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6.435 System Identification (MIT) 6.435 System Identification (MIT)

Description

This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues. This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues.Subjects

mathematical models | mathematical models | time series | time series | state-space | state-space | input-output models | input-output models | model structures | model structures | parametrization | parametrization | identifiability | identifiability | non-parametric methods | non-parametric methods | prediction error | prediction error | parameter estimation | parameter estimation | convergence | convergence | consistency | consistency | andasymptotic distribution | andasymptotic distribution | maximum likelihood estimation | maximum likelihood estimation | recursive estimation | recursive estimation | Kalman filters | Kalman filters | structure determination | structure determination | order estimation | order estimation | Akaike criterion | Akaike criterion | bounded noise models | bounded noise models | robustness | robustnessLicense

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This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation. This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.Subjects

system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification | system identification | estimation | estimation | least squares estimation | least squares estimation | Kalman filter | Kalman filter | noise dynamics | noise dynamics | system representation | system representation | function approximation theory | function approximation theory | neural nets | neural nets | radial basis functions | radial basis functions | wavelets | wavelets | volterra expansions | volterra expansions | informative data sets | informative data sets | persistent excitation | persistent excitation | asymptotic variance | asymptotic variance | central limit theorem | central limit theorem | model structure selection | model structure selection | system order estimate | system order estimate | maximum likelihood | maximum likelihood | unbiased estimates | unbiased estimates | Cramer-Rao lower bound | Cramer-Rao lower bound | Kullback-Leibler information distance | Kullback-Leibler information distance | Akaike?s information criterion | Akaike?s information criterion | experiment design | experiment design | model validation | model validationLicense

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See all metadata14.385 Nonlinear Econometric Analysis (MIT) 14.385 Nonlinear Econometric Analysis (MIT)

Description

This course presents micro-econometric models, including large sample theory for estimation and hypothesis testing, generalized method of moments (GMM), estimation of censored and truncated specifications, quantile regression, structural estimation, nonparametric and semiparametric estimation, treatment effects, panel data, bootstrapping, simulation methods, and Bayesian methods. The methods are illustrated with economic applications. This course presents micro-econometric models, including large sample theory for estimation and hypothesis testing, generalized method of moments (GMM), estimation of censored and truncated specifications, quantile regression, structural estimation, nonparametric and semiparametric estimation, treatment effects, panel data, bootstrapping, simulation methods, and Bayesian methods. The methods are illustrated with economic applications.Subjects

nonlinear | nonlinear | econometric | econometric | analysis | analysis | generalized method of moments | generalized method of moments | GMM | GMM | maximum likelihood estimation | maximum likelihood estimation | MLE | MLE | minimum distance | minimum distance | extremum | extremum | large sample theory | large sample theory | asymptotic theory | asymptotic theory | discrete choice | discrete choice | censoring | censoring | sample selection | sample selection | bootstrap | bootstrap | subsampling | subsampling | finite-sample methods | finite-sample methods | quantile regression | quantile regression | QR | QR | distributional methods | distributional methods | Bayesian methods | Bayesian methods | quasi-Bayesian methods | quasi-Bayesian methods | bounds | bounds | partial identification | partial identification | weak instruments | weak instruments | many instruments | many instruments | instrumental variables | instrumental variables | nonparametric estimation | nonparametric estimation | semiparametric estimation | semiparametric estimation | treatment effects | treatment effects | nonlinear models | nonlinear models | panel data | panel data | economic modeling | economic modelingLicense

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See all metadata16.322 Stochastic Estimation and Control (MIT) 16.322 Stochastic Estimation and Control (MIT)

