=1.16.2) -* SciPy (recommend >=1.2.1) -* Astropy (recommend >=3.1.2) +* Emcee (recommend >=3.1.2) * Matplotlib (recommend >=3.0.3) * Jupyter (recommend >=1.0.0) -All of the packages listed above can easily be installed using either `pip` or Anaconda. - -*e.g.* - -```bash -$ pip install numpy scipy astropy matplotlib jupyter -``` - -or - -```bash -$ conda install numpy scipy astropy matplotlib jupyter -``` - -### Notebooks - -1. [Introduction to Low-Rank Approximation](https://mybinder.org/v2/gh/CosmoStat/Tutorials/master?filepath=%2Flow-rank%2Flow-rank.ipynb) +All of the packages listed above can easily be installed using `pip`. 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+ "\n", + "can be approximated by evaluating $f$ at random points, drawn from a uniform distribution\n", + "between $a$ and $b$:\n", + "\n", + "$$\\int_a^b {\\rm d} x \\, f(x) \\approx \\frac{b-a} N \\sum_{i=1}^N f(x_i),$$\n", + "\n", + "with sample points written as\n", + "\n", + "$$x_i ~ \\sim U_{[a; b]}.$$" + ] + }, + { + "cell_type": "markdown", + "id": "578fec40-49d4-419f-bef9-2b286af2c591", + "metadata": {}, + "source": [ + "This is illustrated in the following example. We pick uniformly drawn random points $x_i$\n", + "and compute the area of the rectangle between $a = -2$ and $b = 5$, which is $(b - a) f(x_i)$.\n", + "\n", + "An (unbiased) estimate of the grey area is the average of all rectangles, which is the above equation.\n", + "\n", + "\n", + "(From https://towardsdatascience.com/the-basics-of-monte-carlo-integration-5fe16b40482d)" + ] + }, + { + "cell_type": "markdown", + "id": "91158d0f-0890-4208-8011-93cb6902d192", + "metadata": {}, + "source": [ + "## Drawing from arbitrary distributions" + ] + }, + { + "cell_type": "markdown", + "id": "cce38eff-88a6-4ce1-9a83-0b6adf0466bf", + "metadata": {}, + "source": [ + "$$F = \\int_a^b {\\rm d} x f(x) = \\int {\\rm d} y \\, p(y) f(y)$$\n", + "\n", + "with variable change\n", + "\n", + "$${\\rm d} y \\, p(y) = \\frac{{\\rm d} x}{b-a}$$,\n", + "\n", + "where $p$ is a normalised probability distribution $\\int {\\rm d} y \\, p(y) = 1$.\n", + "\n", + "This is approximated by\n", + "\n", + "$$F \\approx \\frac 1 N \\sum_{i=1}^N f(y_i)$$\n", + "\n", + "with random points $y_i$ drawn from the distribution $p$, $y \\sim p$." + ] + }, + { + "cell_type": "markdown", + "id": "fc4c50ff-8b7b-4785-b885-c4969d258f27", + "metadata": {}, + "source": [ + "Proof:\n", + "\n", + "$$E \\left[ \\frac 1 N \\sum_{i=1}^N f(y_i) \\right] = \\frac 1 N \\sum_{i=1}^N E \\left[ f(y_i) \\right]\n", + "= \\frac 1 N \\sum_{i=1}^N \\int {\\rm d} y \\, p(y) f(y)\n", + "= \\frac 1 N N F = F\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d6631af1-dbaa-4cf3-aada-0aeb0110e703", + "metadata": {}, + "source": [ + "## Monte-Carlo Markov chain" ] }, { @@ -13,7 +105,7 @@ "id": "b74e2ebc", "metadata": {}, "source": [ - "A Monte-Carlo chain of points $\\{x \\}_{i=1}^N$ represents, when converged, a sample under a posterior function $p(x) = \\pi(x) L(x)$, with $\\pi$ the prior and $L$ the likelihood function. We write\n", + "A Monte-Carlo Markov chain of points $\\{x_i \\}_{i=1}^N$ represents, when converged, a sample under a posterior distribution $p(x) \\propto \\pi(x) L(x)$, with $\\pi$ being the prior and $L$ the likelihood function. We write as above\n", "\n", "$$x \\sim p.$$" ] @@ -47,7 +139,17 @@ "source": [ "For example, for the mean of a parameter we set $f(x) = x$. The mean estimated by MCMC is simply\n", "\n", - "$$\\bar x \\approx \\frac 1 N \\sum_{i=1}^N x_i.$$" + "$$\\bar x \\approx \\frac 1 N \\sum_{i=1}^N x_i.$$\n", + "\n", + "Another example: To plot the 2D $68\\%$ credible region (contour), pixelise $p$ in 2D, sort the pixels by density (= number of sample points in each pixel), and set $f = 1$ in the first $68\\%$ of pixels, and $0$ for the remaining pixels." + ] + }, + { + "cell_type": "markdown", + "id": "06c67f01-269f-4ffb-ac4f-79195bef87fe", + "metadata": {}, + "source": [ + "## Importance sampling" ] }, { @@ -59,12 +161,12 @@ "\n", "$$\\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x),$$\n", "\n", - "which holds if the support of the proposal distribution $q$ is contained in the support of $p$." + "which holds if the support of the proposal distribution $q$ is not smaller than the support of $p$." ] }, { "cell_type": "markdown", - "id": "22736e7b", + "id": "42545e20-0175-4c5d-962c-79ae7a3af804", "metadata": {}, "source": [ "This integral can be estimated with samples under $q$ instead of $p$,\n", @@ -73,16 +175,29 @@ "\n", "if the samples are multiplied by the importance weights\n", "\n", - "$$w_i = \\frac{p(x_i)}{q(x_i)}.