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Ramon Hanssen,
Sandra Verhagen,
and
Sami Samiei-Esfahany
Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results.
Read more
Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results.
Read more
Are you an engineer, scientist or technician? Are you dealing with measurements or big data, but are you unsure about how to proceed? This is the course that teaches you how to find the best estimates of the unknown parameters from noisy observations. You will also learn how to assess the quality of your results.
TU Delft’s approach to observation theory is world leading and based on decades of experience in research and teaching in geodesy and the wider geosciences. The theory, however, can be applied to all the engineering sciences where measurements are used to estimate unknown parameters.
The course introduces a standardized approach for parameter estimation, using a functional model (relating the observations to the unknown parameters) and a stochastic model (describing the quality of the observations). Using the concepts of least squares and best linear unbiased estimation (BLUE), parameters are estimated and analyzed in terms of precision and significance.
The course ends with the concept of overall model test, to check the validity of the parameter estimation results using hypothesis testing. Emphasis is given to develop a standardized way to deal with estimation problems. Most of the course effort will be on examples and exercises from different engineering disciplines, especially in the domain of Earth Sciences.
This course is aimed towards Engineering and Earth Sciences students at Bachelor’s, Master’s and postgraduate level.
Register for this course and see more details by visiting:
OpenCourser.com/course/1515me/observation
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What's inside
Learning objectives
- How to translate real-life estimation problems to easy mathematical models
- Practical understanding of least squares estimation and best linear unbiased estimation, and how to apply these methods
- How to assess and describe the quality of your estimators in the form of precision and confidence interval
- How to check the validity of your estimation results
- How to translate real-life estimation problems to easy mathematical models
- Practical understanding of least squares estimation and best linear unbiased estimation, and how to apply these methods
- How to assess and describe the quality of your estimators in the form of precision and confidence interval
- How to check the validity of your estimation results
Syllabus
Week 1: IntroductionIntroduction on what is “estimation” and when do we need it? What are the generic sources of uncertainty in observations, and what concepts are needed, e.g. deterministic vs. stochastic parameters, random vs. systematic errors, precision vs. accuracy, bias, and the probability distribution function as a metric of randomness. In this week and througout the course, all concepts are explained by various practical examples. Week 2: Mathematical modelsDevelop a systematic approach to translate real-life problems into mathematical models in the form of observation-equation system including four fundamental blocks: vector of observations, vector of unknown parameters, linear (or linearized) functional relation between observations and unknowns, and stochastic characteristics of observations in the form of dispersion (or covariance matrix) of the observation vector. Discussion on different concepts and models.Week 3: Least Squares Estimation (LSE)Given a mathematical model, how to find an estimate that predicts the observations as close as possible? Introduction to (weighted) least squares estimation (WLSE), its mathematical logic and its main properties.
Read more
Syllabus
Week 1: IntroductionIntroduction on what is “estimation” and when do we need it? What are the generic sources of uncertainty in observations, and what concepts are needed, e.g. deterministic vs. stochastic parameters, random vs. systematic errors, precision vs. accuracy, bias, and the probability distribution function as a metric of randomness. In this week and througout the course, all concepts are explained by various practical examples. Week 2: Mathematical modelsDevelop a systematic approach to translate real-life problems into mathematical models in the form of observation-equation system including four fundamental blocks: vector of observations, vector of unknown parameters, linear (or linearized) functional relation between observations and unknowns, and stochastic characteristics of observations in the form of dispersion (or covariance matrix) of the observation vector. Discussion on different concepts and models.Week 3: Least Squares Estimation (LSE)Given a mathematical model, how to find an estimate that predicts the observations as close as possible? Introduction to (weighted) least squares estimation (WLSE), its mathematical logic and its main properties.
Read more
Week 4: Best Linear Unbiased Estimation (BLUE)How to find the most precise and accurate estimate in linear models? Introduction to the concept of Best Linear Unbiased Estimation (BLUE), its theory and implication, and its relation to other estimators such as WLSE, maximum likelihood, and minimum variance estimators.
Week 5: How precise is the estimate?Discussion on how the uncertainty/randomness in observations (depicted by a stochastic model) propagates to the uncertainty/randomness of estimates (depicted by probability density function or covariance matrix of estimators). Introduction to the concept of error propagation and its application in specification of the uncertainty/precision of estimates, inferring confidence intervals or statistical tolerance levels of the results, and describing the expected variability of the results of an estimation.