Description

The major themes of this course are estimation and control of dynamic systems. Preliminary topics begin with reviews of probability and random variables. Next, classical and state-space descriptions of random processes and their propagation through linear systems are introduced, followed by frequency domain design of filters and compensators. From there, the Kalman filter is employed to estimate the states of dynamic systems. Concluding topics include conditions for stability of the filter equations. The major themes of this course are estimation and control of dynamic systems. Preliminary topics begin with reviews of probability and random variables. Next, classical and state-space descriptions of random processes and their propagation through linear systems are introduced, followed by frequency domain design of filters and compensators. From there, the Kalman filter is employed to estimate the states of dynamic systems. Concluding topics include conditions for stability of the filter equations.Subjects

probability | probability | stochastic estimation | stochastic estimation | estimation | estimation | random variables | random variables | random processes | random processes | state space | state space | Wiener filter | Wiener filter | control system design | control system design | Kalman filter | Kalman filterLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course focuses on the design of control systems. Topics covered include: frequency domain and state space techniques; control law design using Nyquist diagrams and Bode plots; state feedback, state estimation, and the design of dynamic control laws; and elementary analysis of nonlinearities and their impact on control design. There is extensive use of computer-aided control design tools. Applications to various aerospace systems, including navigation, guidance, and control of vehicles, are also discussed. This course focuses on the design of control systems. Topics covered include: frequency domain and state space techniques; control law design using Nyquist diagrams and Bode plots; state feedback, state estimation, and the design of dynamic control laws; and elementary analysis of nonlinearities and their impact on control design. There is extensive use of computer-aided control design tools. Applications to various aerospace systems, including navigation, guidance, and control of vehicles, are also discussed.Subjects

estimation of aerospace systems | estimation of aerospace systems | control of aerospace systems | control of aerospace systems | control systems | control systems | frequency domain | frequency domain | state space | state space | control law design | control law design | Nyquist diagram | Nyquist diagram | Bode plot | Bode plot | state feedback | state feedback | state estimation | state estimation | dynamic control | dynamic control | nonlinearities | nonlinearities | nonlinearity | nonlinearity | control design | control design | computer-aided control design | computer-aided control design | feedback control system | feedback control systemLicense

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See all metadata2.160 Identification, Estimation, and Learning (MIT)

Description

This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.Subjects

system identification; estimation; least squares estimation; Kalman filter; noise dynamics; system representation; function approximation theory; neural nets; radial basis functions; wavelets; volterra expansions; informative data sets; persistent excitation; asymptotic variance; central limit theorem; model structure selection; system order estimate; maximum likelihood; unbiased estimates; Cramer-Rao lower bound; Kullback-Leibler information distance; Akaike?s information criterion; experiment design; model validation. | system identification | estimation | least squares estimation | Kalman filter | noise dynamics | system representation | function approximation theory | neural nets | radial basis functions | wavelets | volterra expansions | informative data sets | persistent excitation | asymptotic variance | central limit theorem | model structure selection | system order estimate | maximum likelihood | unbiased estimates | Cramer-Rao lower bound | Kullback-Leibler information distance | Akaike?s information criterion | experiment design | model validationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata14.381 Statistical Method in Economics (MIT) 14.381 Statistical Method in Economics (MIT)

Description

This course is divided into two sections, Part I and Part II. Part I provides an introduction to statistical theory and can be found by visiting 14.381 Fall 2013. Part II, found here, prepares students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, buil This course is divided into two sections, Part I and Part II. Part I provides an introduction to statistical theory and can be found by visiting 14.381 Fall 2013. Part II, found here, prepares students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, builSubjects

statistical theory | statistical theory | econometrics | econometrics | regression analysis | regression analysis | probability | probability | random samples | random samples | asymptotic methods | asymptotic methods | point estimation | point estimation | evaluation of estimators | evaluation of estimators | Cramer-Rao theorem | Cramer-Rao theorem | hypothesis tests | hypothesis tests | Neyman Pearson lemma | Neyman Pearson lemma | Likelihood Ratio test | Likelihood Ratio test | interval estimation | interval estimation | best linear predictor | best linear predictor | best linear approximation | best linear approximation | conditional expectation function | conditional expectation function | building functional forms | building functional forms | regression algebra | regression algebra | Gauss-Markov optimality | Gauss-Markov optimality | finite-sample inference | finite-sample inference | consistency | consistency | asymptotic normality | asymptotic normality | heteroscedasticity | heteroscedasticity | autocorrelation | autocorrelationLicense