$$\n", - "\n", - "Proof:\n", - "\n", - "$$ \\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x) \\approx \\frac 1 N \\sum_{i=1}^N w_i f(y_i),$$\n", + "$$w_i = \\frac{p(x_i)}{q(x_i)},$$\n", "\n", + "since\n", "\n", + "$$ \\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x) \\approx \\frac 1 N \\sum_{i=1}^N w_i f(y_i).$$" + ] + }, + { + "cell_type": "markdown", + "id": "1c4385ad-ebf0-43bf-a937-09a7f149b7d9", + "metadata": {}, + "source": [ "Importance sampling can be useful if sampling under $p$ is very time-consuming of difficult, but evaluating $p$ at points $x_i$ is not. One then choses a simple proposal function $q$, e.g. a (multi-variate) normal.\n", "\n", - "Importance sampling permits to separate sampling (fast; under $q$) and evaluating the original posterior (potentiall slow, but can now be done in parallel using the already sampled points $y_i$)." + "Importance sampling permits to separate sampling (fast; under $q$) and evaluating the original posterior (potentiall slow, but can now be done in parallel using the already sampled points $x_i$)." + ] + }, + { + "cell_type": "markdown", + "id": "ded5de23-66f3-48c5-831b-6e6f1b425cd3", + "metadata": {}, + "source": [ + "### Importance-sampling an existing MCM chain" ] }, { @@ -90,17 +205,17 @@ "id": "01e3f214", "metadata": {}, "source": [ - "Our case is the following. We have already run an MCMC and obtained samples $x \\sim p$ under the posterior $p(x) = L(x) \\pi(x)$.\n", + "A recurring case is the following. We have already run an MCMC and obtained samples $x \\sim p$ under the posterior $p(x) = \\pi(x) L(x)$.\n", "\n", - "However, we would like to get samples under a new, combined, posterior $p_{\\rm comb}(x) = L(x) L_2(x) \\pi(x)$. For example, $L$ is the CMB likelihood, $L_2$ is the one for weak lensing. We want to get the combined weak-lensing + CMB constraints.\n", + "Next, we would like to get samples under a new, combined, posterior $p_{\\rm comb}(x) = \\pi(x) L(x) L_2(x)$. For example, $L$ is the CMB likelihood, $L_2$ is the one for weak lensing. We want to get the combined weak-lensing + CMB constraints.\n", "\n", - "Now, instead of re-running a new chain sampling from $p_2$, we can see that the integral\n", + "Now, instead of re-running a new chain sampling from $p_{\\rm comb}$, we can see that the integral\n", "\n", - "$$\\int {\\rm d} x p_{\\rm comb} f(x) = \\int {\\rm d} x L(x) \\pi(x) L_2(x) f(x)$$\n", + "$$\\int {\\rm d} x p_{\\rm comb} f(x) = \\int {\\rm d} x \\pi(x) L(x) L_2(x) f(x)$$\n", "\n", "has a form similar to the modified one above, if we identify\n", "\n", - "$$q(x) = L(x) \\quad \\mbox{and} \\quad L_2(x) = \\frac{p(x)}{q(x)}.$$" + "$$q(x) = \\pi(x) L(x) \\quad \\mbox{and} \\quad L_2(x) = \\frac{p(x)}{q(x)}.$$" ] }, { @@ -108,7 +223,7 @@ "id": "678f6d9b", "metadata": {}, "source": [ - "So we can use the existing chain points $x$ and multiply each data point $x_i$ with the \"importance weight\" $L_2(x_i)$, and can thus obtain estimators of integrals with the combined posterior $p_{\\rm comb}$!" + "So we can use the existing chain points $x_i$ sampled under $p=q$ and multiply each data point $x_i$ with the \"importance weight\" $L_2(x_i)$, and can thus obtain estimators of integrals with the combined posterior $p_{\\rm comb}$!" ] }, { @@ -121,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 34, "id": "d23712d6", "metadata": {}, "outputs": [], @@ -129,7 +244,6 @@ "%matplotlib inline\n", "\n", "import matplotlib.pylab as plt\n", - "#from scipy.stats import norm\n", "import numpy as np\n", "import emcee" ] @@ -139,12 +253,12 @@ "id": "02225b65-2c7d-4fc3-a752-ff8159be3520", "metadata": {}, "source": [ - "First, we sample a one distribution with emcee to see whether this works." + "First, we sample a 1-D distribution with emcee to see whether this simple case works." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 35, "id": "26860f9e", "metadata": {}, "outputs": [], @@ -157,7 +271,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 36, "id": "4e7a619b", "metadata": {}, "outputs": [], @@ -169,7 +283,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 37, "id": "45f3f7d9", "metadata": {}, "outputs": [], @@ -181,7 +295,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 38, "id": "5da74549", "metadata": {}, "outputs": [], @@ -196,7 +310,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 39, "id": "4dcffc21-a30c-48d5-b014-db396b6a900f", "metadata": {}, "outputs": [], @@ -209,7 +323,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 40, "id": "37e1b0a8-ae4d-4e0b-a768-e896f7f27c64", "metadata": {}, "outputs": [], @@ -221,7 +335,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 41, "id": "6803b569-df99-42da-a7ec-b554ecf75453", "metadata": {}, "outputs": [], @@ -232,13 +346,13 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 44, "id": "15bbb805", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -258,13 +372,14 @@ "pdf = pdf / sum(pdf) / (x[1] - x[0])\n", "\n", "# Plot\n", - "plt.plot(x, pdf)\n", + "plt.plot(x, pdf, label='anaytical')\n", "\n", "# Get chain points\n", "samples = sampler.get_chain(flat=True)\n", "\n", "# Plot estimated pdf which is proprtional to chain points density\n", - "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True)\n", + "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True, label='samples')\n", + "plt.legend()\n", "plt.xlabel('x')\n", "_ = plt.ylabel('probability')" ] @@ -274,13 +389,13 @@ "id": "24eac54e-1c09-4c09-9e56-7c8d4f8d572c", "metadata": {}, "source": [ - "Now we introduce a second non-normaal distribution, and compare sampling under the combined\n", + "Now we introduce a second non-normal distribution, and compare sampling under the combined\n", "pdf versus the importance-sampling trick." ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 45, "id": "c8a39416", "metadata": {}, "outputs": [], @@ -293,7 +408,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 46, "id": "0f0126ec-956d-4075-834f-7829ddf362d0", "metadata": {}, "outputs": [], @@ -306,7 +421,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 47, "id": "58907336-05d6-45d8-acf4-9c81db1087ef", "metadata": {}, "outputs": [], @@ -318,7 +433,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 48, "id": "dcc9999e", "metadata": {}, "outputs": [], @@ -329,7 +444,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 49, "id": "60d5ba22-66af-4c3a-bb18-4556722030fb", "metadata": {}, "outputs": [], @@ -341,7 +456,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 50, "id": "7988743f-4707-4fe1-b1ed-7e7e35e01a2c", "metadata": {}, "outputs": [], @@ -352,13 +467,13 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 55, "id": "8cd91081-3c99-4fa0-be4c-e4fbc5cb3c70", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -376,17 +491,32 @@ "# Normalise to unit area\n", "pdf_comb = pdf_comb / sum(pdf_comb) / (x[1] - x[0])\n", "\n", - "_ = plt.plot(x, pdf_comb)\n", + "_ = plt.plot(x, pdf_comb, label='analytical')\n", "\n", "# Get sample points under combined pdf and plot\n", "samples_comb = sampler_comb.get_chain(flat=True)\n", - "_ = plt.hist(samples_comb[:, 0], 100, histtype=\"step\", density=True)\n", + "_ = plt.hist(\n", + " samples_comb[:, 0],\n", + " 100,\n", + " histtype=\"step\",\n", + " density=True,\n", + " label='combined pdf sampled'\n", + ")\n", "\n", "# Importance sampling: Get weights = pdf2 evaluated at sample points\n", "weights = np.exp(log_prob2(samples[:, 0], μ2, σ2))\n", "\n", "# Plot importance-sampled points by adding those weights to histogram\n", - "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True, weights=weights)\n", + "plt.hist(\n", + " samples[:, 0],\n", + " 100,\n", + " histtype=\"step\",\n", + " density=True,\n", + " weights=weights,\n", + " label='importance sampled'\n", + ")\n", + "plt.legend()\n", + "#plt.ylim()\n", "plt.xlabel('$x$')\n", "_ = plt.ylabel('probability')" ] From 50c2ba63ab1f7386018c9587b014443761179760 Mon Sep 17 00:00:00 2001 From: Martin Kilbinger Date: Thu, 6 Oct 2022 09:33:37 +0200 Subject: [PATCH 4/5] added proof --- importance_sampling.ipynb | 52 +++++++++++++++++++++++++-------------- 1 file changed, 33 insertions(+), 19 deletions(-) diff --git a/importance_sampling.ipynb b/importance_sampling.ipynb index a255a70..54ed599 100644 --- a/importance_sampling.ipynb +++ b/importance_sampling.ipynb @@ -37,6 +37,20 @@ "$$x_i ~ \\sim U_{[a; b]}.