EdX

Stochastic Processes: Data Analysis and Computer Simulation (edX)

Offered by Kyoto University, KyotoUx,
Stochastic Processes: Data Analysis and Computer Simulation (edX)

The course deals with how to simulate and analyze stochastic processes, in particular the dynamics of small particles diffusing in a fluid. The motion of falling leaves or small particles diffusing in a fluid is highly stochastic in nature. Therefore, such motions must be modeled as stochastic processes, for which exact predictions are no longer possible. This is in stark contrast to the deterministic motion of planets and stars, which can be perfectly predicted using celestial mechanics.

Class Deals by MOOC List - Click here and see EdX's Active Discounts, Deals, and Promo Codes.

This course is an introduction to stochastic processes through numerical simulations, with a focus on the proper data analysis needed to interpret the results. We will use the Jupyter (iPython) notebook as our programming environment. It is freely available for Windows, Mac, and Linux through the Anaconda Python Distribution.

The students will first learn the basic theories of stochastic processes. Then, they will use these theories to develop their own python codes to perform numerical simulations of small particles diffusing in a fluid. Finally, they will analyze the simulation data according to the theories presented at the beginning of course.
At the end of the course, we will analyze the dynamical data of more complicated systems, such as financial markets or meteorological data, using the basic theory of stochastic processes.

What you'll learn

  • Basic Python programming
  • Basic theories of stochastic processes
  • Simulation methods for a Brownian particle
  • Application: analysis of financial data

Syllabus

Week 1: Python programming for beginners

  • Using Python, iPython, and Jupyter notebook
  • Making graphs with matplotlib
  • The Euler method for numerical integration
  • Simulating a damped harmonic oscillator

Week 2: Distribution function and random number

  • Stochastic variable and distribution functions
  • Generating random numbers with Gaussian/binomial/Poisson distributions
  • The central limiting theorem
  • Random walk

Week 3: Brownian motion 1: basic theories

  • Basic knowledge of Stochastic process
  • Brownian motion and the Langevin equation
  • The linear response theory and the Green-Kubo formula

Week 4: Brownian motion 2: computer simulation

  • Random force in the Langevin equation
  • Simple Python code to simulate Brownian motion
  • Simulations with on-the-fly animation

Week 5: Brownian motion 3: data analyses

  • Distribution and time correlation
  • Mean square displacement and diffusion constant
  • Interacting Brownian particles

Week 6: Stochastic processes in the real world

  • Time variations and distributions of real world processes
  • A Stochastic Dealer Model I
  • A Stochastic Dealer Model II
  • A Stochastic Dealer Model III
Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Data Science: Capstone (edX) EdX
HarvardX,Harvard University

Data Science: Capstone (edX)

Statistics & Data Analysis Data Science

Show what you’ve learned from the Professional Certificate Program in Data Science. To become an expert data scientist you need practice and experience. By completing this capstone project you will get an opportunity to apply the knowledge and skills in R data analysis that you have gained throughout the series. This final project will test your skills in data visualization, probability, inference and modeling, data wrangling, data organization, regression, and machine learning.

Self Paced
Self-Paced
Probability Machine Learning Regression
Details
Using Python for Research (edX) EdX
HarvardX,Harvard University

Using Python for Research (edX)

CS: Software Engineering CS: Programming

Take your introductory knowledge of Python programming to the next level and learn how to use Python 3 for your research. This course bridges the gap between introductory and advanced courses in Python. While there are many excellent introductory Python courses available, most typically do not go deep enough for you to apply your Python skills to research projects.

Self Paced
Self-Paced
Programming Python Python Programming
Details
Python Data Structures (edX) EdX
University of Michigan,MichiganX

Python Data Structures (edX)

CS: Programming

The second course in Python for Everybody explores variables that contain collections of data like string, lists, dictionaries, and tuples. Learning how to store and represent and manipulate data collections while a program is running is an important part of learning how to program.