Week 6: Does the estimate make sense?Introduction to a probabilistic decision making process (or statistical hypothesis testing) in validating the results of estimation in order to avoid wrong decisions/interpretation of the results. Verify the validity of a chosen mathematical model, and how to detect and identify model misspecifications.
Good to know
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Know what's good ,
what to watch for , and
possible dealbreakers
Ideal for engineers, scientists, and technicians dealing with measurements or big data with uncertainty in their observations who need to improve their estimation and results analysis skills
Introduces a standardized approach to parameter estimation using functional and stochastic models
Covers practical understanding of least squares estimation and best linear unbiased estimation with applications
Provides guidance on assessing and describing the quality of estimators in terms of precision and confidence intervals
Helps learners check the validity of their estimation results using hypothesis testing
Examples and exercises from different engineering disciplines, especially in Earth Sciences
Save this course
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Reviews summary
Observation theory: intermediate level overview
According to students, this intermediate-level course offers an overview of observation theory and estimation. It helps learners understand the underlying principles and applications of observation theory.
Provides an overview of observation theory concepts.
Covers applications of observation theory in various fields.
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 Observation Theory: Estimating the Unknown with these
activities:
Organize and review course notes and materials
Show steps
Organizing and reviewing course notes and materials will help retain information and prepare for assessments.
Show steps
-
Gather all course notes, assignments, quizzes, and exams.
-
Create a system for organizing the materials.
-
Review the materials regularly to reinforce learning.
Participate in a study group to discuss course concepts
Show steps
Discussing course concepts with peers can enhance understanding and identify areas where further clarification is needed.
Show steps
-
Find a study group to join.
-
Meet regularly to discuss course material.
-
Work together to solve problems and clarify concepts.
Follow tutorials on variance-covariance matrix
Show steps
Variance-covariance matrix is fundamental in estimation theory. Following tutorials will provide a deeper understanding of its properties and applications.
Show steps
-
Find tutorials on variance-covariance matrix.
-
Follow the tutorials and take notes.
-
Practice using the variance-covariance matrix to solve estimation problems.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Attend a workshop on uncertainty quantification
Show steps
Attending a workshop on uncertainty quantification will provide valuable insights into the importance and techniques of quantifying uncertainty in estimation.
Browse courses on
Uncertainty Quantification
Show steps
-
Find and register for a workshop on uncertainty quantification.
-
Attend the workshop and take notes.
-
Apply the techniques learned in the workshop to your own estimation problems.
Write a summary of the BLUE estimation process
Show steps
Summarizing the BLUE estimation process in your own words will help you understand and retain the key concepts.
Show steps
-
Explain the concept of best linear unbiased estimation.
-
Describe the steps involved in BLUE estimation.
-
Provide an example of how BLUE estimation can be applied to a real-world problem.
Solve problems related to estimation
Show steps
Practice solving estimation problems using the concepts and methods learned in the course to improve understanding and proficiency.
Show steps
-
Review the concepts of least squares estimation, best linear unbiased estimation, error propagation, and hypothesis testing.
-
Gather practice problems from the course materials or external sources.
-
Solve the practice problems step-by-step, applying the relevant concepts and methods.
-
Check your solutions against known answers or consult with others to verify your approach.
Discuss and solve estimation problems with peers
Show steps
Engage in collaborative problem-solving and knowledge sharing with peers to reinforce concepts and improve understanding.
Show steps
-
Form a study group or join an existing one with peers from the course.
-
Select estimation problems from the course materials or external sources to discuss.
-
Collaborate on solving the problems, sharing different perspectives and approaches.
-
Explain your solutions to each other and provide constructive feedback.
Develop a model for a real-world estimation problem
Show steps
Apply the course concepts to a real-world problem by creating a mathematical and stochastic model for parameter estimation, enhancing practical understanding.
Browse courses on
Mathematical Models
Show steps
-
Identify a real-world problem that involves estimation.
-
Develop a mathematical model that relates the observations to the unknown parameters.
-
Develop a stochastic model that describes the quality of the observations.
-
Use the concepts of least squares estimation and best linear unbiased estimation to estimate the unknown parameters.
-
Validate your model by comparing your results to known values or by conducting experiments.
Practice solving estimation problems
Show steps
Solve various estimation problems to reinforce the concepts learned in the course.
