Introduction to Uncertainty Quantification from Coursera

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Syllabus

Types of Uncertainty and Their Treatment

This module sets the stage for uncertainty quantification by carefully defining the different types of uncertainties that may be present. Lesson one introduces aleatory and epistemic uncertainties. The second lesson helps to build your understanding of aleatory and epistemic uncertainties and tell the difference between the two. The third, and final module discusses from a board perspective how we mathematically treat aleatory and epistemic uncertainty.

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Provides a strong foundation in probability theory, which is essential for quantifying uncertainty in various systems and models, and is a core skill for quantitative fields

Explores Monte Carlo methods, which are widely used for uncertainty propagation and serve as a benchmark for other methods, and are thus highly relevant to industry

Introduces Bayesian inference with a focus on Bayesian parameter estimation, which is a powerful tool for updating beliefs in light of new evidence and data, and is useful for personal growth

Presents advanced numerical methods, namely spectral stochastic methods, which are used in uncertainty propagation, but may require a strong mathematical background

Discusses reliability analysis, which is concerned with estimating small failure probabilities, but this topic is only briefly introduced and may require further study

Taught by Johns Hopkins University, which is known for its research and education in engineering, medicine, and public health, and is thus highly relevant to academia

Reviews summary

Introduction to uq: comprehensive and challenging

According to students, Johns Hopkins University's Introduction to Uncertainty Quantification provides a solid foundation in the field, covering a broad range of key topics from basic probability to advanced methods like Monte Carlo and Bayesian inference. Many learners found the course challenging, noting that the pacing can be fast and it assumes a strong mathematical background, particularly in probability and linear algebra. While some found the assignments difficult, others felt they were crucial for understanding and effectively reinforced concepts. The course is considered useful for those with the necessary prerequisites seeking a comprehensive overview.

Requires a strong math background.

"Definitely requires a strong math background (calc, linear algebra, probability)."

"Assumed too much prior knowledge."

"You need a solid background in linear algebra and probability."

"I struggled because I didn't have the necessary math foundation coming in."

Assignments reinforce concepts learned.

"Assignments were challenging but crucial for understanding."

"Be prepared for tough assignments."

"The assignments, though tough, really helped solidify the concepts."

"They required a lot of work but ultimately I found them beneficial."

Covers many key areas of UQ.

"...and covers a wide range of topics including Monte Carlo and Bayesian methods."

"The section on surrogate models was particularly useful."

"The Monte Carlo simulations were explained well."

"I appreciated the coverage of Monte Carlo and Bayesian methods."

Provides strong fundamentals.

"Excellent course! Provides a solid foundation in UQ..."

"Good introduction, covers the syllabus well."

"Solid course for getting into UQ."

"I got a great introduction to the core concepts."

Explanations could be clearer.

"...the explanations aren't always as clear as they could be."

"Some parts felt disjointed."

"The lectures skipped over important steps."

Many found pace and difficulty high.

"Some parts felt rushed."

"Found this course very difficult. The pace was too fast, especially when introducing advanced topics."

"Felt overwhelmed at times by the complexity of the material."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Introduction to Uncertainty Quantification with these activities:

Review Probability Theory

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Solidify your understanding of probability theory, which is essential for quantifying uncertainty in various systems.

Browse courses on Probability Theory

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Review key concepts like random variables, distributions, and statistical inference.
Work through practice problems to reinforce your understanding.

Read 'Understanding Uncertainty' by Dennis V. Lindley

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Gain a deeper understanding of the philosophical and practical aspects of uncertainty.

View Understanding Uncertainty on Amazon

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Read the book, focusing on chapters related to Bayesian methods and decision theory.
Reflect on how the concepts apply to real-world scenarios.

Monte Carlo Simulation Exercises

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Practice implementing Monte Carlo simulations to propagate uncertainty through various models.

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Choose a model with uncertain inputs.
Implement a Monte Carlo simulation to estimate the distribution of the output.
Analyze the results and compare them to analytical solutions, if available.

Four other activities

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Follow Tutorials on Gaussian Process Surrogates

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Learn how to build and use Gaussian process surrogates for uncertainty propagation.

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Find online tutorials or documentation on Gaussian process regression.
Implement a Gaussian process surrogate for a simple model.
Evaluate the performance of the surrogate and compare it to other methods.