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See all metadata16.885J Aircraft Systems Engineering (MIT) 16.885J Aircraft Systems Engineering (MIT)

Description

Includes audio/video content: AV lectures, AV special element video. 16.885J offers a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams retrospectively analyze an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Oral and written versions of the case study are delivered. For the Fall 2005 term, the class focuses on a systems engineering analysis of the Space Shuttle. It offers study of both design and operations of the shuttle, with frequent lectures by outside experts. Students choose specific s Includes audio/video content: AV lectures, AV special element video. 16.885J offers a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams retrospectively analyze an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Oral and written versions of the case study are delivered. For the Fall 2005 term, the class focuses on a systems engineering analysis of the Space Shuttle. It offers study of both design and operations of the shuttle, with frequent lectures by outside experts. Students choose specific sSubjects

16.885 | 16.885 | ESD.35 | ESD.35 | aircraft systems | aircraft systems | aircraft systems engineering | aircraft systems engineering | lifecycle | lifecycle | cost estimation | cost estimation | weight estimation | weight estimation | aircraft performance | aircraft performance | aircraft safety | aircraft safety | aircraft reliability | aircraft reliability | subsystems | subsystems | risk analysis | risk analysis | risk management | risk management | system realization | system realization | retrospective analysis | retrospective analysis | key design drivers | key design drivers | design drivers | design drivers | design decisions | design decisions | aircraft attributes | aircraft attributes | operational experience | operational experience | case study | case study | case studies | case studies | air transportation system | air transportation system | air defense system | air defense system | systems engineering | systems engineering | interface management | interface management | interface verification | interface verification | interface validation | interface validation | subsystem architecture | subsystem architecture | performance issues | performance issues | design closure | design closure | complex systems | complex systems | space shuttle | space shuttle | space systems | space systems | NASA | NASA | sound barrier | sound barrier | ascent | ascent | aeronautics | aeronautics | liftoff | liftoff | takeoff | takeoffLicense

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See all metadata18.443 Statistics for Applications (MIT) 18.443 Statistics for Applications (MIT)

Description

This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. The course topics include hypothesis testing and estimation. It also includes confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. The course topics include hypothesis testing and estimation. It also includes confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation.Subjects

hypothesis testing and estimation; confidence intervals; chi-square tests; nonparametric statistics; analysis of variance; regression; correlation | hypothesis testing and estimation; confidence intervals; chi-square tests; nonparametric statistics; analysis of variance; regression; correlation | hypothesis testing and estimation | hypothesis testing and estimation | confidence intervals | confidence intervals | chi-square tests | chi-square tests | nonparametric statistics | nonparametric statistics | analysis of variance | analysis of variance | regression | regression | correlation | correlationLicense

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See all metadata18.466 Mathematical Statistics (MIT) 18.466 Mathematical Statistics (MIT)

Description

This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis. This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.Subjects

decision theory | decision theory | testing simple hypothesis | testing simple hypothesis | Neyman-Pearson Lemma | Neyman-Pearson Lemma | Bayes decision theory | Bayes decision theory | sufficiency | sufficiency | estimation | estimation | convexity | convexity | Lehmann-Scheff'e property | Lehmann-Scheff'e property | Exponential families | Exponential families | Stein?s phenomenon | Stein?s phenomenon | James-Stein estimators | James-Stein estimators | M-estimation | M-estimation | Solari?s example | Solari?s example | Wilks?s theorem | Wilks?s theorem | stochastic processes | stochastic processes | probability theory | probability theory | confidence intervals | confidence intervals | large sample theory | large sample theory | sequential analysis | sequential analysis | asymptotic efficiency | asymptotic efficiencyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.435 System Identification (MIT)