Browse courses on
Estimation
Show steps
-
Identify the unknown parameters and observations.
-
Establish a mathematical model relating the observations to the parameters.
-
Apply the least squares or best linear unbiased estimation method to find the parameter estimates.
-
Analyze the precision and significance of the estimates.
Follow tutorials on advanced estimation techniques
Show steps
Enhance knowledge and skills by exploring advanced estimation techniques through guided tutorials, broadening understanding beyond the course content.
Browse courses on
Monte Carlo Methods
Show steps
-
Identify areas where you want to deepen your understanding of estimation techniques.
-
Search for online tutorials or courses that cover these advanced techniques.
-
Follow the tutorials, taking notes and practicing the concepts.
-
Apply the techniques to solve real-world estimation problems.
Use statistical software for model validation
Show steps
Gain practical experience in using statistical software for model validation, which is a crucial step in ensuring the reliability of estimation results.
Browse courses on
Model Validation
Show steps
-
Import data into statistical software.
-
Fit a model to the data.
-
Perform hypothesis tests to validate the model.
-
Interpret the results and draw conclusions.
Contribute to an open-source project related to estimation theory
Show steps
Contributing to an open-source project will provide hands-on experience in applying estimation theory and enhance your understanding of its practical applications.
Show steps
-
Find an open-source project related to estimation theory.
-
Review the project's documentation and codebase.
-
Identify an area where you can contribute.
-
Make a pull request to the project.
-
Collaborate with other contributors to improve the project.
Organize and review course notes and materials
Show steps
Organizing and reviewing course notes and materials will help retain information and prepare for assessments.
Show steps
Show steps
Show steps
- Gather all course notes, assignments, quizzes, and exams.
- Create a system for organizing the materials.
- Review the materials regularly to reinforce learning.
Participate in a study group to discuss course concepts
Show steps
Discussing course concepts with peers can enhance understanding and identify areas where further clarification is needed.
Show steps
Show steps
Show steps
- Find a study group to join.
- Meet regularly to discuss course material.
- Work together to solve problems and clarify concepts.
Follow tutorials on variance-covariance matrix
Show steps
Variance-covariance matrix is fundamental in estimation theory. Following tutorials will provide a deeper understanding of its properties and applications.
Show steps
Show steps
Show steps
- Find tutorials on variance-covariance matrix.
- Follow the tutorials and take notes.
- Practice using the variance-covariance matrix to solve estimation problems.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Attend a workshop on uncertainty quantification
Show steps
Attending a workshop on uncertainty quantification will provide valuable insights into the importance and techniques of quantifying uncertainty in estimation.
Browse courses on
Uncertainty Quantification
Show steps
Show steps
Show steps
- Find and register for a workshop on uncertainty quantification.
- Attend the workshop and take notes.
- Apply the techniques learned in the workshop to your own estimation problems.
Write a summary of the BLUE estimation process
Show steps
Summarizing the BLUE estimation process in your own words will help you understand and retain the key concepts.
Show steps
Show steps
Show steps
- Explain the concept of best linear unbiased estimation.
- Describe the steps involved in BLUE estimation.
- Provide an example of how BLUE estimation can be applied to a real-world problem.
Solve problems related to estimation
Show steps
Practice solving estimation problems using the concepts and methods learned in the course to improve understanding and proficiency.
Show steps
Show steps
Show steps
- Review the concepts of least squares estimation, best linear unbiased estimation, error propagation, and hypothesis testing.
- Gather practice problems from the course materials or external sources.
- Solve the practice problems step-by-step, applying the relevant concepts and methods.
- Check your solutions against known answers or consult with others to verify your approach.
Discuss and solve estimation problems with peers
Show steps
Engage in collaborative problem-solving and knowledge sharing with peers to reinforce concepts and improve understanding.
Show steps
Show steps
Show steps
- Form a study group or join an existing one with peers from the course.
- Select estimation problems from the course materials or external sources to discuss.
- Collaborate on solving the problems, sharing different perspectives and approaches.
- Explain your solutions to each other and provide constructive feedback.
Develop a model for a real-world estimation problem
Show steps
Apply the course concepts to a real-world problem by creating a mathematical and stochastic model for parameter estimation, enhancing practical understanding.
Browse courses on
Mathematical Models
Show steps
Show steps
Show steps
- Identify a real-world problem that involves estimation.
- Develop a mathematical model that relates the observations to the unknown parameters.
