diff --git a/Notebooks/Lecture1.ipynb b/Notebooks/Lecture1.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..cdff2cf722793dcc733cc63f615f4b656780884f --- /dev/null +++ b/Notebooks/Lecture1.ipynb @@ -0,0 +1,1887 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\t\n", + "\t\n", + "# part 1\n", + "\t\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "3c152b43", + "metadata": { + "collapsed": false, + "id": "44427C9739024026A4C897D8E6AD79B8", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "
\t\n", + "\t\n", + "# 高级心理统计[Advanced Statistics in Psychological Science]\n", + "## 《贝叶斯统计及其在Python中的实现》 [Bayesian inference in Python]\n", + "## Instructor： 胡传鹏（博士）[Dr. Hu Chuan-Peng]\n", + "### 南京师范大学心理学院[School of Psychology, Nanjing Normal University]\n", + "\t\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "d2b325df", + "metadata": { + "collapsed": false, + "id": "3838D48714B2463C83EF78BDC23758C7", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "
\n", + "\t\n", + "研究人类心理与行为的规律，容易吗？\n", + "\t\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "ef4b6d7c", + "metadata": { + "collapsed": false, + "id": "722B560AB14C42FEAFA907AC6DC6D292", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "## Outlines\n", + "* 1. 为什么要学习本课程 [Why Bayesia inference]\n", + "* 2. 本课程的内容将是什么 [What is the syllabus]\n", + "* 3. 如何学好这门课[How can I learn this course well]" + ] + }, + { + "cell_type": "markdown", + "id": "51c6ff3f-2c30-4f57-b1e4-7f8c30caca4d", + "metadata": { + "id": "9CD453483FDF4EAC8BD652AF2DE6812D", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "## 1. 为什么要学习本课程 [Why Bayesia inference]\n", + "\n", + "### 1.1 为什么心理学需要更好的方法【Why does psychological science need better methods?]\n", + "\n", + "#### 原因1: 复杂的研究问题" + ] + }, + { + "cell_type": "markdown", + "id": "4fa75bb6-a4cf-49c8-a932-87abca98af37", + "metadata": { + "collapsed": true, + "id": "0D3A4878173746D7ADD25C7A3A15B2A9", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "![Image Name](https://cdn.kesci.com/upload/image/rhdcyu860w.gif?imageView2/0/w/960/h/960)\n", + "\n", + "\n", + "Source: https://www.science.org/toc/science/309/5731" + ] + }, + { + "cell_type": "markdown", + "id": "e5e145de", + "metadata": { + "collapsed": false, + "id": "675C0668AAD748039C048C541A141B6E", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "Q1: What is the Uiverse Made of [physics ]\n", + "\n", + "Q2: What is the Biological Basis of Consciouness [psychological science]" + ] + }, + { + "cell_type": "markdown", + "id": "1c9f54a6-6401-4a02-8195-c715fd3d44db", + "metadata": { + "collapsed": false, + "id": "38E2EDC2C3A54F15BBBF28A25F9CDD68", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 问题\n", + "同样重要和复杂的问题，是否意味着类似复杂和高级的方法？" + ] + }, + { + "cell_type": "markdown", + "id": "ee3d9074-24f5-45b2-90b4-68f5cf5031b9", + "metadata": { + "id": "7D43885A2D07479C96006E7E12D9EEF7", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 物理学中的方法 [Methods in Physics]:\n", + "\n", + "Example 1: Webb telescope (韦伯望远镜) [**equipment**]" + ] + }, + { + "cell_type": "markdown", + "id": "286968e3", + "metadata": { + "collapsed": true, + "id": "CC7CD6845ED3486EBD8D258473C50753", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "![Image Name](https://cdn.kesci.com/upload/image/rhdd0r46k3.png?imageView2/0/w/720/h/640)\n" + ] + }, + { + "cell_type": "markdown", + "id": "aa0b7267", + "metadata": { + "collapsed": false, + "id": "4291074DF34847E29D0CE63EF1680A94", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "Example 2: Big-team science (CERN, the European Organization for Nuclear Research) [**equipment & practices**]\n", + "\n", + "Example 