Create a Blog Post on Aleatory vs. Epistemic Uncertainty

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Solidify your understanding of the different types of uncertainty by explaining them in a clear and concise manner.

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Research aleatory and epistemic uncertainty.
Write a blog post explaining the differences between them with examples.
Share your blog post on social media or relevant online forums.

UQ for a Simple Engineering System

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Apply UQ techniques to a simple engineering system to quantify the impact of uncertainty on its performance.

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Select a simple engineering system (e.g., a beam under load).
Identify sources of uncertainty in the system (e.g., material properties, dimensions).
Propagate the uncertainty through the system using Monte Carlo simulation or other methods.
Analyze the results and draw conclusions about the system's reliability.

Read 'Bayesian Data Analysis' by Gelman et al.

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Deepen your understanding of Bayesian methods for uncertainty quantification.

View Bayesian Data Analysis (Chapman & Hall/CRC... on Amazon

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Read the book, focusing on chapters related to Bayesian inference and model checking.
Work through the examples and exercises in the book.

Career center

Learners who complete Introduction to Uncertainty Quantification will develop knowledge and skills that may be useful to these careers:

Statistical Modeler

A statistical modeler uses statistical techniques to create models that represent real-world processes, and this course can provide an important background. Uncertainty quantification is a key element of statistical modeling, and this course will expose a learner to the different kinds of uncertainty, as well as methods of representing them in order to manage them. The course’s introduction to probability theory, uncertainty propagation, and random processes are integral to developing detailed and powerful statistical models. The course is useful for a statistical modeler who wants to build models that can manage complex systems.

See salaries and explore the career path for Statistical Modeler

Data Scientist

A data scientist uses mathematical and statistical methods to analyze data, and this course can be highly valuable for that. Understanding uncertainty quantification is essential when working with complex datasets and models. The course's material on probability theory, uncertainty propagation, and surrogate modeling are directly applicable to building and interpreting robust predictive models, a core task of a data scientist. The course’s coverage of Monte Carlo methods is also helpful when assessing the accuracy of models. This course helps build a foundation for data scientists seeking to work with models that include uncertainty in their predictions.

See salaries and explore the career path for Data Scientist

Risk Analyst

A risk analyst identifies, assesses, and mitigates risks across various industries. This course on uncertainty quantification is directly relevant to those interested in a career as a risk analyst, as it equips learners with the tools necessary to quantify, communicate, and better manage uncertainty. The course's coverage of uncertainty propagation, reliability analysis, and Bayesian methods is essential for modeling risk exposure. It prepares learners to understand how uncertainty affects system outcomes, and how to model low probability events. This course helps build a foundation for a risk analyst seeking to effectively manage uncertainty.

See salaries and explore the career path for Risk Analyst

Statistician

A statistician develops and applies statistical theories and methods to collect, interpret, and analyze data, and this course can be useful for statisticians. The course focuses on quantifying uncertainty, a critical aspect of statistical modeling. The course introduces probability theory, uncertainty propagation, and random processes, which all help a statistician build a toolbox of techniques. The Bayesian inference techniques also help when addressing uncertainty. This course may be useful for statisticians seeking new techniques.

See salaries and explore the career path for Statistician

Biostatistician

A biostatistician applies statistical methods to biological and health-related data and, because much biological data is noisy, this course may be useful. The course provides a background for quantifying uncertainty, a key element of biostatistical work. The course teaches probability, uncertainty propagation, surrogate modeling, and Bayesian methods, all of which can be applied to developing reliable models for biological and health datasets. This course may be useful for biostatisticians looking to better manage uncertainty.

See salaries and explore the career path for Biostatistician

Research Scientist

A research scientist explores and investigates complex scientific questions by using the scientific method, and the skills learned in this course may help a research scientist. Uncertainty quantification is a critical aspect of modeling and interpreting scientific data. The course's coverage of probability theory and uncertainty propagation is useful for any research scientist needing to build models that reflect reality. Random processes and Bayesian methods taught in the course help a research scientist develop robust analyses and draw meaningful conclusions from data. This course may be useful for research scientists looking to incorporate uncertainty into their research.

See salaries and explore the career path for Research Scientist

Geoscientist

A geoscientist studies the Earth and its processes, and this course can be of use. Uncertainty quantification is essential when interpreting geological data. This course introduces techniques like uncertainty propagation, random processes, and Bayesian methods, which provide a basis for modeling uncertainty in diverse earth systems. This course helps a geoscientist quantify the uncertainty in geologic models. This course may be useful for those looking to work with uncertainty in the Earth sciences.