- Develop a stochastic model that describes the quality of the observations.
- Use the concepts of least squares estimation and best linear unbiased estimation to estimate the unknown parameters.
- Validate your model by comparing your results to known values or by conducting experiments.
Practice solving estimation problems
Show steps
Solve various estimation problems to reinforce the concepts learned in the course.
Browse courses on
Estimation
Show steps
Show steps
Show steps
- Identify the unknown parameters and observations.
- Establish a mathematical model relating the observations to the parameters.
- Apply the least squares or best linear unbiased estimation method to find the parameter estimates.
- Analyze the precision and significance of the estimates.
Follow tutorials on advanced estimation techniques
Show steps
Enhance knowledge and skills by exploring advanced estimation techniques through guided tutorials, broadening understanding beyond the course content.
Browse courses on
Monte Carlo Methods
Show steps
Show steps
Show steps
- Identify areas where you want to deepen your understanding of estimation techniques.
- Search for online tutorials or courses that cover these advanced techniques.
- Follow the tutorials, taking notes and practicing the concepts.
- Apply the techniques to solve real-world estimation problems.
Use statistical software for model validation
Show steps
Gain practical experience in using statistical software for model validation, which is a crucial step in ensuring the reliability of estimation results.
Browse courses on
Model Validation
Show steps
Show steps
Show steps
- Import data into statistical software.
- Fit a model to the data.
- Perform hypothesis tests to validate the model.
- Interpret the results and draw conclusions.
Contribute to an open-source project related to estimation theory
Show steps
Contributing to an open-source project will provide hands-on experience in applying estimation theory and enhance your understanding of its practical applications.
Show steps
Show steps
Show steps
- Find an open-source project related to estimation theory.
- Review the project's documentation and codebase.
- Identify an area where you can contribute.
- Make a pull request to the project.
- Collaborate with other contributors to improve the project.
Career center
Learners who complete Observation Theory: Estimating the Unknown will develop knowledge and skills
that may be useful to these careers:
Surveyor
Surveyor
Surveyors measure and map land and water features. Observation Theory: Estimating the Unknown will help students learn the methods for analyzing and interpreting data for Earth Sciences. The course delves into Observation Theory, functional modeling, stochastic models, and model validation, all critical elements to excel in this field.
Hydrologist
Hydrologist
Hydrologists study the movement and distribution of water on, above, and below the surface of the Earth. Observation Theory: Estimating the Unknown will help students learn the methods for analyzing and interpreting data for Earth Sciences. The course delves into Observation Theory, functional modeling, stochastic models, and model validation, all critical elements to excel in this field.
Geophysicist
Geophysicist
Geophysicists study the physical properties of the Earth and its atmosphere. Observation Theory: Estimating the Unknown will help students learn the methods for analyzing and interpreting data for Earth Sciences. The course delves into Observation Theory, functional modeling, stochastic models, and model validation, all critical elements to excel in this field.
Geodesist
Geodesist
Geodesists measure the size and shape of the Earth, its gravity field, and its geoid. Observation Theory: Estimating the Unknown will help students learn the methods for analyzing and interpreting data for Earth Sciences. The course delves into Observation Theory, functional modeling, stochastic models, and model validation, all critical elements to excel in this field.
Agricultural Statistician
Agricultural Statistician
Agricultural Statisticians collect, analyze, and interpret data related to agriculture and natural resources. Observation Theory: Estimating the Unknown will help build a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Agricultural Statistics.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. Observation Theory: Estimating the Unknown will help build a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Quantitative Analysis.
Actuary
Actuary
Actuaries analyze the financial risks associated with insurance, investments, and other financial products. Observation Theory: Estimating the Unknown will help build a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Actuarial Science.
Mathematician
Mathematician
Mathematicians analyze quantitative relationships and develop mathematical models to solve practical problems. Observation Theory: Estimating the Unknown will help students build a foundation in mathematical modeling and estimation techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Mathematics.
Biostatistician
Biostatistician
Biostatisticians apply statistical methods to medical and health-related research. Observation Theory: Estimating the Unknown will help build a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Biostatistics.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to improve the efficiency and effectiveness of organizations. Observation Theory: Estimating the Unknown will help students build a foundation in mathematical modeling and estimation techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Operations Research.
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data. Observation Theory: Estimating the Unknown will help build a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Statistics.