Self Paced
Self-Paced
Programming Python Data Structures
Details
Datos para la efectividad de las políticas públicas (edX) EdX
Inter-American Development Bank - IDB,IDBx

Datos para la efectividad de las políticas públicas (edX)

Management & Leadership Economics & Finance

Este curso te ayudará a tomar el control de los datos y familiarizarte con las herramientas para utilizarlos en la planificación, gestión y evaluación de políticas publicas. En esta era de la información, los datos están disponibles en todos lados y crecen a una tasa exponencial. ¿Cómo podemos darles sentido a todos los datos y aprovecharlos en el momento de tomar decisiones?, ¿cómo los utilizamos para que nos ayuden a guiar la gestión y planificación de nuestras políticas? Tanto si eres ciudadano como planificador de políticas, deberías poder responder a estas preguntas.

Self Paced
Self-Paced
Data Data Analysis Datalogy
Details
SQL for Data Science (edX) EdX
IBM

SQL for Data Science (edX)

Statistics & Data Analysis Data Science

Learn how to use and apply the powerful language of SQL to better communicate and extract data from databases - a must for anyone working in the data science field. Much of the world's data lives in databases. SQL (or Structured Query Language) is a powerful programming language that is used for communicating with and extracting various data types from databases.

Self Paced
Self-Paced
Python Databases SQL
Details
Introduction to Linear Models and Matrix Algebra (edX) EdX
HarvardX,Harvard University

Introduction to Linear Models and Matrix Algebra (edX)

Sci: Biology & Life Sciences Statistics & Data Analysis

Learn to use R programming to apply linear models to analyze data in life sciences. Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory data analysis course, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language.

Self Paced
Self-Paced
Algebra Linear Algebra Matrix
Details
Analyzing and Visualizing Data with Power BI (edX) EdX
Davidson College,DavidsonX

Analyzing and Visualizing Data with Power BI (edX)

Statistics & Data Analysis Computer Science

Step up your analytics game and learn one of the most in-demand job skills in the United States. Power BI is a robust business analytics and visualization tool from Microsoft that helps data professionals bring their data to life and tell more meaningful stores. This four-week course is a beginner's guide to working with data in Power BI and is perfect for professionals. You'll become confident in working with data, creating data visualizations, and preparing reports and dashboards.

Self Paced
Self-Paced
Data Analysis Data Visualization Power BI
Details
How to analyze a microbiome (edX) EdX
KU Leuven University,KULeuvenX

How to analyze a microbiome (edX)

Sci: Biology & Life Sciences Statistics & Data Analysis

Learn common analysis techniques to make sense of microbial sequencing data. Microorganisms play a major role in the biosphere and within our bodies, but only a tiny fraction has been cultured so far. Microbiome data, that is the genetic information of microorganisms, is therefore an important window into the hidden microbial world.

Self Paced
Self-Paced
Biology Data Analysis Microbiome
Details
Python for Data Science (edX) EdX
University of California, San Diego,UC San DiegoX

Python for Data Science (edX)

Statistics & Data Analysis CS: Programming

Learn to use powerful, open-source, Python tools, including Pandas, Git and Matplotlib, to manipulate, analyze, and visualize complex datasets. In the information age, data is all around us. Within this data are answers to compelling questions across many societal domains (politics, business, science, etc.). But if you had access to a large dataset, would you be able to find the answers you seek?

Self Paced
Self-Paced
Programming Python Machine Learning
Details
Data Science and Machine Learning Capstone Project (edX) EdX
IBM

Data Science and Machine Learning Capstone Project (edX)

Statistics & Data Analysis Data Science

Create a project that you can use to showcase your Data Science skills to prospective employers. Apply various data science and machine learning techniques to analyze and visualize a data set involving a real life business scenario and build a predictive model. Now that you've taken several courses on data science and machine learning, it’s time to put your learning to work on a data problem involving a real life scenario. Employers really care about how well you can apply your knowledge and skills to solve real world problems, and the work you do in this capstone project will make you stand out in the job market.

Self Paced
Self-Paced
Python Machine Learning Data Science
Details
High-Dimensional Data Analysis (edX) EdX
HarvardX,Harvard University

High-Dimensional Data Analysis (edX)

Sci: Biology & Life Sciences Statistics & Data Analysis

A focus on several techniques that are widely used in the analysis of high-dimensional data. If you’re interested in data analysis and interpretation, then this is the data science course for you. We start by learning the mathematical definition of distance and use this to motivate the use of the singular value decomposition (SVD) for dimension reduction and multi-dimensional scaling and its connection to principle component analysis.

Self Paced
Self-Paced
Machine Learning Clustering Data Analysis
Details