3: **Mathematics**" + ] + }, + { + "cell_type": "markdown", + "id": "e5aaf896-93ba-4eec-aa33-8f20d01c7501", + "metadata": { + "id": "58FA36357F4343D38B6AF90BDD4AE2F5", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 其他研究人类智能的领域所采用的方法 [Methods in other fields that also study \"intelligence\"]\n", + "\n", + "**AI**\n", + "\n", + "\n", + "![Image Name](https://cdn.kesci.com/upload/image/rhdd1sr5y2.png?imageView2/0/w/640/h/640)\n" + ] + }, + { + "cell_type": "markdown", + "id": "25c0a697-6d3c-4ba1-87a1-4e751ac78a49", + "metadata": { + "collapsed": false, + "id": "8CC769416F0048BCA9800D597430F7A1", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 心理科学的研究方法 [What do psychological scientists have?]\n", + "你们能够想到的研究方法包括哪些？" + ] + }, + { + "cell_type": "markdown", + "id": "22c0a59f-75cd-438d-b6d6-e57387dc272b", + "metadata": { + "collapsed": true, + "id": "8ABBBA8C18E64A60BBD994839DBBB954", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "![Image Name](https://cdn.kesci.com/upload/image/rhdd2dgwc8.png?imageView2/0/w/640/h/640)\n" + ] + }, + { + "cell_type": "markdown", + "id": "c705f696", + "metadata": { + "id": "3EB4A250D8EA460C91E69DDE129F456C", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "**实证研究：**\n", + "* 质性研究\n", + "* 观察法\n", + "* 问卷\n", + "* 行为实验\n", + "* 眼动、生理数据记录\n", + "* EEG/ERP/MEG\n", + "* fMRI/PET/fNIRs\n", + "* TMS/tDCS\n", + "* ..." + ] + }, + { + "cell_type": "markdown", + "id": "ef08f1c3", + "metadata": { + "id": "1099CD2609B14FC98B9199570CB1EC90", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "**统计方法：**\n", + "* t-test\n", + "* ANOVA\n", + "* Correlation\n", + "* Structural equation model (SEM)\n", + "* ?" + ] + }, + { + "cell_type": "markdown", + "id": "b2deedd2", + "metadata": { + "id": "B9CD0257490C4D7EAD946F808396794B", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 相关方法课程：\n", + "* 心理测量\n", + "* 心理统计（包括SPSS等）\n", + "* 实验心理学（包括Eprime等）\n", + "* ？" + ] + }, + { + "cell_type": "markdown", + "id": "f64c2e5f", + "metadata": { + "id": "3EFA113998AB4146A01BCFEB310DE280", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "* 更好的仪器\n", + "* **更好的统计/数据分析**\n", + "* 更好的实践 (e.g., big-team science)" + ] + }, + { + "cell_type": "markdown", + "id": "52bbc6a2-f165-4c3e-9792-ca81cc8ca423", + "metadata": { + "id": "7E33B6BBE590490F912D1DC3F2A9EBDB", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 原因2: 更复杂的数据\n", + "\n", + "* 数据字化的时代，大数据\n", + "* 神经成像/生理数据\n", + "* 多模态的数据融合" + ] + }, + { + "cell_type": "markdown", + "id": "e0c9551d", + "metadata": { + "id": "2278FC4931A74B4CA1F993CB92E42D6F", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "### 1.2 确实有更好的统计方法" + ] + }, + { + "cell_type": "markdown", + "id": "6e127fb1", + "metadata": { + "id": "584D67832525481E99EAAAF215C39F42", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "贝叶斯统计 (Bayesian inference)\n", + "\n", + "\n", + "![Image Name](https://cdn.kesci.com/upload/image/rhdf3bb12c.png?imageView2/0/w/640/h/640)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "1ed0f312", + "metadata": { + "id": "963D62D14B5E484B8D354DDDB717CD69", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "* 灵活/强大/能用\n", + "* 易用\n", + "* 可拓展性强\n", + "* 方便交流\n", + "* ..." + ] + }, + { + "cell_type": "markdown", + "id": "ec099ac3", + "metadata": { + "id": "A47CEFD8018F4137A9EEFB9FA524E8F6", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 灵活/强大/通用\n", + "\n", + "不需要解析解\n", + "\n", + "贝叶斯分析在多个学科中得到广泛应用，尤其是AI" + ] + }, + { + "cell_type": "markdown", + "id": "00bad60c-8aca-44a7-afa6-4ef626c5d4a6", + "metadata": { + "id": "99BAB33F937C4C3AA1248EDD7C2AA43E", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### （相对）易用\n", + "\n", + "概率编程语言(Probabilistic