Data Engineer
Data Engineer
Data Engineers combine programming skills with an understanding of data engineering principles and best practices to establish an organization’s framework for working with big data and other complex data sets. Observation Theory: Estimating the Unknown will help build a foundation for understanding big data and the methods to best analyze them. This course will also introduce concepts of least squares estimation and best linear unbiased estimation with application in the real world. These skills will be essential to a career in Data Engineering.
Data Scientist
Data Scientist
Data Scientists collect, analyze, and interpret data from a variety of sources to help businesses make informed decisions. Observation Theory: Estimating the Unknown will help build a foundation for understanding big data and the methods to best analyze it. The course delves into the fundamentals of describing the quality of data, methods for error propagation, and decision making processes when analyzing data. These skills will be essential to a career in Data Science.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. Observation Theory: Estimating the Unknown will help students build a foundation in mathematical modeling and estimation techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for developing robust and reliable software systems.
Educational Statistician
Educational Statistician
Educational Statisticians apply statistical methods to educational research and evaluation. Observation Theory: Estimating the Unknown may be of interest to students interested in careers in Educational Statistics, by building a foundation in mathematical and statistical modeling techniques. The course covers concepts such as least squares estimation, best linear unbiased estimation, error propagation, and model validation. These skills are essential for a career in Educational Statistics.
For more career information including salaries, visit:
OpenCourser.com/course/1515me/observation
Reading list
We've selected 50 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Observation Theory: Estimating the Unknown.
Classic reference for the field of adjustment computations and spatial data analysis. It could be used along with the course for prerequisite background knowledge and extra depth.
Presents a comprehensive overview of the foundations of mathematical statistics, covering topics such as probability, random variables, sampling distributions, and statistical inference. Serves as an excellent reference for readers seeking a thorough understanding of statistical principles.
This is an excellent resource for understanding the theoretical aspects behind many of the concepts touched on in the course.
Provides a comprehensive overview of the theory and practice of parameter estimation and inverse problems, with a focus on engineering and scientific applications. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
Presents a comprehensive and advanced treatment of statistical inference, covering topics such as Bayesian analysis, decision theory, and nonparametric methods. Suitable for readers with a strong foundation in probability and statistics, seeking to deepen their understanding of statistical theory and its applications.
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Provides a comprehensive overview of inverse problem theory and methods for model parameter estimation. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
Save
Provides a comprehensive overview of deep learning, covering topics such as neural networks, convolutional neural networks, and recurrent neural networks. Suitable for readers seeking to gain a deep understanding of deep learning techniques and their applications in various fields.
Provides an excellent foundation in mathematics for those in engineering fields, particularly electrical, communications, and systems engineering.
This book, serving as a good foundational text in addition to the course, covers the theory and applications of least-squares estimation thoroughly.
This textbook provides a comprehensive and accessible introduction to the key concepts and methods of modern statistics, including machine learning.
Used commonly by those in engineering and science fields, this book provides both a general background as well as more in-depth statistical applications.
Provides a great supplemental source for matrix theory and applications, especially for those in the engineering field.
This textbook provides a comprehensive introduction to the fundamental concepts and methods of probability and statistics, with a strong focus on applications.
Provides an accessible and easy-to-understand introduction to the fundamental concepts of statistics. may also serve as a useful reference for individuals with limited prior statistical knowledge.
Save
Provides a concise overview of statistical inference, covering topics such as Bayesian analysis, hypothesis testing, and regression analysis. Serves as a valuable resource for readers seeking a broad understanding of statistical concepts and their applications.
Provides a comprehensive treatment of convex optimization, covering topics such as convex sets, duality theory, and optimization algorithms. Suitable for readers seeking a deeper understanding of convex optimization techniques and their applications in various fields.
Save
Offers a comprehensive introduction to machine learning, covering topics such as supervised learning, unsupervised learning, and deep learning. Suitable for readers seeking to gain a broad understanding of machine learning principles and algorithms.
Provides a comprehensive overview of the statistical theory of estimation and minimum mean square error estimation. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
Save
Provides a comprehensive overview of linear models in statistics. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
Provides a comprehensive treatment of linear estimation and statistical inference. It valuable resource for students and researchers in statistics, engineering, and other fields.
This textbook provides a comprehensive and rigorous introduction to statistical inference, covering the latest developments in theory and practice.
