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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT) 8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories. This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | correlation functions | and scaling theory | The renormalization approach to collective phenomena | The renormalization approach to collective phenomena | Dynamic critical behavior | Dynamic critical behavior | Random systems | Random systems | correlation functions | correlation functions | and scaling theory | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

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18.441 Statistical Inference (MIT) 18.441 Statistical Inference (MIT)

Description

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics). Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

Subjects

probability | probability | statistical inference | statistical inference | Point and interval estimation | Point and interval estimation | The maximum likelihood method | The maximum likelihood method | Hypothesis testing | Hypothesis testing | Likelihood-ratio tests | Likelihood-ratio tests | Bayesian methods | Bayesian methods | Nonparametric methods | Nonparametric methods | Analysis of variance | Analysis of variance | regression analysis | regression analysis | correlation | correlation | Chi-square goodness of fit tests | Chi-square goodness of fit tests | Likelihood-ratio tests and Bayesian methods | Likelihood-ratio tests and Bayesian methods | regression analysis and correlation | regression analysis and correlation | probability | statistical inference | probability | statistical inference | Analysis of variance | regression analysis and correlation | Analysis of variance | regression analysis and correlation

License

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18.443 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 | correlation

License

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations. Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | Microcanonical | canonical | canonical | grand canonical partition-functions | grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | correlation functions and susceptibilities | Kubo formulae | Kubo formulae | Evolution of distribution functions | Evolution of distribution functions | Boltzmann and Smoluchowski equations | Boltzmann and Smoluchowski equations | correlation functions | correlation functions | susceptibilities | susceptibilities

License

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8.334 Statistical Mechanics II: Statistical Mechanics of Fields (MIT)

Description

This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in 8.334, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored including the hydrodynamic limit and classical field theories.

Subjects

the hydrodynamic limit and classical field theories | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory | The renormalization approach to collective phenomena | Dynamic critical behavior | Random systems | correlation functions | and scaling theory | Phase transitions and broken symmetries: universality | correlation functions | and scaling theory

License

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.htm

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18.441 Statistical Inference (MIT)

Description

Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).

Subjects

probability | statistical inference | Point and interval estimation | The maximum likelihood method | Hypothesis testing | Likelihood-ratio tests | Bayesian methods | Nonparametric methods | Analysis of variance | regression analysis | correlation | Chi-square goodness of fit tests | Likelihood-ratio tests and Bayesian methods | regression analysis and correlation | probability | statistical inference | Analysis of variance | regression analysis and correlation

License

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. Mathematical modeling of diffusion phenomena: Central limit theorems, the continuum limit, first passage, persistence, continuous-time random walks, Levy flights, fractional calculus, random environments, advection-diffusion, nonlinear diffusion, free-boundary problems. Applications may include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | Discrete and continuum modeling of diffusion processes in physics | chemistry | chemistry | and economics | and economics | central limit theorems | central limit theorems | ontinuous-time random walks | ontinuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes. 5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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14.123 Microeconomic Theory III (MIT) 14.123 Microeconomic Theory III (MIT)

Description

This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation. This half-semester course discusses decision theory and topics in game theory. We present models of individual decision-making under certainty and uncertainty. Topics include preference orderings, expected utility, risk, stochastic dominance, supermodularity, monotone comparative statics, background risk, game theory, rationalizability, iterated strict dominance multi-stage games, sequential equilibrium, trembling-hand perfection, stability, signaling games, theory of auctions, global games, repeated games, and correlation.

Subjects

microeconomics | microeconomics | microeconomic theory | microeconomic theory | preference | preference | utility representation | utility representation | expected utility | expected utility | positive interpretation | positive interpretation | normative interpretation | normative interpretation | risk | risk | stochastic dominance | stochastic dominance | insurance | insurance | finance | finance | supermodularity | supermodularity | comparative statics | comparative statics | decision theory | decision theory | game theory | game theory | rationalizability | rationalizability | iterated strict dominance | iterated strict dominance | iterated conditional dominance | iterated conditional dominance | bargaining | bargaining | equilibrium | equilibrium | sequential equilibrium | sequential equilibrium | trembling-hand perfection | trembling-hand perfection | signaling games | signaling games | auctions | auctions | global games | global games | repeated games | repeated games | correlation | correlation

License

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9.29J Introduction to Computational Neuroscience (MIT) 9.29J Introduction to Computational Neuroscience (MIT)

Description

Mathematical introduction to neural coding and dynamics. Convolution, correlation, linear systems, Fourier analysis, signal detection theory, probability theory, and information theory. Applications to neural coding, focusing on the visual system. Hodgkin-Huxley and related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Mathematical introduction to neural coding and dynamics. Convolution, correlation, linear systems, Fourier analysis, signal detection theory, probability theory, and information theory. Applications to neural coding, focusing on the visual system. Hodgkin-Huxley and related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission.

