![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\" "\\"Open"){kind=icon}
![\"Download\"](\"https://img.shields.io/badge/Github-Download-blue.svg\" "\\"Download"){kind=icon}
"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "T28xpViC5wn5",
"nbpages": {
"level": 1,
"link": "[2.1 Multivariate Distributions: Example from Texbook](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1-Multivariate-Distributions:-Example-from-Texbook)",
"section": "2.1 Multivariate Distributions: Example from Texbook"
}
},
"source": [
"# 2.1 Multivariate Distributions: Example from Texbook"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "QntnRXpV5wn6",
"nbpages": {
"level": 1,
"link": "[2.1 Multivariate Distributions: Example from Texbook](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1-Multivariate-Distributions:-Example-from-Texbook)",
"section": "2.1 Multivariate Distributions: Example from Texbook"
}
},
"source": [
"Created by Christian Villa Santos (cvillas2@nd.edu)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "g2x5Xi1ccieF",
"nbpages": {
"level": 2,
"link": "[2.1.1 Objective](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.1-Objective)",
"section": "2.1.1 Objective"
}
},
"source": [
"## 2.1.1 Objective"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "dFRWciH29j63",
"nbpages": {
"level": 2,
"link": "[2.1.1 Objective](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.1-Objective)",
"section": "2.1.1 Objective"
}
},
"source": [
"The objective is to illustrate the example of the Multivariate Normal Distribution provided in Chapter 2 of the the textbook: Uncertatinty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "7Hwt0AZ0cqMI",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
"## 2.1.2 Theory"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "c2oIPasS7Eqr",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
" As we can infer from the name, a multivariate normal distribution is a case in which we have multiple variables. A univariate normal distribution, with only one variable X1, is defined by the mean and the variance while a multivariate normal distribution has a vector of means and a covariance matrix containing variances on the principal diagonal and the off-diagonal. "
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "0w-6hO2OAzKS",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
"First, lets define some terms. The *joint cumulative distribution function* (joint CDF) is the probability that each random variable is smaller than a given number and is given by: \n",
"\n",
"\n",
"\n",
"The difference of the joint CDF results in the probability that each random variable is within a range and is given by: \n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "01NYEDTPCCVz",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
"If we derive the joint CDF we can obtain the *joint probability density function*\n",
"(joint PDF). \n",
"\n",
"\n",
"\n",
"Therefore, the joint CDF is the integral of the joint PDF. For a single variable the PDF is given by: \n",
"\n",
"\n",
"\n",
"Integrating from the second to last variable we get a function of x1 that is called the *marginal* probability density function for random variable X1. The marginal cumulative distribution function for X1 is: \n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "lk5OQXXxXucB",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
"The marginal distribution of a variable can be seen as the probability distribution of X2 ignoring information about X1 by integrating out X1 and vice versa."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "6DzzRxQGKQ8k",
"nbpages": {
"level": 2,
"link": "[2.1.2 Theory](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.2-Theory)",
"section": "2.1.2 Theory"
}
},
"source": [
"Going back to the multivariate normal distribution, the PDF for a multivariate normal PDF of *k* variables is given by: \n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "xnJKgZMJa4Wf",
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
"## 2.1.3 Graphical Representations"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "m4vkVAG0-_aV",
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
" A bivariate normal distrubution is a case of the multivariate and has only two variables. Therefore, it has five parameters: two means, two standard deviations and the product moment correlation between the two variables. It is often imposible to draw figures for systems containing more than this amount of variables. \n",
" \n",
"The peak or centroid is the vector of the means. The values for the standard deviations will dictate the shape of the figure such as circle, ellipse or tilted ellipse. "
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "f5uLM75UMxGS",
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
"Here is an illustration fo how the joint bivariate normal density function looks like. \n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
"Figure 1 in Tacq (2010)."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "DYhZP4BANNkp",
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
"The orthogonal projections of the marginal distributions are illustrated below.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[2.1.3 Graphical Representations](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3-Graphical-Representations)",
"section": "2.1.3 Graphical Representations"
}
},
"source": [
"Figure 2 in Tacq (2010)."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "27TR6pJFiowt",
"nbpages": {
"level": 3,
"link": "[2.1.3.1 Equal-Density Contours](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3.1-Equal-Density-Contours)",
"section": "2.1.3.1 Equal-Density Contours"
}
},
"source": [
"### 2.1.3.1 Equal-Density Contours"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "Qvi4_tHuiuft",
"nbpages": {
"level": 3,
"link": "[2.1.3.1 Equal-Density Contours](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.3.1-Equal-Density-Contours)",
"section": "2.1.3.1 Equal-Density Contours"
}
},
"source": [
"\n",
"\n",
"Figure 4 in Tacq (2010).\n",
"\n",
"In an ellipse the places with equal height have the same probability and that is the reason for the name of equal-density contours. For the tilted ellipse, that is not the case (it does not have the same height). "
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "j3PwvYHtbJT1",
"nbpages": {
"level": 2,
"link": "[2.1.4 Why are multivariate distributions important?](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.4-Why-are-multivariate-distributions-important?)",
"section": "2.1.4 Why are multivariate distributions important?"
}
},
"source": [
"## 2.1.4 Why are multivariate distributions important?"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "jE4PeZ-GbYwr",
"nbpages": {
"level": 2,
"link": "[2.1.4 Why are multivariate distributions important?](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.4-Why-are-multivariate-distributions-important?)",
"section": "2.1.4 Why are multivariate distributions important?"
}
},
"source": [
"1. Multivariate Distributions are correlations between variables. \n",
"\n",
" For example, higher values of the correlations between variables are represented by thinner ellipses. On the other hand, if there is a lower correlation values the ellipse will be more fat with a larger proportion of a population. \n",
"\n",
"2. It has statistic applications on linear regression analysis and its extension, structural equation models, discriminant analysis, multivariate analysis of variance, canonical correlation analysis.\n",
"\n",
"3. Tha paper from J Tacq, listed on the references, provides examples on the topic.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "BU6D1uUMjfgM",
"nbpages": {
"level": 2,
"link": "[2.1.5 Python Code](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.5-Python-Code)",
"section": "2.1.5 Python Code"
}
},
"source": [
"## 2.1.5 Python Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 799
},
"colab_type": "code",
"executionInfo": {
"elapsed": 1392,
"status": "ok",
"timestamp": 1592485958667,
"user": {
"displayName": "Christian Villa Santos",
"photoUrl": "",
"userId": "10580019565710676337"
},
"user_tz": 240
},
"id": "AhBK6vxsLXhH",
"nbpages": {
"level": 2,
"link": "[2.1.5 Python Code](https://ndcbe.github.io/cbe67701-uncertainty-quantification/02.01-Contributed-Example.html#2.1.5-Python-Code)",
"section": "2.1.5 Python Code"
},
"outputId": "7d37e17e-2eb9-4a54-cbde-3eb7620516a2"
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
}
],
"metadata": {
"colab": {
"name": "02.01-Contributed-Example.ipynb",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 1
}