$$" ] }, + { + "cell_type": "markdown", + "id": "e9ac7929-7982-4437-be1d-0a7912a69795", + "metadata": {}, + "source": [ + "Proof:\n", + " \n", + "$$E \\left[ \\frac{b-a} N \\sum_{i=1}^N f(x_i) \\right]\n", + "= \\frac{b-a} N \\sum_{i=1}^N E \\left[ f(x_i) \\right]\n", + "= \\frac{b-a} N \\left( N \\frac 1 {b-a} \\int_a^b {\\rm d} x \\, f(x) \\right)\n", + "= F\n", + "$$" + ] + }, { "cell_type": "markdown", "id": "578fec40-49d4-419f-bef9-2b286af2c591", @@ -236,7 +250,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 1, "id": "d23712d6", "metadata": {}, "outputs": [], @@ -258,7 +272,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 2, "id": "26860f9e", "metadata": {}, "outputs": [], @@ -271,7 +285,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 3, "id": "4e7a619b", "metadata": {}, "outputs": [], @@ -283,7 +297,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 4, "id": "45f3f7d9", "metadata": {}, "outputs": [], @@ -295,7 +309,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 5, "id": "5da74549", "metadata": {}, "outputs": [], @@ -310,7 +324,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 6, "id": "4dcffc21-a30c-48d5-b014-db396b6a900f", "metadata": {}, "outputs": [], @@ -323,7 +337,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 7, "id": "37e1b0a8-ae4d-4e0b-a768-e896f7f27c64", "metadata": {}, "outputs": [], @@ -335,7 +349,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 8, "id": "6803b569-df99-42da-a7ec-b554ecf75453", "metadata": {}, "outputs": [], @@ -346,13 +360,13 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 10, "id": "15bbb805", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -380,7 +394,7 @@ "# Plot estimated pdf which is proprtional to chain points density\n", "plt.hist(samples[:, 0], 100, histtype=\"step\", density=True, label='samples')\n", "plt.legend()\n", - "plt.xlabel('x')\n", + "plt.xlabel('$x$')\n", "_ = plt.ylabel('probability')" ] }, @@ -395,7 +409,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 11, "id": "c8a39416", "metadata": {}, "outputs": [], @@ -408,7 +422,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 12, "id": "0f0126ec-956d-4075-834f-7829ddf362d0", "metadata": {}, "outputs": [], @@ -421,7 +435,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 13, "id": "58907336-05d6-45d8-acf4-9c81db1087ef", "metadata": {}, "outputs": [], @@ -433,7 +447,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 14, "id": "dcc9999e", "metadata": {}, "outputs": [], @@ -444,7 +458,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 15, "id": "60d5ba22-66af-4c3a-bb18-4556722030fb", "metadata": {}, "outputs": [], @@ -456,7 +470,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 16, "id": "7988743f-4707-4fe1-b1ed-7e7e35e01a2c", "metadata": {}, "outputs": [], @@ -467,13 +481,13 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 17, "id": "8cd91081-3c99-4fa0-be4c-e4fbc5cb3c70", "metadata": {}, "outputs": [ { "data": { - "image/png": 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LsbPiiZnVutLPWmltot2tsYz9+cEIzzQA4v3vsj4bMGCApqWlnbLs+++/p3v37g5FVD917NiRtLS0Cq8X4qSZM2fSvHlzfv3rXwftNYL6uZoZy6W9zmNP/h4A4pvFkzreXcbNNc/lK2hYltOenxnLL5KX8fyUfsGJ1dQLIrJGVU+bsGWnqoypQ/bk7yHv+1m8cuGnZ1zQcF9eQQ1FZRoaO1Vlaoz/KZ9QVNZ12uui4V3iGNCx5enFeCoQ3yzeN7fD20rZl3fa1QiMCYglDmPqmHsv6VLlbfxPaXntO3ICVa3yiDdjLHEYE+J8V/JLSiRSW9GnQwvgp1aE935VHS8s5uiJIqKjImsyXNMAWOIwJsR5L9KUpa3ZOvk/vuXeVsSZ2HvkhCUOU2WWOIwJVd5quEmJjGn1HsdPFvNxcs1ezXJfXgGd2zSv0X2a+s8Sh4fvdEAN8e+ELM/555/Pl19+WWOvWZmMjAy+/PJLX0mT+qyqpd+XL1/O008/zXvvvRfkyKrAWw13nosNu4/w5NW9CAur2f6IHOsgN9VgicMjOz+7wnHwVeXfCVme2kwaRUVFZGRkMH/+/AaROOqb6MYRXNO3zEvXnJF9RyxxmKqzeRwOat7cfYpg+fLlXHjhhYwbN45OnToxY8YMXn/9dQYNGoTL5WL79u2AuzT67bffzoABA+jSpYvvv+OCggKmT5+Oy+Wib9++vnIYc+fOZezYsVx88cWMHDmSGTNm8Pnnn9OnTx9mz55NRkYGw4YNo1+/fvTr18+XyJYvX86IESMYP3483bp1Y8qUKb4yJKtXr+b888+nd+/eDBo0iLy8vHJLkfvLz8/niiuuoHfv3vTq1cs3o/2xxx5j4MCB9OrVi9tuu833OiNGjOCee+5hwIABdO/endWrV3PNNdeQnJzsK83uLac+ZcoUunfvzvjx4zl27PSS4R999BFDhgyhX79+TJgwwXcRqQ8//JBu3brRr18//v3vf9fML7WG5R53lz4Z2yeeJo1q7polGtuBjKjJTFhxeY3t0zQgZZXMrW+3QMqqV1aWuqoC2Z+3pPiyZcs0NjZWs7OztaCgQOPj4/WRRx5RVdVnnnlGf/nLX6qquzT66NGjtbi4WLds2aLt27fX48eP69NPP+0re/79999rhw4d9Pjx4/rKK69o+/btfSXbly1b5it1rqqan5+vx48fV1XVLVu2qPd9WrZsmcbExOiuXbu0uLhYBw8erJ9//rmeOHFCk5KS9Ouvv1ZV1dzcXC0sLCy3FLm/RYsW6S233OJ7fPjwYVX9qZy8qurUqVN18eLFqqp64YUX6v333+97D9q1a+d7f9q3b6/79+/XnTt3KuArvz59+nR96qmnfNuvXr1ac3JydNiwYXr06FFVVZ01a5b+7ne/0+PHj2tCQoJu2bJFS0pKdMKECae8N9VVo2XVH43RV1dmaK+5vfTbXYdqZJf+n8sLfv8fK69uKoSVVQ9tAwcOpF27djRu3Jhzzz2XSy+9FOC0suDXXXcdYWFhJCcn06lTJzZt2sSKFSt8Zc+7devGOeecw5YtWwC45JJLfCXbSyssLOTWW2/F5XIxYcIENm7c6Htu0KBBJCQkEBYWRp8+fcjIyGDz5s20a9fOVxgwJiaGiIiIckuR+3O5XHz88cc88MADfP7558TGuuuCLVu2jPPOOw+Xy8Unn3zCd9/5LjvP2LFjfdv27NnT9/506tSJXbt2AdChQweGDh0KlF1GftWqVWzcuJGhQ4fSp08f5s2bxw8//MCmTZtISkoiOTkZEfG9f6Fm4Wr3hbxc7Wv+ipJto6NqfJ+mYQhqH4eIXAb8GQgHXlbVWaWeHw48A6QAE1V1kd9zxYC30yFTVcd6licBC4BWwBrgBlU9SR1XU2XBS2vWrFm5z82ePZu2bdvy7bffUlJSQlTUT39I/OPxL71eFi2nFLm/Ll26sHbtWpYsWcJDDz3EyJEjuf/++7nzzjtJS0ujQ4cOzJw501cm3T+GisrIB1Im/ZJLLvEVXPRat25dubGGkg27jxAdU/Wy9IFoE9MY9tb4bk0DELQWh4iEA88DlwM9gEki0qPUapnAjcD8MnZxXFX7eG5j/Zb/Hpitqp2BQ8DNNR58CHvjjTcoKSlh+/bt7Nixg65duzJs2DBfufItW7aQmZlZ5jU1oqOjycv76SI+ubm5tGvXjrCwMF577TWKi4srfO2uXbuyZ88eVq9eDUBeXh5FRUXlliL3l52dTdOmTZk6dSr33Xcfa9eu9SWJ1q1bc/ToUV85+KrIzMz0XTCqrDLygwcP5osvvvBdxjY/P58tW7bQrVs3MjIyfP1HpRNLqGgUHryTAm2sxWGqKZgtjkHANlXdASAiC4BxgO98iKpmeJ4rCWSH4v6362LAOyxoHjATeOFMg/WfhVsTqjOTNxCJiYkMGjSII0eO8Ne//pWoqCjuvPNO7rjjDlwuFxEREcydO/eU/9C9UlJSCA8Pp3fv3tx4443ceeedXHvttbz66qtcdtllFbZOABo1asTChQu5++67OX78OE2aNGHp0qXlliL3l56ezn333UdYWBiRkZG88MILtGjRgltvvZVevXpx9tlnn3ZtjEB07dqV559/nptuuokePXpwxx13nPJ8XFwcc+fOZdKkSZw44R5B9MQTT9ClSxfmzJnDFVdcQdOmTRk2bNgpSdVpxSVKOHBh1zhWBamAdZynvPrxk8U12vFuGoCyOj5q4gaMx316yvv4BuAv5aw7FxhfalkRkAasAq7yLGuNOxl51+kAbKgsloCuOV4H+F833Ogp1woPFTX1ufpy237VR2N08brdNTpww39f/1qdqfpojGbsP1pj+zf1C+V0jofyPI5zVHW3iHQCPhGRdCA30I1F5DbgNnD/l25MXfLu+myGACO7t4F1Nbdf/5Z1y8ZtmYC7Su45rSpubRrjL5iJYzfuFoFXgmdZQFR1t+fnDhFZDvQF3gRaiEiEqhZVtE9VnQPMAfeFnKpzAKFm7ty5TocQUjp27MiGDRucDqNG+VcwWJMQT2qjmv2K+lcz8CaQvUfsuhymaoI5HHc1kCwiSSLSCJgILA5kQxE5S0Qae+63BoYCGz1Np2W4T4MBTAPeqW6A2gCufmhqT018nrLzs3l28H/I+34W2ZG1c0LAZo+bqgpa4vC0CO4CUoHvgX+p6nci8piIeIfWDhSRLGAC8KKIeAfxdwfSRORb3Ililqp6O9UfAO4VkW24h+T+rTrxRUVFceDAAUsepkaoKgcOHDhlSHN1vfttNjFRtXcW2S7oZKoqqJ9OVV0CLCm17BG/+6txn24qvd2XQJlDnNQ9SmvQmcaWkJBAVlYWOTk5Z7orYwD3PyMJCWdeT+rj7/ZyWa+z+fD06ilBYZeQNVUVyp3jQRUZGUlSUpLTYRhzmg+4k4Tv9vNhUu0M6rAKuaaqrOSIMaFitruRLQgFvz14ynXCg8n6OExVNdgWhzEhJzcTWibyeOeF/DUyvEau8BeIvXaqylSRtTiMCTGX9mxbq693+FghJ4oqLjdjjD9LHMaEmIu7tan117TTVaYqLHEYE2JaNG1U66+5J9dOV5nAWeIwJgTsyDnq6OvvyT3u6OubusUShzEh4OONzl4Y40drcZgqsFFVxjhttov/ys1kb1jt920ARDeOsFNVpkqsxWGM03IzOffkP3n1vHdr9WXjm8XjSkqETr/mvUO/qNXXNnWbJQ5jnDLbBTNjOdY0nuISZUTX2m1xpI5PJX1nJn2KXuYEB2r1tU3dZonDGKfkZsLMXB5NWkBMVAR9O7RwJIyzY+wSsqZqLHEY4yBV5dMtOQxLjiMiiNcXr0i7WHfiKCwO6ArOxljiMMZJG/ccYV/eCUZ0jXMmgNhE7v3SXWzaih2aQFniMKa2ePo0vMUMAZZvdpf1v9CpxHFPOssmbgVsEqAJnCUOY2qLp0+D3EzfouWb99EzPoY20c71M5ztOVVlczlMoCxxGOOgtZmHuaiWR1OV5u3jsNnjJlCWOIxxkHsYrkOnqTxim0QCsPeItThMYCxxGOOgmKgI+jg0DNdLRADr4zCBs5IjxtS22ESYGUs2cQzvEscVb11Odn42QNCv9lcR6+MwgQpqi0NELhORzSKyTURmlPH8cBFZKyJFIjLeb3kfEVkpIt+JyHoRud7vubkislNE1nlufYJ5DMbUuHvS2XT7Ls4v+DPDu8SRnZ9N+rR00qel19pV/8piLQ4TqKC1OEQkHHgeuATIAlaLyGJV3ei3WiZwI/DrUpsfA36uqltFJB5YIyKpqnrY8/x9qrooWLEbE2wrtu4H4ILOreE7h4Px2HukgJISJSxMnA7FhLhgtjgGAdtUdYeqngQWAOP8V1DVDFVdD5SUWr5FVbd67mcD+wBnexCNqUErtu2nU1wz4ls0cToUn6ISZX++TQI0lQtm4mgP7PJ7nOVZViUiMghoBGz3W/yk5xTWbBFpXM52t4lImoik5eTkVPVljQmaE0XFfLXjIMM6t3Y6lNNYP4cJREiPqhKRdsBrwHRV9bZKHgS6AQOBlsADZW2rqnNUdYCqDoiLs8aKCR3fZB7meGExQ0MwcVg/hwlEMBPHbqCD3+MEz7KAiEgM8D7wW1Vd5V2uqnvU7QTwCu5TYsbUGSu27ic8THhq489xzXM5OpKqtD2HbRKgqVwwh+OuBpJFJAl3wpgITA5kQxFpBLwFvFq6E1xE2qnqHnEPPr8K2FCjURsTZCu27ad3Qixbj+0hfVq60+H4NAoPsxaHCUjQWhyqWgTcBaQC3wP/UtXvROQxERkLICIDRSQLmAC8KCLe8SXXAcOBG8sYdvu6iKQD6UBr4IlgHYMxNS33WCHrsw5zQXLonT6NbxFFlrU4TACCOgFQVZcAS0ote8Tv/mrcp7BKb/cP4B/l7PPiGg7TmFqzcscBStQ9DPeVbKejOVX7s5qw+5AlDlO5kO4cN6a+WbEth2aNwumb2MLpUE7TvkUTdluLwwTASo4YU4tWbN3PeZ1aEenQ1f7KE19YxAf5Uylp04KCwouIigx3OiQTwgL69IrIv0XkChEJrU+7MXVMxoFj7tniISY1K5tHe31AWKPD1kFuKhVoIvg/3COitorILBHpGsSYjKnXhiWHXuIA96mqkpMtGPv+YFzzXIxeNNrpkEyICihxqOpSVZ0C9AMygKUi8qWITBeRyGAGaEx90jamMZ3bNHc6jDIlnNWE/O0zeKjH+6RPS/dV7DWmtID7OESkFTAVuAH4BngduACYBowIRnDG1BclJUoYUJLwJCmv3gM4W0K9LGfHRhEm2MgqU6mAEoeIvAV0xV3+40pV3eN5aqGIpAUrOGPqhdkuwnIzydLWFOj+kJr05y8yPIy2MTaXw1Qu0D6Ol1S1h6r+rzdpeIsLquqAoEVnTF002wUzY90/AXIz+etFa7ngxLPOxhWA9i1sLoepXKCJo6zZ2StrMhBj6o3cTJiZ6/7p8cW2/XRpG5p9G/7an2VzOUzlKjxVJSJn4y6F3kRE+gLeK7zEAE2DHJsx9cbXOw8y+bxEFh10OpKKPbZjErEn96CzO0BLu6CTKVtlfRyjcV+hLwH4k9/yPOA3QYrJmHrnRFEJQ89tHfKJI/bkHjoWzCeDydAy0elwTIiqMHGo6jxgnohcq6pv1lJMxtQ74WHCeZ1aumtGG1PHVXaqaqqn4GBHEbm39POq+qcyNjPGlJKSEEt0lE15MvVDZaeqmnl+hn6vnjEhKK+gkGhg6LmhOVvcJzYRZsZSEtsBrOKIqURlp6pe9Pz8Xe2EY0z98tWOg4wCzu/cyulQKnaPe25JGNDq8Y+h2NlwTGir7FRVhQPPVfW/azYcY+qXL7bvZxTQL/Esp0MJWIeWTSHH6ShMKKvsVNWaWonCmHrqy20HAOpUmfJESxymEoGMqjLGVENxTAdSc6/kSON2xDgdTBWc08qmaJmKVXaq6hlV/ZWIvAto6edVdWzQIjOmjnvv4lR+uWAdSd2fYf88d/mRUCtsWJYOLS1xmIpVdqrqNc/Pp6uzcxG5DPgzEA68rKqzSj0/HHgGSAEmquoiv+emAQ95Hj7hbf2ISH9gLtAE9/XMf6mqpyU1Y5z25PqpRHffT2R4fMgWNixLoiUOU4kKa1Wp6hrPz09x16Y6BBwEVnqWlUtEwoHngcuBHsAkEelRarVM3DPT55fatiXwKHAeMAh4VES8vYsvALcCyZ7bZRUeoTEOOa77GSKv8NH4VKdDqRI7VWUqE+ilY68AtgPPAn8BtonI5ZVsNgjYpqo7VPUksAAY57+Cqmao6nqgpNS2o4GPVfWgqh4CPgYuE5F2QIyqrvK0Ml4FrgrkGIypTZkHjgEwNAQvE1uZttFRTodgQlygF3L6I3CRqm4DEJFzgfeBDyrYpj2wy+9xFu4WRCDK2ra955ZVxvLTiMhtwG0AiYlWc8fUri+27wdgaKjP3yhDWJgVNzQVC7Ssep43aXjswF3oMGSp6hxVHaCqA+Li