Description

This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; bounded but unknown noise model; and robustness and practical issues.Subjects

mathematical models | time series | state-space | input-output models | model structures | parametrization | identifiability | non-parametric methods | prediction error | parameter estimation | convergence | consistency | andasymptotic distribution | maximum likelihood estimation | recursive estimation | Kalman filters | structure determination | order estimation | Akaike criterion | bounded noise models | robustnessLicense

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Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site. Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equations | Navier-Stokes equations | Navier-Stokes equationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment. This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equationsLicense

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This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for EnvironmSubjects

probability | probability | statistics | statistics | events | events | random variables | random variables | univariate distributions | univariate distributions | multivariate distributions | multivariate distributions | uncertainty propagation | uncertainty propagation | Bernoulli trials | Bernoulli trials | Poisson processed | Poisson processed | conditional probability | conditional probability | Bayes rule | Bayes rule | random sampling | random sampling | point estimation | point estimation | interval estimation | interval estimation | hypothesis testing | hypothesis testing | analysis of variance | analysis of variance | linear regression | linear regression | computational analysis | computational analysis | data analysis | data analysis | environmental engineering | environmental engineering | applications | applications | MATLAB | MATLAB | numerical modeling | numerical modeling | probabilistic concepts | probabilistic concepts | statistical methods | statistical methods | field data | field data | laboratory data | laboratory data | numerical techniques | numerical techniques | Monte Carlo simulation | Monte Carlo simulation | variability | variability | sampling | sampling | data sets | data sets | computer | computer | uncertainty | uncertainty | interpretation | interpretation | quantitative data | quantitative dataLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course examines the fundamentals of detection and estimation for signal processing, communications, and control. Topics covered include: vector spaces of random variables; Bayesian and Neyman-Pearson hypothesis testing; Bayesian and nonrandom parameter estimation; minimum-variance unbiased estimators and the Cramer-Rao bounds; representations for stochastic processes, shaping and whitening filters, and Karhunen-Loeve expansions; and detection and estimation from waveform observations. Advanced topics include: linear prediction and spectral estimation, and Wiener and Kalman filters. This course examines the fundamentals of detection and estimation for signal processing, communications, and control. Topics covered include: vector spaces of random variables; Bayesian and Neyman-Pearson hypothesis testing; Bayesian and nonrandom parameter estimation; minimum-variance unbiased estimators and the Cramer-Rao bounds; representations for stochastic processes, shaping and whitening filters, and Karhunen-Loeve expansions; and detection and estimation from waveform observations. Advanced topics include: linear prediction and spectral estimation, and Wiener and Kalman filters.Subjects

stochastic process | stochastic process | detection | detection | estimation | estimation | signal processing | signal processing | communications | communications | control | control | vector spaces | vector spaces | Bayesian | Bayesian | Neyman-Pearson | Neyman-Pearson | minimum-variance unbiased estimator | minimum-variance unbiased estimator | Cramer-Rao bounds | Cramer-Rao bounds | shaping filter | shaping filter | whitening filter | whitening filter | Karhunen-Loeve expansion | Karhunen-Loeve expansion | waveform observation | waveform observation | linear prediction | linear prediction | spectral estimation | spectral estimation | Wiener filter | Wiener filter | Kalman filter | Kalman filterLicense

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See all metadata16.885J Aircraft Systems Engineering (MIT) 16.885J Aircraft Systems Engineering (MIT)