See salaries and explore the career path for Geoscientist

Simulation Engineer

A simulation engineer creates and uses computer models to simulate real-world systems, and this course can be useful for the role. The principles of uncertainty quantification, especially those that center on uncertainty propagation and surrogate modeling, taught in this course, are crucial for developing accurate simulations, as they allow an engineer to simulate scenarios under uncertainty, accounting for a range of possibilities. Learning about Monte Carlo methods and sensitivity analysis enables a simulation engineer to build robust and reliable simulation models. This class may be useful for simulation engineers in need of skills to handle uncertainty.

See salaries and explore the career path for Simulation Engineer

Quantitative Analyst

A quantitative analyst, sometimes called a quant, develops and implements mathematical and statistical models for financial markets. This course on uncertainty quantification provides important skills for a quant, offering a background in probabilistic modeling and risk analysis. The course introduces crucial concepts like uncertainty propagation, reliability analysis, and Bayesian methods that are used to model financial instrument behavior and manage risk in the financial sector. The course’s focus on random processes and sensitivity analysis helps a quant understand the dynamics of financial systems and measure their reactions to market variations. This course may build a foundation for those interested in careers in quantitative finance.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

An operations research analyst applies mathematical and analytical methods to help organizations make better decisions, and this course may be helpful. The course teaches uncertainty quantification, which helps an analyst build models that can account for the variability common in operations. The course introduces uncertainty propagation, surrogate modeling, and reliability analysis, which helps an analyst build models that represent complexity. The Bayesian methods discussed are also pertinent to decision making. This course may be useful for those seeking work in operations research.

See salaries and explore the career path for Operations Research Analyst

Actuary

An actuary assesses and manages financial risks, and this course can provide a background for actuaries who must deal with uncertainty. This course provides the essential skills in probability, random processes, and reliability analysis for actuaries to quantify uncertainty and assess risk. The course’s discussion of uncertainty propagation and Bayesian inference are useful for developing models that account for multiple sources of uncertainty. This course may be useful for actuaries looking to better quantify uncertainty.

See salaries and explore the career path for Actuary

Financial Modeler

A financial modeler builds quantitative models to forecast financial outcomes, and this course can help build skills for the role. Techniques in uncertainty quantification, particularly probability theory and uncertainty propagation, taught in this course, are directly applicable to a financial modeler interested in building models that reflect uncertainty in the financial landscape. The course covers Monte Carlo methods and sensitivity analysis, which helps a financial modeler assess the robustness of forecasts. The course may help those who seek work in financial modeling by teaching tools for modeling uncertainty.

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Civil Engineer

A civil engineer designs, constructs, and maintains infrastructure projects, and this course can help. Uncertainty quantification is important for assessing the reliability and safety of civil structures, especially under varied conditions; this course provides a background in this. The course's coverage of random processes and reliability analysis helps a civil engineer model the effects of various uncertainties on structural integrity. Learning about uncertainty propagation and sensitivity analysis allows a civil engineer to understand how different elements of a design affect its overall safety and robustness. This course may be useful for civil engineers looking to quantify and reduce uncertainties.

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Aerospace Engineer

An aerospace engineer designs, develops, and tests aircraft and spacecraft. This course on uncertainty quantification provides crucial tools for an aerospace engineer to address the uncertainties inherent in aerospace systems. Uncertainty propagation, surrogate modeling, and reliability analysis, covered in this course, are essential for modeling and analyzing the performance of aircraft and spacecraft systems. The course provides a basis for handling a wide range of variables and helps an aerospace engineer build robust and reliable designs, accounting for uncertainty. This course may build a foundation for those working in aerospace engineering.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

A mechanical engineer designs, develops, and tests mechanical devices and systems. This course on uncertainty quantification is relevant to mechanical engineers who need to account for variability in their designs. The course introduces uncertainty propagation, surrogate modeling, and reliability analysis, which helps a mechanical engineer understand and predict system behavior under uncertain conditions. An understanding of random processes helps design robust and reliable mechanical systems. The course may be useful for mechanical engineers looking to reduce variability in designs.

See salaries and explore the career path for Mechanical Engineer

Introduction to Uncertainty Quantification

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Reviews summary

Introduction to uq: comprehensive and challenging

Activities

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