Subjects

neural coding | neural coding | dynamics | dynamics | convolution | convolution | correlation | correlation | linear systems | linear systems | Fourier analysis | Fourier analysis | signal detection theory | signal detection theory | probability theory | probability theory | information theory | information theory | neural excitability | neural excitability | stochastic models | stochastic models | ion channels | ion channels | cable theory | cable theory | 9.29 | 9.29 | 8.261 | 8.261

License

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22.903 Photon and Neutron Scattering Spectroscopy and Its Applications in Condensed Matter (MIT) 22.903 Photon and Neutron Scattering Spectroscopy and Its Applications in Condensed Matter (MIT)

Description

The purpose of this course is to discuss modern techniques of generation of x-ray photons and neutrons and then follow with selected applications of newly developed photon and neutron scattering spectroscopic techniques to investigations of properties of condensed matter which are of interest to nuclear engineers. The purpose of this course is to discuss modern techniques of generation of x-ray photons and neutrons and then follow with selected applications of newly developed photon and neutron scattering spectroscopic techniques to investigations of properties of condensed matter which are of interest to nuclear engineers.

Subjects

Nuclear engineering | Nuclear engineering | photon | photon | neutron | neutron | scattering | scattering | spectroscopy | spectroscopy | neutron sources | neutron sources | photon sources | photon sources | neutron scattering theory | neutron scattering theory | light and X-ray scattering theory | light and X-ray scattering theory | linear response theory | linear response theory | inelastic neutron scattering spectroscopy | inelastic neutron scattering spectroscopy | quasielastic neutron scattering spectroscopy | quasielastic neutron scattering spectroscopy | photon correlation spectroscopy | photon correlation spectroscopy | inelastic X-ray scattering spectroscopy | inelastic X-ray scattering spectroscopy

License

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RES.LL-005 D4M: Signal Processing on Databases (MIT) RES.LL-005 D4M: Signal Processing on Databases (MIT)

Description

Includes audio/video content: AV lectures. D4M is a breakthrough in computer programming that combines graph theory, linear algebra, and databases to address problems associated with Big Data. Search, social media, ad placement, mapping, tracking, spam filtering, fraud detection, wireless communication, drug discovery, and bioinformatics all attempt to find items of interest in vast quantities of data. This course teaches a signal processing approach to these problems by combining linear algebraic graph algorithms, group theory, and database design. This approach has been implemented in software The class will begin with a number of practical problems, introduce the appropriate theory and then apply the theory to these problems. Students will apply these ideas in the final project of their Includes audio/video content: AV lectures. D4M is a breakthrough in computer programming that combines graph theory, linear algebra, and databases to address problems associated with Big Data. Search, social media, ad placement, mapping, tracking, spam filtering, fraud detection, wireless communication, drug discovery, and bioinformatics all attempt to find items of interest in vast quantities of data. This course teaches a signal processing approach to these problems by combining linear algebraic graph algorithms, group theory, and database design. This approach has been implemented in software The class will begin with a number of practical problems, introduce the appropriate theory and then apply the theory to these problems. Students will apply these ideas in the final project of their

Subjects

big data | big data | data analytics | data analytics | dynamic distributed dimensional data model | dynamic distributed dimensional data model | D4M | D4M | associate arrays | associate arrays | group theory | group theory | entity analysis | entity analysis | perfect Power Law | perfect Power Law | bio sequence correlation | bio sequence correlation | Accumulo | Accumulo | Kronecker graphs | Kronecker graphs

License

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14.381 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, buil

Subjects

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 | autocorrelation

License

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18.443 Statistics for Applications (MIT) 18.443 Statistics for Applications (MIT)

Description

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics. Note: Please see the syllabus for a description of the different versions of 18.443 taught at MIT. This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics. Note: Please see the syllabus for a description of the different versions of 18.443 taught at MIT.

Subjects

hypothesis testing | hypothesis testing | hypothesis estimation | hypothesis estimation | confidence intervals | confidence intervals | chi-square tests | chi-square tests | nonparametric statistics | nonparametric statistics | analysis of variance | analysis of variance | regression | regression | correlation | correlation | decision theory | decision theory | Bayesian statistics | Bayesian statistics

License

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14.32 Econometrics (MIT) 14.32 Econometrics (MIT)

Description

Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement. Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

Subjects

econometrics | econometrics | statistical methods | statistical methods | differences-in-differences | differences-in-differences | 2SLS | 2SLS | FGLS | FGLS | serial correlation | serial correlation | IV | IV | two-stage least squares | two-stage least squares | multivariate regression | multivariate regression | simultaneous equations | simultaneous equations | econometric models | econometric models | program evaluation | program evaluation | linear regression | linear regression | instrumental variables | instrumental variables | panel data methods | panel data methods | measurement error | measurement error | limited dependent variable models | limited dependent variable models