Programming Languages)的发展和普及\n", + "\n", + "\n", + "PPLs: *computational languages for statistical modeling*\n", + "\n", + "* PyMC\n", + "* Stan\n", + "* NumPyro\n", + "* Pyro\n", + "* BUGS\n", + "* ..." + ] + }, + { + "cell_type": "markdown", + "id": "e5a52f7f-6654-4158-b4f4-1a07f5051035", + "metadata": { + "collapsed": true, + "id": "7224C81362ED40E88884DB9A2541A17D", + "jupyter": {}, + "mdEditEnable": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "大部分情况下，开发者使用它可以轻松地定义概率模型，然后程序会自动地求解模型。\n", + "\n", + "\n", + "![Image Name](https://cdn.kesci.com/upload/image/rhdf4r9fbh.png?imageView2/0/w/640/h/640)\n", + "\n", + "\n", + "Source: https://towardsdatascience.com/intro-to-probabilistic-programming-b47c4e926ec5\n" + ] + }, + { + "cell_type": "markdown", + "id": "bfac15b7-da82-4018-b5ee-8119494f4dd2", + "metadata": { + "id": "7EF6CC6C622D4508B6030A2CFFE11B92", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 可拓展\n", + "\n", + "贝叶斯概念已经应用到以深度学习为中心的新技术的发展，包括深度学习框架(TensorFlow, Pytorch)，创建表示能力更强、数据驱动的模型" + ] + }, + { + "cell_type": "markdown", + "id": "b906104e", + "metadata": { + "id": "F96BC6BE697740AFAAE1152721DB15E6", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "##### 方便交流\n", + "大部分PPLs都有类似的数据结构，但是不同的学科使用的语言不同。\n", + "\n", + "心理学/社会科学/神经科学：\n", + "* **PyMC3**\n", + "* Stan\n", + "* BUGS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\t\n", + "\t\n", + "# part 2\n", + "\t\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "B1CD9D9075E8417B8A12276281A87272", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "### 例1：社会关系地位与幸福感的关系\n", + "\n", + "实例的数据来自[ Many Labs 2 项目](osf.io/uazdm/)中的一个研究。\n", + "\n", + "该研究探究了社会关系地位对于幸福感的影响 “Sociometric status and well-being”， (Anderson, Kraus, Galinsky, & Keltner, 2012)。\n", + "\n", + "该数据集包括6905个被试的数据。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "84B17C132F804024858A286483EAFD88", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (theano.link.c.cmodule): install mkl with `conda install mkl-service`: No module named 'mkl'\n" + ] + } + ], + "source": [ + "# import modules\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import pymc3 as pm\n", + "import xarray as xr\n", + "\n", + "%config InlineBackend.figure_format = 'retina'\n", + "az.style.use(\"arviz-darkgrid\")\n", + "rng = np.random.default_rng(1234)\n", + "\n", + "import matplotlib\n", + "matplotlib.rcParams['figure.figsize'] = [4, 3]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "75694A4449E849718D46562560D4A45A", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [], + "source": [ + "# 导入数据\n", + "SMS_data = pd.read_csv('/home/mw/input/Bayesian3285/data_chp1_SMS_Well_being.csv')[['uID','variable','factor','Country']]\n", + "\n", + "# 把数据分为高低两种社会关系的地位的子数据以便画图与后续分析\n", + "plot_data = [\n", + " sorted(SMS_data.query('factor==\"Low\"').variable[0:3000]),\n", + " sorted(SMS_data.query('factor==\"High\"').variable[0:3000])]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "62D3505AFED84C6491DD5CD6DEEBE5CD", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 通过画图对于两种社会关系地位对幸福感的影响\n", + "\n", + "图中横坐标代表高低两种社会关系地位，纵坐标代表了主观幸福感评分。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "E3425865C50D4CBB81E3B30E2895C3C4", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [], + "source": [ + "# import matplotlib\n", + "# a = sorted([f.name for f in matplotlib.font_manager.fontManager.ttflist])\n", + "\n", + "# for i in a:\n", + "# print(i)\n", + "\n", + "# 字体样式\n", + "font = {'family' : 'Source Han Sans CN'}\n", + "# 具体使用\n", + "plt.rc('font',**font)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "59C5972D76C34D0CB9137A7B46DD0154", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:45: UserWarning: This figure was using constrained_layout, but that is incompatible with subplots_adjust and/or tight_layout; disabling constrained_layout.