Focuses on the theory of biased estimators and provides a comprehensive presentation of generalized least squares. It covers a wide range of topics, including the Gauss-Markov theorem, the estimation of variance components, and the analysis of variance.
This textbook provides a comprehensive and up-to-date treatment of statistical decision theory and Bayesian analysis, covering both theory and practice.
Provides a comprehensive overview of remote sensing techniques and their applications in environmental monitoring, natural resource management, and land use planning. Suitable for readers seeking to gain a broad understanding of remote sensing principles and their use in environmental studies.
This textbook provides a comprehensive and up-to-date treatment of Bayesian methods for data analysis, covering both theory and practice.
This textbook provides a comprehensive and accessible introduction to mathematical statistics, covering the latest developments in theory and practice.
This textbook provides a comprehensive and accessible introduction to Bayesian data analysis, covering the latest developments in theory and practice.
Could be a valuable resource for those in the engineering fields looking for more in-depth theory on probability and random processes.
Presents a concise and accessible introduction to applied linear algebra, covering topics such as matrix operations, vector spaces, and linear transformations. Suitable for readers seeking to gain a solid foundation in linear algebra for applications in engineering and other fields.
This textbook provides a balanced and comprehensive treatment of probability and statistical inference, emphasizing the connections between the two.
This textbook provides a comprehensive and accessible introduction to time series analysis, covering both theory and practice.
This textbook provides a comprehensive and accessible introduction to regression analysis and generalized linear models, covering both theory and practice.
Provides a comprehensive treatment of stochastic modeling and mathematical statistics. It valuable resource for students and researchers in statistics, engineering, and other fields.
This textbook provides a comprehensive and accessible introduction to nonparametric statistics, covering both theory and practice.
This textbook combines classical and contemporary approaches to probability and statistics, providing a balanced and comprehensive treatment.
This textbook provides a comprehensive and accessible introduction to statistical quality control, covering both theory and practice.
This textbook provides a comprehensive and up-to-date treatment of linear statistical models, with a focus on flexibility, modeling, and computation.
Provides a practical introduction to applied statistics for students in the agricultural, biological, and environmental sciences. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
Provides a practical introduction to statistical methods for students in the social sciences. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
This textbook provides a concise and accessible introduction to the entire field of statistics, from fundamental concepts to advanced topics.
Provides a comprehensive overview of applied multivariate statistical analysis. It covers a wide range of topics, including least squares estimation, maximum likelihood estimation, and Bayesian estimation.
This textbook provides an introduction to probability, focusing on the basic principles and the applications of probability in engineering and science.
Provides a comprehensive overview of machine learning from a probabilistic perspective. It covers a wide range of topics, including Bayesian estimation, Bayesian model selection, and Bayesian computation.
Provides a comprehensive overview of Monte Carlo statistical methods. It covers a wide range of topics, including Bayesian estimation, Bayesian model selection, and Bayesian computation.
Provides a comprehensive treatment of statistics for spatial data. It valuable resource for students and researchers in statistics, geography, and other fields.
Provides a gentle introduction to Bayesian statistics using the R and Stan programming languages. It covers a wide range of topics, including Bayesian estimation, Bayesian model selection, and Bayesian computation.
Provides a comprehensive treatment of GPS for land surveyors. It valuable resource for students and practitioners in surveying.
Provides a comprehensive treatment of surveying with construction applications. It valuable resource for students and practitioners in surveying and construction.
Provides a comprehensive treatment of engineering surveying. It valuable resource for students and practitioners in surveying.
Save
Provides a comprehensive treatment of elementary surveying. It valuable resource for students and beginners in surveying.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/1515me/observation
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Effort
4 to 6 hours per week for 6 weeks
Level
Intermediate
Via
edX
Institution
Delft University of Technology
Instructors
Ramon Hanssen
Sandra Verhagen
Sami Samiei-Esfahany
Session
November 6, 2024
- December 18, 2024
Language
English
Transcript
English
Good to know
Ideal for engineers, scientists, and technicians dealing with measurements or big data with uncertainty in their observations who need to improve their estimation and results analysis skills
Introduces a standardized approach to parameter estimation using functional and stochastic models
Covers practical understanding of least squares estimation and best linear unbiased estimation with applications
Provides guidance on assessing and describing the quality of estimators in terms of precision and confidence intervals
Helps learners check the validity of their estimation results using hypothesis testing
Examples and exercises from different engineering disciplines, especially in Earth Sciences
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