4pwOxzQwX2xzJ45z46zogql/KkwcInKNiFwDpInIEhG50dNp/S6Vl2vbDXTwe5zgWRaI8rbd7blfnX0aU2tWbnfP3xCpm/+9H2p0NgA6u5fDkZhQVFmL40rPLQrYC1yI+/riObhHNVVkNZAsIkki0giYCCwOMK5U4FIROcvTKX4pkOq5+uARERks7m/kz4F3AtynMbXmQP5Jp0M4I28Oc5+FltxdlaxpGqLKJgBOr+6OVbVIRO7CnQTCgb+r6nci8hiQpqqLRWQg8BZwFnCliPxOVXuq6kEReZyfWjWPqar3SgZ38tNw3A+ouJ/FGFMN57Rq5j4hbUwZJJApECISBdwM9MTd+gBAVW8KXmg1Z8CAAZqWluZ0GKYBGL1oNNn52YB7sl9qHRuK67X5xzyuefdnhDU6DNTtYzHVJyJrVHVA6eWBdo6/BpyNe5jsp7j7FkK6c9wYJ2TnZ5O+M5OxMfPr9B/axJZNyd8+g/SdmaRPS/clQ2Mg8MTRWVUfBvI9M7ivIPChtcY0DLPdZUWytHWdnL/hr0mjcOKiGzsdhglRgSaOQs/PwyLSC4gF2gQnJGPqqNxMAIadfJYhnere/I3SrPSIKU+gEwDneEY3PYx7ZFRzz31jTCk92sVwVrNGTodxxpJaN3OPpTSmlIASh6q+7Ln7KdApeOEYU/fV9dNUXp3i3FeOPnqiyOFITKgJtFZVKxF5TkTWisgaEXlGROp+W9yYIDj/3Prx1ejU2p04dubkOxyJCTWB9nEsAPYB1wLjgf3AwmAFZUxdNiippdMh1Iik1u5yKTv2H3U4EhNqAu3jaKeqj/s9fkJErg9GQMbUdU0bBfq1Cm3e8uo7rMVhSgm0xfGRiEwUkTDP7TrcM8KNMcDBOl5ipCze66Tv3G+Jw5yqsiKHeSJyBPeFk+YDJz23BXhKlhtjfqqGWx/ZqSpTWmW1qqJrKxBj6ipvmZHfJCXSrg5cU7yqdubkExbjdBQmlAR8MlZExgLDPQ+Xq+p7wQnJmLolOz+b6Oxn+PLENTCz7lxbPFD5J4ux/yCNv0CH484Cfgls9Nx+KSL/G8zAjKlLsnMLnA7BmFoTaIvjZ0AfVS0BEJF5wDfAg8EKzBhjTGiqyrjBFoD3mhixNR+KMXWLt2+jkbaiY6umUE8HHzWOCHTwpWkoAv1E/D/gGxGZ62ltrAGeDF5YxoS+7Pxs1kz5luM7ZjAsuZ5e1z42kc0RE52OwoSYShOHiIQBJcBg4N/Am8AQVbWZ46bBW5t5iGMnixmWXD/qU53mnnTu6PyJ01GYEFNp4vD0a9yvqntUdbHn9mMtxGZMyPt8aw7hYcKQelKfqiyd27hLjxQUFjsciQkVgZ6qWioivxaRDiLS0nsLamTG1AGfb91P3w4tiI6KdDqUoOnS1j0Yd3uOTQQ0boEmjuuBO3GXVU/zu1VIRC4Tkc0isk1EZpTxfGMRWeh5/isR6ehZPkVE1vndSkSkj+e55Z59ep+zC0oZx6TvzuXvh2+CmbEQm+h0OEHhTRxb91riMG6BjqrqgTtxXAAo8Dnw14o2EJFw4HngEiALWC0ii1V1o99qNwOHVLWziEwEfg9cr6qvA6979uMC3lbVdX7bTVHVShOXMcGmCjEn9sDMXKdDCZokT3n1LXvzHI7EhIpAWxzzgO7As8BzuBPJvEq2GQRsU9UdquqtbzWu1Drj/PazCBgpIlJqnUmebY0JORlRk9HYDk6HEVSNPMNxt1iLw3gEmjh6qeotqrrMc7sV6FXJNu2BXX6PszzLylxHVYuAXKB0L+P1wD9LLXvFc5rq4TISDQAicpuIpIlIWk5OTiWhGlM1qgrA7ed+gtyzweFoasfLO0fCbJfTYZgQEGjiWCsig70PROQ8AujjOFOe1zmmqv7fzCmq6gKGeW43lLWtqs5R1QGqOiAurp6OsTeO2ew5bXNRt4bz2Uo6MR9yM50Ow4SAQBNHf+BLEckQkQxgJTBQRNJFZH052+wG/NvwCZ5lZa4jIhG4Z6Qf8Ht+IqVaG6q62/MzD3ep90EBHoMxNWbZJncrdkTXhjM2w9PIMibgzvHLqrHv1UCyiCThThATgcml1lkMTMOdiMYDn6jnHIBn4uF1uFsVeJZFAC1Udb+IRAJjgKXViM2YavGWGQGILyyibUyUwxEZU/sCShyq+kNVd6yqRSJyF+4rBYYDf1fV70TkMSBNVRcDfwNeE5FtuOtg+dc2GA7sUtUdfssaA6mepBGOO2m8VNXYjKmu7PxsVly3ln6Pf0xqo0lOh1OrIsPL7E40DVBQL46sqkuAJaWWPeJ3vwCYUM62y3GXOfFflo/7tJkxjlmxdT/FJQ3vvE2n1s3dw1dMg2dlL42pok827SO2Sf2dKV6e5LbNnQ7BhAhLHMZU0adb9nFhl4Yzmsqrq2cG+dETRQ5HYpxmicOYKtp/9GSDGoYLEN8snjlZ1zA6IZ7v9xxxOhzjMEscxlSRCAyvr9ffKEfq+FQ+vmo12ZERbMy2xNHQWeIwpoq+avIrWj3dpt4WNSxP25jGAEz7qLfNIG/ggjqqypj65MDREwC0KdlXr4salsdb3eeKlu/x/sExDkdjnGSJw5hK+E/6KznZAmjYZTe27j0KDW9QmfFjp6qMqUR2fjbp09IZLK8Qs3+m0+E4qkVkWxp3uR9XUiKjF412OhzjEEscxgTg+MliPt+awyU92jodiqNeGfU2ed/PIn1npq8VZhoeSxzGBODzrTkUFJZwaY+znQ7FUUmtm9EkMtzpMIzDLHEYE4CPN+4lOiqC8zq1dDoUR4WHCd3bRTsdhnGYJQ5jAvDUd8NZHnE3keH2lekZH+t0CMZh9i0wJgAdC+bTqmiv02GEhJ7xMU6HYBxmw3GNKYd3GG58YRE7raXhk5LQAoAWkW1wzXNPBIxvFk/q+FQHozK1yb4NxpQjOz+b9T9fT2pWNkPObeV0OCGji6dK7sjmz5I+LZ30aek2wqqBscRhTAW81xa/tGfDHobrL8LT+vo267CzgRjHWOIwpgJL0n8EaPDzN8ryXfYRThaVOB2GcYAlDmMq8P569ymYNtF2bfHSThaVWIn1BsoShzEV2J6T/9OD2ESYGdvgquJWZN2uw06HYBwQ1MQhIpeJyGYR2SYiM8p4vrGILPQ8/5WIdPQs7ygix0Vknef2V79t+otIumebZ8VbstOYIAjz/3Tdk+6uintPumPxhJI20Y0tcTRQQUscIhIOPA9cDvQAJolIj1Kr3QwcUtXOwGzg937PbVfVPp7b7X7LXwBuBZI9t8uCdQym4VJVABtNVYE+HVpY4miggtniGARsU9UdqnoSWACMK7XOOGCe5/4iYGRFLQgRaQfEqOoqdX+zXwWuqvHITYP3/R73aKorXPEORxK6+iaexc79+ez3XKfENBzBTBztgV1+j7M8y8pcR1WLgFzA+y9ekoh8IyKfisgwv/WzKtknACJym4ikiUhaTk7OmR2JaXDeT3d3ik/+wGV9GuUYlOSu25WWcdDhSExtC9WZ43uARFU9ICL9gbdFpGdVdqCqc4A5AAMGDNAgxGjqIf+LNsUXFjXIK/0FytU+lqjIML7eecjpUEwtC2aLYzfQwe9xgmdZmeuISAQQCxxQ1ROqegBAVdcA24EunvUTKtmnMdWWnZ/Nqxd9Rt73s0jNstnQFWkUEUafDi34OuOA06GYWhbMxLEaSBaRJBFpBEwEFpdaZzEwzXN/PPCJqqqIxHk61xGRTrg7wXeo6h7giIgM9vSF/Bx4J4jHYBqgt77ZTeMIG6keiEFJrdiYbXM5GpqgfTs8fRZ3AanA98C/VPU7EXlMRMZ6Vvsb0EpEtgH3At4hu8OB9SKyDnen+e2q6j2ReifwMrANd0vkg2Adg2mYFn+bzaU9G/YFmyrlmdNy57qrKLETwQ1OUPs4VHUJsKTUskf87hcAE8rY7k3gzXL2mQb0qtlIjfnJ4WOFXNOvPWx2OpIQ5pnL0mh2LzKiJuPCBhA0JNYeN6aU1s0bM6xza6fDqBPC7tnAuLglla9o6pVQHVVlTK3xH0mlhWexNOwXRDz+ow3DDdD557Zix144eqKI5o3tT0pDYC0O0+Bl52eTPi2d+7u+x9FtD9Di5I9WWqQKhnVuTXxhEUMW9GX0otFOh2NqgSUOYzwWrcmi29nRTodR5/TveBapWdlce9YCu6BTA2GJwxjgu+xcvt11mOsHdqh8ZXOKxhHhAHy+1So0NBSWOIwB5n+VSeOIMK7pm1D5yqZMp5SgN/Wa9WQZA7yzLpsxKfHENo10OpQ6LTayDa55LgDim8WTOj7V4YhMMFiLwxjcI4Imn2enqc5EXHRjevMU6dPSSZ+Wbv0d9ZglDmOArm2j6Zd4ltNh1GkXd23DZ5tz7DrkDYAlDtOgrc86DMCkQR2wi0memVE92pJ3ooivd1qZ9frOEodp0NrPHQTAz7+60uFI6r4LOrcmKjKMpd/vdToUE2SWOEyD9WNuAa2K3H/kwo7sqmRtU6HYRJr8v5asaPxLPt6413fpXVM/WeIwDda8lRlOh1B/3JMOM3NpXbSX3YePs+nHPKcjMkFkw3FNg3TsZBHzv8rkAe8CT5lw331TbSLw4YYfnQ7DBJElDtMglfzJxdntwRWZSHyzeJhm8w1qyuCkVkz68gr+3jEKZrus5lc9ZInDNDiFxSU0L8gmOzKR9T9fb6OpatiVveM5O3sfkAi5mU6HY4LA+jhMg/P2Nz9dpt6SRs27vJddPbG+sxaHaVAuXTSaPfnZPJbkOUVlatxZzRo5HYIJMkscpkHZk59N3vezyIiaDDPt3Lsx1RHUU1UicpmIbBaRbSIyo4znG4vIQs/zX4lIR8/yS0RkjYike35e7LfNcs8+13lubYJ5DKb+KC5xzy3o2tauuWHMmQha4hCRcOB54HKgBzBJRHqUWu1m4JCqdgZmA7/3LN8PXKmqLmAa8Fqp7aaoah/PbV+wjsHUL/9emwXAf49MdjiSesw7rNlvSHPu8UIHAzLBEMwWxyBgm6ruUNWTwAJgXKl1xgHzPPcXASNFRFT1G1X1ltb8DmgiIo2DGKup5woKi/nTx1sA+JnLOm+DxjMR0H8I7jvrdlewgamLgpk42gP+dRyyPMvKXEdVi4BcoFWpda4F1qrqCb9lr3hOUz0sNizGBGDelxnsyS0AbCRVbZv/VaaVIKlnQno4roj0xH366r/8Fk/xnMIa5rndUM62t4lImoik5eTYJS0bskP5JxmzbLS7Q9zUuk0/5pH2wyGnwzA1KJiJYzfgf2WcBM+yMtcRkQggFjjgeZwAvAX8XFW3ezdQ1d2en3nAfNynxE6jqnNUdYCqDoiLi6uRAzJ101MfbaY9OWy+PcvpUBqkFk0jeemzHU6HYWpQMBPHaiBZRJJEpBEwEVhcap3FuDu/AcYDn6iqikgL4H1ghqp+4V1ZRCJEpLXnfiQwBtgQxGMwddy3uw7zzoE7cSUlMj71fOILi5wOqcGIbxaPKymR4nP+hy9O3sPO/XZN8voiaInD02dxF5AKfA/8S1W/E5HHRGSsZ7W/Aa1EZBtwL+AdsnsX0Bl4pNSw28ZAqoisB9bhbrG8FKxjMHVbcYny8DsbCIs8TPrOTNKnpZOaF3HaqB8THKnjU0nfmckn16QRFnmYv62wVkd9IQ2h02rAgAGalpbmdBimFo1eNNp3zev4wiJ3wrBie7VvZizMzGXQqxdxXPfTtkk7ll73kdNRmQCJyBpVHVB6uc0cN/VSdn42hdv+wKbwieijh921vo1jvszZR0ReFq4kpyMxNSGkR1UZUx3eGeKNwt0fbxt+6yDPhMCIsDAe6rMCgF0HjzkclDlTljhMvfPiZ+5BeOu5zvoynOY3IfDui90z9md7JmKaussSh6lXvt55kD9+5P7DpI8etn6NENI2JgqAf3+zmzU2r6NOs8Rh6o39R0+QMG8Q2xtNAuwUVahqFxvFI+9s8J1SNHWPdY6beuFkUQl3vr6W3IRIsiPtWhuhKr6wiOz4X3EUGP7PNnwx5T9Oh2SqwRKHqfN8Q2+jIL4Q0qfZ6alQlZoXAbmZ5IS35eLEfezcn09S62ZOh2WqyE5VmTov23Nxplva/5vUrOzKNzDO8XSWxxXvdT9cuI6i4hJGLxqNa54L1zwXoxeNdjhIUxlrcZg6zVsDaW30vbRc8aONoqpj1u06zNMfbSE7P9vXUnTNczkclamMJQ5TZ839YidPLvme6O7QsvBH97BPU2fEN4snu/sMXt8HLSLbOh2OqQJLHKZO8S8lAhDdHdo1iwcynQvKVEvq+FROFpUw+aVVbMjOZd2uw/Tp0MLpsEwArI/D1CnZ+dmk78zkgx3HGN30H6yd+i0fjU91OixTTY0iwnhhan/aREcx7e9fs+nHI06HZAJgicPUGT96ruDXsWA+CbKfp8anEBluH+E6bbaLuD+24ZPwu4iKDGPqy187HZEJgH3rTJ2wbNM+xjz3OQB/mdwXsAl+9UJuJszMJSIsjK9OXsu7RbcDsHL7AYcDMxWxPg4T0g4fO8lj723k32t307VtNNnAmJR4+I+7eJ6PjaaqWzzFD32/N09pmHYzY4FEbvjbVzz4s+7cNLSj/YMQgixxmJBUWFzC66t+4NlPtnHkeCH/fXFnfnFxZwa87lnBalDVbZX8/lY1/RWtl+6FpVAc04Hwe+1Cn6HEEocJKSeKinnnm2yeTJ9KSfhBSIRzC4u497sIuNSSRb0Xm0h8YREXdWgM/NSKjHl9JJ9O/JgI69MKCZY4TEjYk3ucN9dkMWfnzWjEIcKlJc+e9x8uWpDM6F6DcUVmwzwX8cVOR2qC6p50/MfI7cg5Sqfn2+NKgktmf8YvRyYzJqWdJRCHWeIwjtl3pIDlm3NY/G02X2zfjypEdz/E/53/CRd0bu07t51qw20brE5xzdHYDgAsyL+V8xY+wyNrJ6ERh2jTpB3/scvQOsISh6k1OXkn+CbzEGszD7NiWw4bdrvH7Md0+QPNux0EIL4YhiXHORmmCTFyzwbiF41mVMdsoplBpLbi4KZZlHSa5StP0jrqbFKvTaVRhLVEakNQE4eIXAb8GQgHXlbVWaWebwy8CvQHDgDXq2qG57kHgZuBYuC/VTU1kH0aZxUVl5Bz9ATZh4+zfV8+2/cfZfu+fB7PmEg7zeGPCfFkR0ZADETHuLdp1yye1A3uYZnMdtloKXOa1PGp7s+Fp6zMroPHWJLejY827mVt5iFKOs2i/+u9AWgaFsc9XeeS3Daac+OaEdsk0kZm1TBRDc7FVEQkHNgCXAJkAauBSaq60W+dO4EUVb1dRCYCV6vq9SLSA/gnMAiIB5YCXTybVbjPsgwYMEDT0tJq9Phqmvf34P11aOnlvsfe509dn3KeD2ifJXCyuISTxSUUFrl/niwqIfmfQ2h8dDcFzdrz5ZXLOHaymLyCIvIKCjly3P0zr6CI3OOF7M0rYO+RE7x18r9IkP2MTEhgX+Tp//21anw2H177IVF/6eMewx+b6KmYGmu1pkzFZrvcn5lyHG50NtNi/sb2qN8gkYcoOdmC/O0z+KLxf9Ne9pMT3pYnkxfSomkjYqIiiGkS6b5FRRIVGUbjiHAaR4bROMJzP8J9PyI8jDBxzxsKDxPCBMJEPDcIfzYFyd3102e5HhGRNao64LTlQUwcQ4CZqjra8/hBAFX9X791Uj3rrBSRCOBHIA6Y4b+udz3PZhXusyzVTRy3v7aGz7bmlPvH2vfOVfK8/3tcOgGEsoyoyXQsmO/76a9Z51mERR4ud9v4wiLmXJ3GOc/FV5wQvH8M6uGXztSyUolltLd1W03exAPQ7NxZhDU6fNpyOPV70vnkPxEBwd3CaZT0v0jkIbTwLE7ufBDKafiU1x4qr6Ek5WxR1vrv3n0B58Y1L+cVKlZe4gjmqar2wC6/x1nAeeWto6pFIpILtPIsX1Vq2/ae+5XtEwARuQ24zfPwqIhsrsYxALQG9ldz21BTpWNxfwbH+H5WxQag462eD+vvAjlNsAHuDfh0QoP9nYS4EDuWM6p75TmW8j73Py0/9XtyRQW7/PxM4qmu1p0fP6PfyTllLay3neOqOgeYc6b7EZG0sjJuXVRfjqW+HAfYsYSq+nIswTqOYA5B2A108Huc4FlW5jqeU1WxuDvJy9s2kH0aY4wJomAmjtVAsogkiUgjYCKwuNQ6i4FpnvvjgU/U3SGwGJgoIo1FJAlIBr4OcJ/GGGOCKGinqjx9FncBqbiHzv5dVb8TkceANFVdDPwNeE1EtgEHcScCPOv9C9gIFAG/UNVigLL2Gaxj8Djj010hpL4cS305DrBjCVX15ViCchxBG1VljDGmfrJplsYYY6rEEocxxpgqscRRDhGZICLfiUiJiAzwW95RRI6LyDrP7a9OxlmZ8o7D89yDIrJNRDaLyGinYqwOEZkpIrv9fg8/czqmqhKRyzzv/TYRmVH5FqFLRDJEJN3zuwjtMg1+ROTvIrJPRDb4LWspIh+LyFbPz7OcjDFQ5RxLUL4nljjKtwG4BvisjOe2q2ofz+32Wo6rqso8Dk9Zl4lAT+Ay4P88ZWLqktl+v4clTgdTFZ73+nngcqAHMMnzO6nLLvL8LurS/Ie5uD///mYA/1HVZOA/nsd1wVxOPxYIwvfEEkc5VPV7Va3ubPOQUcFxjAMWqOoJVd0JbMNdG8zUjkHANlXdoaongQW4fyemFqnqZ7hHdPobB8zz3J8HXFWbMVVXOccSFJY4qidJRL4RkU9FZJjTwVRTWSVh2pezbqi6S0TWe5rodeJ0gp/68P77U+AjEVnjKfdTl7VV1T2e+z8CbZ0MpgbU+PekQScOEVkqIhvKuFX0n98eIFFV+wL3AvNFJKZ2Ii5bNY8j5FVyXC8A5wJ9cP9O/uhkrIYLVLUf7lNvvxCR4U4HVBM8E5Lr8pyFoHxP6m2tqkCo6qhqbHMCOOG5v0ZEtuMu+e5Yh2B1joM6UL4l0OMSkZeA94IcTk0L+fe/KlR1t+fnPhF5C/epuLL6B+uCvSLSTlX3iEg7YJ/TAVWXqu713q/J70mDbnFUh4jEeTuRRaQT7nIoO5yNqlrKK+tSJ3i+0F5X4x4EUJfUm/I5ItJMRKK994FLqXu/D3/+pZCmAe84GMsZCdb3pEG3OCoiIlcDz+G+Psj7IrLOcx2Q4cBjIlIIlAC3q2qtdEhVR3nHUVFZlzriDyLSB/dphAzgvxyNporKK8njcFjV1RZ4S9wXg4gA5qvqh86GFBgR+ScwAmgtIlnAo8As4F8icjPwA3CdcxEGrpxjGRGM74mVHDHGGFMldqrKGGNMlVjiMMYYUyWWOIwxxlSJJQ5jjDFVYonDGGNMlVjiMMYYUyWWOIwxxlSJJQ5jHCAiy0TkEs/9J0TkOadjMiZQNnPcGGc8irsCQRugLzDW4XiMCZjNHDfGISLyKdAcGKGqeU7HY0yg7FSVMQ4QERfQDjhpScPUNZY4jKllnoqlr+O+0txRESnrcp/GhCxLHMbUIhFpCvwb+B9V/R54HHd/hzF1hvVxGGOMqRJrcRhjjKkSSxzGGGOqxBKHMcaYKrHEYYwxpkoscRhjjKkSSxzGGGOqxBKHMcaYKvn/25I+d4LMJ6gAAAAASUVORK5CYII=\n", 