\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 画图对比两种社会地位对幸福感的影响\n", + "def adjacent_values(vals, q1, q3):\n", + " upper_adjacent_value = q3 + (q3 - q1) * 1.5\n", + " upper_adjacent_value = np.clip(upper_adjacent_value, q3, vals[-1])\n", + "\n", + " lower_adjacent_value = q1 - (q3 - q1) * 1.5\n", + " lower_adjacent_value = np.clip(lower_adjacent_value, vals[0], q1)\n", + " return lower_adjacent_value, upper_adjacent_value\n", + "\n", + "def set_axis_style(ax, labels):\n", + " ax.xaxis.set_tick_params(direction='out')\n", + " ax.xaxis.set_ticks_position('bottom')\n", + " ax.set_xticks(np.arange(1, len(labels) + 1), labels=labels)\n", + " ax.set_xlim(0.25, len(labels) + 0.75)\n", + " ax.set_xlabel('社会关系地位')\n", + "\n", + "fig, ax1 = plt.subplots(nrows=1, ncols=1, figsize=(9, 4), sharey=True)\n", + "\n", + "parts = ax1.violinplot(\n", + " plot_data, showmeans=False, showmedians=False,\n", + " showextrema=False)\n", + "\n", + "for pc in parts['bodies']:\n", + " pc.set_facecolor('#D43F3A')\n", + " pc.set_edgecolor('black')\n", + " pc.set_alpha(1)\n", + "\n", + "quartile1, medians, quartile3 = np.percentile(plot_data, [25, 50, 75], axis=1)\n", + "whiskers = np.array([\n", + " adjacent_values(sorted_array, q1, q3)\n", + " for sorted_array, q1, q3 in zip(plot_data, quartile1, quartile3)])\n", + "whiskers_min, whiskers_max = whiskers[:, 0], whiskers[:, 1]\n", + "\n", + "inds = np.arange(1, len(medians) + 1)\n", + "ax1.scatter(inds, medians, marker='o', color='white', s=30, zorder=3)\n", + "ax1.vlines(inds, quartile1, quartile3, color='k', linestyle='-', lw=5)\n", + "ax1.vlines(inds, whiskers_min, whiskers_max, color='k', linestyle='-', lw=1)\n", + "\n", + "# set style for the axes\n", + "labels = ['低','高']\n", + "plt.xticks(np.arange(2)+1, labels)\n", + "plt.xlabel('社会关系地位')\n", + "plt.ylabel('幸福感')\n", + "\n", + "plt.subplots_adjust(bottom=0.15, wspace=0.05)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "D161E5B1ECE1430D9CCABC74C9FEF64C", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 通过t检验，分析两种社会关系地位下幸福感的差异\n", + "\n", + "结果发现，两种社会关系水平下被试的主观幸福感边缘显著，*t*(6903) = -1.76, p = .08。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "2174B974752E40D4AB61ACB340D8B1C0", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "低社会关系：0.014 ± 0.66； 高社会关系：-0.014 ± 0.67\n" + ] + }, + { + "data": { + "text/plain": [ + "Ttest_indResult(statistic=1.7593310889762195, pvalue=0.07856558333862036)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import stats\n", + "SMS_low = SMS_data.query('factor==\"Low\"').variable.values\n", + "SMS_high = SMS_data.query('factor==\"High\"').variable.values\n", + "print(\n", + " f\"低社会关系：{np.around(np.mean(SMS_low),3)} ± {np.around(np.std(SMS_low),2)}；\",\n", + " f\"高社会关系：{np.around(np.mean(SMS_high),3)} ± {np.around(np.std(SMS_high),2)}\")\n", + " \n", + "stats.ttest_ind(\n", + " a= SMS_low,\n", + " b= SMS_high, \n", + " equal_var=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "D6D5A5DD5EE14EAD8785CF9AD1A07EC6", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 通过贝叶斯推断替代*t*检验\n", + "\n", + "零假设显著性检验（Null hypothesis significance test, NHST）的框架之下，*t*检验只提供了一个二分的结果：拒绝或者无法拒绝$H_0$。 但 *p* = 0.078这样的结果无法支持$H_0$\n", + "\n", + "贝叶斯推断是否可以带来不一样的结果？\n", + "\n", + "一个简单的线性模型：\n", + "\n", + "1. 通过建立线性模型去替代原本的*t*检验模型。\n", + "\n", + "2. 通过PyMC对后验进行采样\n", + "\n", + "3. 