Description

Aircraft are complex products comprised of many subsystems which must meet demanding customer and operational lifecycle value requirements. This course adopts a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams "retrospectively analyze" an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Finally, the student teams deliver oral and written versions of the case study. Aircraft are complex products comprised of many subsystems which must meet demanding customer and operational lifecycle value requirements. This course adopts a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams "retrospectively analyze" an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Finally, the student teams deliver oral and written versions of the case study.Subjects

aircraft systems | aircraft systems | aircraft systems engineering | aircraft systems engineering | lifecycle | lifecycle | cost estimation | cost estimation | weight estimation | weight estimation | aircraft performance | aircraft performance | aircraft safety | aircraft safety | aircraft reliability | aircraft reliability | subsystems; risk analysis | subsystems; risk analysis | risk management | risk management | system realization | system realization | retrospective analysis | retrospective analysis | key design drivers | key design drivers | design drivers | design drivers | design decisions | design decisions | aircraft attributes | aircraft attributes | operational experience | operational experience | case study | case study | case studies | case studies | air transportation systems | air transportation systems | air defense system | air defense system | systems engineering | systems engineering | interface management | interface management | interface verification | interface verification | subsystem architecture | subsystem architecture | performance issures | performance issures | design closure | design closure | complex systems | complex systems | 16.885 | 16.885 | ESD.35 | ESD.35License

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See all metadata16.30 Feedback Control Systems (MIT) 16.30 Feedback Control Systems (MIT)

Description

This course will teach fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, you should be able to design controllers using state-space methods and evaluate whether these controllers are robust to some types of modeling errors and nonlinearities. You will learn to: Design controllers using state-space methods and analyze using classical tools. Understand impact of implementation issues (nonlinearity, delay). Indicate the robustness of your control design. Linearize a nonlinear system, and analyze stability. This course will teach fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, you should be able to design controllers using state-space methods and evaluate whether these controllers are robust to some types of modeling errors and nonlinearities. You will learn to: Design controllers using state-space methods and analyze using classical tools. Understand impact of implementation issues (nonlinearity, delay). Indicate the robustness of your control design. Linearize a nonlinear system, and analyze stability.Subjects

control design | control design | control analysis | control analysis | state-space methods | state-space methods | linear systems | linear systems | estimation filters | estimation filters | dynamic output feedback | dynamic output feedback | full state feedback | full state feedback | state estimation | state estimation | output feedback | output feedback | nonlinear analysis | nonlinear analysis | model uncertainty | model uncertainty | robustness | robustnessLicense

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See all metadata16.885J Aircraft Systems Engineering (MIT) 16.885J Aircraft Systems Engineering (MIT)

Description

Aircraft are complex products comprised of many subsystems which must meet demanding customer and operational lifecycle value requirements. This course adopts a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams "retrospectively analyze" an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Finally, the student teams deliver oral and written versions of the case study. Aircraft are complex products comprised of many subsystems which must meet demanding customer and operational lifecycle value requirements. This course adopts a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams "retrospectively analyze" an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Finally, the student teams deliver oral and written versions of the case study.Subjects

aircraft systems | aircraft systems | aircraft systems engineering | aircraft systems engineering | lifecycle | lifecycle | cost estimation | cost estimation | weight estimation | weight estimation | aircraft performance | aircraft performance | aircraft safety | aircraft safety | aircraft reliability | aircraft reliability | subsystems; risk analysis | subsystems; risk analysis | risk management | risk management | system realization | system realization | retrospective analysis | retrospective analysis | key design drivers | key design drivers | design drivers | design drivers | design decisions | design decisions | aircraft attributes | aircraft attributes | operational experience | operational experience | case study | case study | case studies | case studies | air transportation systems | air transportation systems | air defense system | air defense system | systems engineering | systems engineering | interface management | interface management | interface verification | interface verification | subsystem architecture | subsystem architecture | performance issures | performance issures | design closure | design closure | complex systems | complex systems | 16.885 | 16.885 | ESD.35 | ESD.35License

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See all metadata14.385 Nonlinear Econometric Analysis (MIT)