License

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5.74 Introductory Quantum Mechanics II (MIT) 5.74 Introductory Quantum Mechanics II (MIT)

Description

This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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14.382 Econometrics I (MIT) 14.382 Econometrics I (MIT)

Description

This course focuses on the specification and estimation of the linear regression model. The course departs from the standard Gauss-Markov assumptions to include heteroskedasticity, serial correlation, and errors in variables. Advanced topics include generalized least squares, instrumental variables, nonlinear regression, and limited dependent variable models. Economic applications are discussed throughout the course. This course focuses on the specification and estimation of the linear regression model. The course departs from the standard Gauss-Markov assumptions to include heteroskedasticity, serial correlation, and errors in variables. Advanced topics include generalized least squares, instrumental variables, nonlinear regression, and limited dependent variable models. Economic applications are discussed throughout the course.

Subjects

Economics | Economics | econometrics | econometrics | linear regression model | linear regression model | Gauss-Markov | Gauss-Markov | heteroskedasticity | heteroskedasticity | serial correlation | serial correlation | errors | errors | variables | variables | generalized least squares | generalized least squares | instrumental variables | instrumental variables | nonlinear regression | nonlinear regression | limited dependent variable models | limited dependent variable models

License

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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.

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

License

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9.63 Laboratory in Cognitive Science (MIT) 9.63 Laboratory in Cognitive Science (MIT)

Description

9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports. 9.63 teaches principles of experimental methods in human perception and cognition, including design and statistical analysis. The course combines lectures and hands-on experimental exercises and requires an independent experimental project. Some experience in programming is desirable. To foster improved writing and presentation skills in conducting and critiquing research in cognitive science, students are required to provide reports and give oral presentations of three team experiments. A fourth individually conducted experiment includes a proposal with revision, and concluding written and oral reports.

Subjects

cognitive science | cognitive science | human perception | human perception | cognition | cognition | statistical analysis | statistical analysis | signal detection theory | signal detection theory | single factor design | single factor design | factorial design | factorial design | matlab | matlab | correlational studies | correlational studies | ethics in research | ethics in research

License

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolation

License

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.htm

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14.32 Econometrics (MIT) 14.32 Econometrics (MIT)

Description

This course covers the statistical tools needed to understand empirical economic research and to plan and execute independent research projects. Topics include statistical inference, regression, generalized least squares, instrumental variables, simultaneous equations models, and the evaluation of government policies and programs.Technical RequirementsAny text editor can be used to view the .asc files found on this course site. Please refer to the course materials for any specific instructions or recommendations. Any number of software tools can be used to import the data files found on this course site. Please refer to the course materials for any specific instructions or recommendations. This course covers the statistical tools needed to understand empirical economic research and to plan and execute independent research projects. Topics include statistical inference, regression, generalized least squares, instrumental variables, simultaneous equations models, and the evaluation of government policies and programs.Technical RequirementsAny text editor can be used to view the .asc files found on this course site. Please refer to the course materials for any specific instructions or recommendations. Any number of software tools can be used to import the data files found on this course site. Please refer to the course materials for any specific instructions or recommendations.

Subjects

probability | probability | distribution | distribution | sampling | sampling | confidence intervals | confidence intervals | bivariate regression | bivariate regression | residuals | residuals | fitted values | fitted values | goodness of fit | | goodness of fit | | multivariate regression | multivariate regression | heteroscedasticity | heteroscedasticity | linear probability models | linear probability models | serial correlation | serial correlation | measurement error | measurement error | goodness of fit | goodness of fit

License

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.htm

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses. This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | canonical | and grand canonical partition-functions | Microcanonical | canonical | and grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | and Kubo formulae | correlation functions and susceptibilities | and Kubo formulae | Evolution of distribution functions: Boltzmann and Smoluchowski equations | Evolution of distribution functions: Boltzmann and Smoluchowski equations

License

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.htm

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18.443 Statistics for Applications (MIT) 18.443 Statistics for Applications (MIT)

Description

This course offers a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. OCW offers an earlier version of this course, from Fall 2003. This newer version focuses less on estimation theory and more on multiple linear regression models. In addition, a number of Matlab examples are included here. This course offers a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. OCW offers an earlier version of this course, from Fall 2003. This newer version focuses less on estimation theory and more on multiple linear regression models. In addition, a number of Matlab examples are included here.

Subjects

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 | correlation

License

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.htm

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18.366 Random Walks and Diffusion (MIT) 18.366 Random Walks and Diffusion (MIT)

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Subjects

Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | Discrete and continuum modeling of diffusion processes in physics | chemistry | and economics | central limit theorems | central limit theorems | continuous-time random walks | continuous-time random walks | Levy flights | Levy flights | correlations | correlations | extreme events | extreme events | mixing | mixing | renormalization | renormalization | and percolation | and percolation | percolation | percolation

License

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.htm

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