通过Arviz对结果进行展示，辅助统计推断" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "3461187F468F46DBB18F8C3F4C3EE76C", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [], + "source": [ + "# 通过pymc建立基于贝叶斯的线性模型\n", + "x = pd.factorize(SMS_data.factor)[0] # high为0，low为1\n", + "\n", + "with pm.Model() as linear_regression:\n", + " sigma = pm.HalfCauchy(\"sigma\", beta=2)\n", + " β0 = pm.Normal(\"β0\", 0, sigma=5)\n", + " β1 = pm.Normal(\"β1\", 0, sigma=5)\n", + " x = pm.Data(\"x\", x)\n", + " # μ = pm.Deterministic(\"μ\", β0 + β1 * x)\n", + " pm.Normal(\"y\", mu=β0 + β1 * x, sigma=sigma, observed=SMS_data.variable)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "105F06D55D5542ABB329490BCD2F22D7", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "可以通过pymc自带的可视化工具将模型关系可视化。\n", + "\n", + "x 为自变量，其中1为低社会关系，0为高社会关系。\n", + "\n", + "参数 $\\beta0$ 是线性模型的截距，而 $\\beta1$ 是斜率。\n", + "\n", + "截距代表了高社会关系地位被试的幸福感；而截距加上斜率表示低社会关系地位被试的幸福感。\n", + "\n", + "参数$sigma$是残差，因变量$y$即主观幸福感。\n", + "\n", + "模型图展示了各参数通过怎样的关系影响到因变量。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "BECEC5A3264F49F59EF4D89F47F57785", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.model_to_graphviz(linear_regression)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "27050DEF12FD4AAEB72B694ECA3DA602", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [β1, β0, sigma]\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 6 seconds.\n" + ] + } + ], + "source": [ + "# 模型拟合过程 (mcmc采样过程)\n", + "with linear_regression:\n", + " idata = pm.sample(2000, tune=1000, target_accept=0.9, return_inferencedata=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "4E09582EC9134F1C95875C19D60B3494", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 参数的后验分布\n", + "这里的模型分析结果展示了各参数的分布(后验)情况" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "E54DEC474F6049F89408157C78B15D7D", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_trace(idata);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "9C2986E309324D9BAE4DE77FDA3B7090", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "下图反应了参数β1的可信度，即两个社会关系下幸福感差异的可信度。\n", + "\n", + "结果显示，两个社会关系下幸福感差异的可信度为96%。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "2E8C5D580A384AB5A8F2F85A8F765460", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(0.960125)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "(idata.posterior.β1 > 0).mean().values" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "F500A43067C4488F94A672EB6A77BE57", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_posterior(idata, var_names=['β1'], kind='hist',ref_val=0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "3E302511A7FB4C0E8BFBD80013CBCA5E", + "jupyter": {}, + "notebookId": "630c7d9f30feb16a92822876", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "az.plot_posterior(idata, var_names=['β1'], kind='hist', rope = [-0.1, 0.1], hdi_prob=.95)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "B533467B3553473BB862E806B5830837", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 模型诊断\n", + "\n", + "通过模型思维进行数据分析需要注意模型检验，即检验模型是否能有效的反应数据的特征。" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "303C9F7A2BD142B69A945635458C4401", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "下表格为模型参数的基本信息：\n", + "\n", + "mean和sd 为各参数的均值和标准差；\n", + "hdi 3%-97% 为参数分布的可信区间；\n", + "msce mean和sd 为mcmc采样标准误统计量的均值和标准差；\n", + "ess bulk和tail 反应了mcmc采样有效样本数量相关性能；\n", + "r hat 为参数收敛性的指标。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "CA789587B08D4E828FD0598C0B45A171", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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meansdhdi_3%hdi_97%mcse_meanmcse_sdess_bulkess_tailr_hat