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\n", 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" ] From b65570de7351cc46420add867ad6e3c121e5e0cf Mon Sep 17 00:00:00 2001 From: Martin Kilbinger Date: Thu, 6 Oct 2022 09:47:40 +0200 Subject: [PATCH 5/5] fixed typos --- importance_sampling.ipynb | 21 ++++++++++++++------- 1 file changed, 14 insertions(+), 7 deletions(-) diff --git a/importance_sampling.ipynb b/importance_sampling.ipynb index 54ed599..5f9ae56 100644 --- a/importance_sampling.ipynb +++ b/importance_sampling.ipynb @@ -56,7 +56,11 @@ "id": "578fec40-49d4-419f-bef9-2b286af2c591", "metadata": {}, "source": [ - "This is illustrated in the following example. We pick uniformly drawn random points $x_i$\n", + "This is illustrated in the following example.\n", + "\n", + "The goal is to estimate the grey area under the curve.\n", + "\n", + "We pick uniformly drawn random points $x_i$\n", "and compute the area of the rectangle between $a = -2$ and $b = 5$, which is $(b - a) f(x_i)$.\n", "\n", "An (unbiased) estimate of the grey area is the average of all rectangles, which is the above equation.\n", @@ -90,7 +94,10 @@ "\n", "$$F \\approx \\frac 1 N \\sum_{i=1}^N f(y_i)$$\n", "\n", - "with random points $y_i$ drawn from the distribution $p$, $y \\sim p$." + "with random points $y_i$ drawn from the distribution $p$, $y \\sim p$.\n", + "\n", + "Note that the distribution $p$ is not evaluated in the sum. It only serves as a kind of\n", + "weight. The density of sample points $y_i$ is proportional to this weight. " ] }, { @@ -155,7 +162,7 @@ "\n", "$$\\bar x \\approx \\frac 1 N \\sum_{i=1}^N x_i.$$\n", "\n", - "Another example: To plot the 2D $68\\%$ credible region (contour), pixelise $p$ in 2D, sort the pixels by density (= number of sample points in each pixel), and set $f = 1$ in the first $68\\%$ of pixels, and $0$ for the remaining pixels." + "Another example: To plot the 2D $68\\%$ credible region (contour), pixelise yout prior range in 2D. (Ignoring further dimensions is equivalent of marginalising over those dimensions.) Then sort the pixels by density (= number of sample points in each pixel), and set $f = 1$ in the first $68\\%$ of pixels, and $0$ for the remaining pixels, and plot $f$." ] }, { @@ -185,7 +192,7 @@ "source": [ "This integral can be estimated with samples under $q$ instead of $p$,\n", "\n", - "$$y \\sim q,$$\n", + "$$x \\sim q,$$\n", "\n", "if the samples are multiplied by the importance weights\n", "\n", @@ -193,7 +200,7 @@ "\n", "since\n", "\n", - "$$ \\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x) \\approx \\frac 1 N \\sum_{i=1}^N w_i f(y_i).$$" + "$$ \\int {\\rm d} x \\, p(x) f(x) = \\int {\\rm d} x \\, q(x)\\frac{p(x)}{q( x)} f(x) \\approx \\frac 1 N \\sum_{i=1}^N w_i f(x_i).$$" ] }, { @@ -201,7 +208,7 @@ "id": "1c4385ad-ebf0-43bf-a937-09a7f149b7d9", "metadata": {}, "source": [ - "Importance sampling can be useful if sampling under $p$ is very time-consuming of difficult, but evaluating $p$ at points $x_i$ is not. One then choses a simple proposal function $q$, e.g. a (multi-variate) normal.\n", + "Importance sampling can be useful if sampling under $p$ is very time-consuming of difficult, but evaluating $p$ at points $x_i$ is not. One then chooses a simple proposal function $q$, e.g. a (multi-variate) normal.\n", "\n", "Importance sampling permits to separate sampling (fast; under $q$) and evaluating the original posterior (potentiall slow, but can now be done in parallel using the already sampled points $x_i$)." ] @@ -227,7 +234,7 @@ "\n", "$$\\int {\\rm d} x p_{\\rm comb} f(x) = \\int {\\rm d} x \\pi(x) L(x) L_2(x) f(x)$$\n", "\n", - "has a form similar to the modified one above, if we identify\n", + "has the same form to the modified one above, if we identify\n", "\n", "$$q(x) = \\pi(x) L(x) \\quad \\mbox{and} \\quad L_2(x) = \\frac{p(x)}{q(x)}.$$" ]