Description

This course presents micro-econometric models, including large sample theory for estimation and hypothesis testing, generalized method of moments (GMM), estimation of censored and truncated specifications, quantile regression, structural estimation, nonparametric and semiparametric estimation, treatment effects, panel data, bootstrapping, simulation methods, and Bayesian methods. The methods are illustrated with economic applications.Subjects

nonlinear | econometric | analysis | generalized method of moments | GMM | maximum likelihood estimation | MLE | minimum distance | extremum | large sample theory | asymptotic theory | discrete choice | censoring | sample selection | bootstrap | subsampling | finite-sample methods | quantile regression | QR | distributional methods | Bayesian methods | quasi-Bayesian methods | bounds | partial identification | weak instruments | many instruments | instrumental variables | nonparametric estimation | semiparametric estimation | treatment effects | nonlinear models | panel data | economic modelingLicense

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See all metadata6.830 Database Systems (MIT) 6.830 Database Systems (MIT)

Description

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken MIT course 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. Topics related to the engineering and design of database systems, including: data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel, and he This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken MIT course 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend. Topics related to the engineering and design of database systems, including: data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel, and heSubjects

engineering and design of database systems | data models | engineering and design of database systems | data models | database and schema design | database and schema design | schema normalization and integrity constraints | schema normalization and integrity constraints | query processing | query processing | query optimization and cost estimation | query optimization and cost estimation | transactions | transactions | recovery | recovery | concurrency control | concurrency control | isolation and consistency | isolation and consistency | distributed | distributed | parallel | parallel | heterogeneous databases | heterogeneous databases | adaptive databases | adaptive databases | trigger systems | trigger systems | pub-sub systems | pub-sub systems | semi structured data and XML querying | semi structured data and XML queryingLicense

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See all metadata16.322 Stochastic Estimation and Control (MIT)

Description

The major themes of this course are estimation and control of dynamic systems. Preliminary topics begin with reviews of probability and random variables. Next, classical and state-space descriptions of random processes and their propagation through linear systems are introduced, followed by frequency domain design of filters and compensators. From there, the Kalman filter is employed to estimate the states of dynamic systems. Concluding topics include conditions for stability of the filter equations.Subjects

probability | stochastic estimation | estimation | random variables | random processes | state space | Wiener filter | control system design | Kalman filterLicense

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See all metadata1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for EnvironmSubjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative dataLicense

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See all metadata1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for EnvironmSubjects

probability | statistics | events | random variables | univariate distributions | multivariate distributions | uncertainty propagation | Bernoulli trials | Poisson processed | conditional probability | Bayes rule | random sampling | point estimation | interval estimation | hypothesis testing | analysis of variance | linear regression | computational analysis | data analysis | environmental engineering | applications | MATLAB | numerical modeling | probabilistic concepts | statistical methods | field data | laboratory data | numerical techniques | Monte Carlo simulation | variability | sampling | data sets | computer | uncertainty | interpretation | quantitative dataLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision(millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamen The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision(millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamenSubjects

Global Positioning System | Global Positioning System | Earth Sciences | Earth Sciences | geophysical applications | geophysical applications | GPS | GPS | engineering applications | engineering applications | kinematic positioning | kinematic positioning | precision | precision | accuracy | accuracy | moving objects | moving objects | coordinate | coordinate | time | time | systems | systems | satellite | satellite | geodetic | geodetic | orbital | orbital | motions | motions | pseudo ranges | pseudo ranges | carrier phases | carrier phases | stochastic | stochastic | mathematics | mathematics | models | models | data | data | analysis | analysis | estimation | estimationLicense

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See all metadata2.007 Design and Manufacturing I (MIT) 2.007 Design and Manufacturing I (MIT)

Description

Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering. See this MIT News story for more background, a photo gallery, and videos about this course. Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering. See this MIT News story for more background, a photo gallery, and videos about this course.Subjects

engineering design | engineering design | synthesis | synthesis | analysis | analysis | robustness | robustness | manufacturability | manufacturability | active learning | active learning | idea generation | idea generation | estimation | estimation | materials selection | materials selection | visual thinking | visual thinking | kinematics | kinematics | machine elements | machine elements | robotics | robotics | mechanical engineering | mechanical engineering | student work | student work | contest | contestLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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