β0-0.0140.011-0.0340.0080.00.04233.04505.01.0
β10.0280.016-0.0020.0580.00.04381.04873.01.0
sigma0.6610.0060.6500.6710.00.04904.04846.01.0
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" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "β0 -0.014 0.011 -0.034 0.008 0.0 0.0 4233.0 4505.0 \n", + "β1 0.028 0.016 -0.002 0.058 0.0 0.0 4381.0 4873.0 \n", + "sigma 0.661 0.006 0.650 0.671 0.0 0.0 4904.0 4846.0 \n", + "\n", + " r_hat \n", + "β0 1.0 \n", + "β1 1.0 \n", + "sigma 1.0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.summary(idata)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "A4F6079034BB4F4B8F8F8D27C8E8384F", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "### 后验预测检验 ppc (posterior predictive check)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "185D0307378F4B5B8CCE748A6655D9A7", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with linear_regression:\n", + " pm.set_data({\"x\": np.array([0,1])})\n", + " ppc_y = pm.sample_posterior_predictive(idata, var_names=[\"y\"],keep_size=True)[\"y\"] # keep size不是data的size 而是mcmc的size" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "id": "D27A38FFC2E14DE7AE59DED2B16E366B", + "jupyter": {}, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:30: UserWarning: This figure was using constrained_layout, but that is incompatible with subplots_adjust and/or tight_layout; disabling constrained_layout.\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "labels = ['低', '高']\n", + "obs_low = SMS_data.query('factor==\"Low\"').variable\n", + "obs_high = SMS_data.query('factor==\"High\"').variable\n", + "ppc_y2 = [j for i in ppc_y for j in i]\n", + "ppc_low = [i[1] for i in ppc_y2]\n", + "ppc_high = [i[0] for i in ppc_y2]\n", + "# reg_post = idata.posterior.stack(chain_draw=(\"chain\", \"draw\"))\n", + "# ppc_x = np.repeat([0,1],len(reg_post.sigma)/2)\n", + "# ppc_y = reg_post['β0'] + reg_post['β1']*ppc_x\n", + "# ppc_low = ppc_y[ppc_x==1].values\n", + "# ppc_high = ppc_y[ppc_x==0].values\n", + "\n", + "fig, ax = plt.subplots()\n", + "part1 = ax.violinplot(\n", + " [list(obs_low),list(obs_high)], \n", + " [1,4], points=100, widths=0.3, \n", + " showmeans=True, showextrema=True, showmedians=True)\n", + "part2 = ax.violinplot(\n", + " [list(ppc_low),list(ppc_high)], \n", + " [2,5], points=100, widths=0.3, \n", + " showmeans=True, showextrema=True, showmedians=True)\n", + "part1['bodies'][0].set_label('观测数据')\n", + "part2['bodies'][0].set_label('预测数据')\n", + "# Add some text for labels, title and custom x-axis tick labels, etc.\n", + "ax.set_ylabel('幸福感')\n", + "ax.set_title('Posterior predictive check')\n", + "plt.xticks([1.5,4.5], labels)\n", + "ax.legend()\n", + "\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "BAB9CCCD2FF146C7BC6AD1BC5620C2C7", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "### 例2: 贝叶斯推断在认知模型中的应用" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "E9BB887BEC8B4E57A2A4CDD0E593140B", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "在实验数据的收集时，研究者往往会采集个体反应的正确率与反应时。\n", + "\n", + "而传统分析方法并不能同时对两种数据进行分析，从而推断潜在的认知机制。比如，个体是否愿意牺牲更多的反应时间去获得一个更准确的判断。\n", + "\n", + "认知模型能有效的弥补这一问题，比如 drift-diffusion model, DDM。" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "9EE8BDEF0D5E469BA39B4207CBD1943D", + "jupyter": {}, + "mdEditEnable": false, + "notebookId": "630abaa16bfce48b61ae22ae", + "scrolled": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "![DDM1](https://cdn.kesci.com/upload/image/rhb2957an5.png?imageView2/0/w/960/h/960)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\t\n", + "\t\n", + "# part 3\n", + "\t\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "id": "902790CE7702411FAE6FEDCD1778F265", + "jupyter": {}, + "scrolled": true, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "# 高级心理统计[Advanced Statistics in Psychological Science]\n", + "## 《贝叶斯统计及其在Python中的实现》 [Bayesian inference in Python]\n", + "## Instructor： 胡传鹏（博士）[Dr. Hu Chuan-Peng]\n", + "### 南京师范大学心理学院[School of Psychology, Nanjing Normal University]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "69BF69EFF2354118980B461AA8F07618", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "# 2. 课程内容\n", + "### 2.0 课时\n", + "8.29 ～ 12.30，18周\n", + "\n", + "### 2.1 教学目标：\n", + "\n", + "（1）理解贝叶斯推断的基本原理；\n", + "\n", + "（2）了解PyMC3的语法和结构；\n", + "\n", + "（3）可以使用PyMC3解决相对简单的统计推断问题（如层级线性模型）" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ADF7B6A407A74D0E88F39365B6E8AA7D", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "### 2.2 考核方式：\n", + "\n", + "#### 考勤\n", + "10%\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8F0E5620697843FBA1FBC610A0098A91", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 小作业\n", + "45%\n", + "\t\n", + "（1）简单的代码作业 notebook\n", + "\t\n", + "（2）概念理解 notebook\n", + "\t\n", + "（3）workflow notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3CA761A93F8A494B9F2FD03788586D9D", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 大作业：\n", + "真实的数据分析 45%\n", + "* 合作完成\n", + "* 包括代码与文字报告\n", + "* 进行汇报 \n", + "* 标准：分工合理、数据分析流程完整、汇报展示清晰美观" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "729FB35E6B804D4EA29FA22A0C33DBC3", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "### 2.3 课程风格：\n", + "\t（1）内容有挑战、考核不复杂\n", + "\t（2）1/3一节课展示或互动抄代码\n", + "\t（3）专门设有答疑时间，助教给大家答疑解惑\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4217DF922416401BAADE894DC43A299F", + "jupyter": {}, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "### 2.4 课程大纲\n", + "#### 0 Intro （第一课）\n", + "* 1 课程介绍\n", + "#### I Basics：\n", + "* 2 贝叶斯与频率主义的对比、概率（离散、连续）/条件概率；\n", + "* 3 贝叶斯法则/联合分布；\n", + "* 4 ～ 6. Likelihood, Prior （PPC）, Denominator, Posterior （PPC）[student’s Guide, Part II]\n", + "\n", + "#### II 现代贝叶斯统计的内在工作机制（sampler）\n", + "* 7 MCMC\n", + "\n", + "#### III Bayesian Workflow\n", + "* 8 LM + PyMC3\n", + "* 9 诊断\n", + "* 10 比较\n", + "* 11 推断\n", + "\n", + "#### IV Applications\n", + "* 12 GLM & more LM\n", + "* 13 层级模型 LMM （RT/调查数据）\n", + "* 14 GLMM (信号检验论)\n", + "* 15 扩展示例\n", + "\n", + "#### V 讲座与作业展示\n", + "* 学术报告：劳俊鹏博士 (Google)\n", + "* 大作业" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DA887F72A67F483DBAA22663296C8F57", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "#### 2.5 参考书\n", + "\n", + "\n", + "![Image Name](https://ts1.cn.mm.bing.net/th?id=AMMS_56bf8f54d4ebfaa69e6430302ae0ea6d&w=100&h=150&c=7&rs=1&qlt=80&pcl=f9f9f9&o=6&cdv=1&dpr=2&pid=16.1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "F3D963DF51C745D686F9D69100F3E2F4", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "![Image Name](https://tse1-mm.cn.bing.net/th/id/OIP-C.KSBduDlouNql_1z-nwkohgAAAA?pid=ImgDet&rs=1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "22C59B1E41BB408195A92E2E1F1B4E54", + "jupyter": {}, + "mdEditEnable": false, + "slideshow": { + "slide_type": "slide" + }, + "tags": [], + "trusted": true + }, + "source": [ + "\n", + "![Image Name](https://tse3-mm.cn.bing.net/th/id/OIP-C.sypTLOUunm6FyDTJrVKQTgHaL3?w=119&h=191&c=7&r=0&o=5&dpr=2&pid=1.7)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.9.13 64-bit (windows store)", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.9.13" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "7698be9997df07547d4a08fe6d7a8ab77df170c0c470ab0ace6a1c514673cd42" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}