. "Other Statistics (rather Than Geostatistics) Kas"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Basics of statistics"@en . . "4" . "The objectives of this course are:\r\n-acquire the skills of collecting, classification and organization of data, their analysis and graphical presentation using\r\nappropriate computer programs (Excel, Statistica,..) as a tool in solving various statistical tasks that appear in geodesy\r\nand geoinformatics\r\n-help students to overcome more easily the other courses that follow, particularly analysis and processing of geodetic\r\nmeasurements\r\n- Demonstrate competences in theoretical principles, procedures of computing and visualising the surveying data.\r\n- Understand mathematical methods and physical laws applied -----Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in\r\nthe field of geodesy and geoinformatics.\r\n-Use information technology in solving geodetic and geoinformation tasks -Recognise problems and tasks in the application of geodetic and geoinformation principles and methods, and select\r\nproper procedures for their solution.\r\n-Be able to collect data and their presentation in the form of tables or graphs\r\n-Define mean and dispersion measures\r\n-Define basic terms in the probability theory Define discrete and continuous random variables and their distributions\r\n-Define and apply statistical tests -- Define regresion analysis, covariance and correlation\r\n-Be able to apply methods of interpolation in geodesy and geoinformatics\r\n- Be able to apply methods of appoximation in geodesy and geoinformatics" . . "Presential"@en . "TRUE" . . "Modern astrostatistics"@en . . "3" . "Randomness, uncertainties and deviations from the norm surround us in everyday life. A major asset of any scientist is to see beyond the complexity of noise, scatter and biases, and to find an underlying -often surprisingly simple- explanation for the noisy data. This course is specialized to astronomical data analysis, but the topics discussed will also foster an improved understanding of Google, Facebook and other free social media services.\n\nTopics that will be covered include:\n\nDescriptive statistics: Finding meaning in a huge data set.\nInference statistics: Constraining a physical model by data.\nFiltering, e.g. for gravitational wave detections and source detection.\nRandom fields: Sky surveys and structure formation in cosmology.\nSampling methods: Making huge data analyses numerically feasible.\nBayesian Hierarchical Models: How to disentangle a seemingly complex analysis.\nPrior Theory and Information Measures: How not to hide prejudices in an analyses.\nMissing data and elusive physics: What to do if your sought signal hides in the dark figures?\nMachine learning: Finding patterns which escape humans.\n\nOutcome:\nPrincipal course objective: After completion of this course, you will be able to correctly interpret noisy data. You will be able to design and apply statistical methods to answer scientific questions. You will be able to measure parameters, discover astronomical objects, or discover elusive signals in noisy data.\n\nUpon completion of this course, you will be able to:\n\nRecognize the most common distributions of noisy astronomical data\nIdentify signals in noisy data\nReject theories which are incompatible with data\nDesign own statistical methods to analyze complex data\nCategorize astronomical objects\nSolve simple Bayesian Hierarchical Models\nDiscover prejudices in analyses\nExplain basic machine learning algorithms" . . "Presential"@en . "TRUE" . . "Modern astrostatistics"@en . . "3" . "Randomness, uncertainties and deviations from the norm surround us in everyday life. A major asset of any scientist is to see beyond the complexity of noise, scatter and biases, and to find an underlying -often surprisingly simple- explanation for the noisy data. This course is specialized to astronomical data analysis, but the topics discussed will also foster an improved understanding of Google, Facebook and other free social media services.\r\n\r\nTopics that will be covered include:\r\n\r\nDescriptive statistics: Finding meaning in a huge data set.\r\n\r\nInference statistics: Constraining a physical model by data.\r\n\r\nFiltering, e.g. for gravitational wave detections and source detection.\r\n\r\nRandom fields: Sky surveys and structure formation in cosmology.\r\n\r\nSampling methods: Making huge data analyses numerically feasible.\r\n\r\nBayesian Hierarchical Models: How to disentangle a seemingly complex analysis.\r\n\r\nPrior Theory and Information Measures: How not to hide prejudices in an analyses.\r\n\r\nMissing data and elusive physics: What to do if your sought signal hides in the dark figures?\r\n\r\nMachine learning: Finding patterns which escape humans.\n\nOutcome:\nAfter completion of this course, you will be able to correctly interpret noisy data. You will be able to design and apply statistical methods to answer scientific questions. You will be able to measure parameters, discover astronomical objects, or discover elusive signals in noisy data.\r\n\r\nUpon completion of this course, you will be able to:\r\n\r\nRecognize the most common distributions of noisy astronomical data\r\n\r\nIdentify signals in noisy data\r\n\r\nReject theories which are incompatible with data\r\n\r\nDesign own statistical methods to analyze complex data\r\n\r\nCategorize astronomical objects\r\n\r\nSolve simple Bayesian Hierarchical Models\r\n\r\nDiscover prejudices in analyses\r\n\r\nExplain basic machine learning algorithms" . . "Presential"@en . "FALSE" . . "Statistical learning"@en . . "8" . "Students will acquire the knowledge to conduct \r\nstatistical analysis on a variety of data sets using a \r\nwide range of modern computerized methods. The \r\nstudents will learn how to recognize which tools \r\nare needed to analyze different types of datasets, \r\nhow to apply these tools in each case, and how to \r\nemploy diagnostics to assess the quality of their \r\nresults. They will learn about statistical models, their \r\ncomplexity and their relative benefits depending \r\non the available data. Some of the tools that the \r\nstudents will come to learn well include linear simple \r\nand multiple regression, nearest neighbors methods,\r\nshrinkage methods (ridge, lasso), dimension \r\nreduction methods (principal components), logistic \r\nregression, linear discriminant analysis, tree-based \r\nmethods, model selection algorithms with criterion \r\nor by resampling techniques and clustering. \r\nThe focus of the course will be less on theory \r\nand more on providing the students with as much \r\nintuition as possible and acquainting them with as \r\nmany methods as possible. The course will make \r\nsubstantial use of the R statistical programming \r\nlanguage and its libraries. \n\nOutcome: Not Provided" . . "Presential"@en . "TRUE" . . "Time series analysis"@en . . "8" . "Stochastic processes, weak and strong stationarity. \r\nAutoregressive and moving average based models \r\nfor stationary and non-stationary time series. \r\nTrend and seasonal behaviour, sample \r\nautocorrelation function and sample partial \r\nautocorrelation function. Parameter estimations, \r\nmodel identification, prediction. ARMA, ARIMA \r\nand SARIMA models. Properties, estimation and \r\nexamples. ARCH and GARCH models for volatility.\n\nOutcome: Not Provided" . . "Presential"@en . "TRUE" . . "Multivariate analysis"@en . . "8" . "This course studies topics from multivariate \r\nstatistical analysis. Topics covered include: \r\nrandom vectors, measures of center and variation \r\nin multivariate moments. Multivariate normal \r\ndistribution. Tests for normality. Estimation of \r\nthe mean vector and the variance analysis, \r\nindependence, multivariate –covariance matrix. \r\nWishart and Hotelling distributions. Statistical \r\ninference. Union – Intersection Test. Confidence \r\nregions. Multivariate analysis of variance and \r\nmultivariate regression analysis. Least squares \r\nmethod and Wilks distribution. Analysis of \r\ncovariance. Principal components, Factor analysis, \r\nDiscriminant analysis, Cluster analysis. The R \r\nstatistical programming language will be used for \r\napplying the introduced methods in a range of Data \r\nScience problems.\n\nOutcome: Not Provided" . . "Presential"@en . "TRUE" . . "Bayesian statistics"@en . . "8" . "This course introduces Bayesian Statistics, \r\nan intuitive approach to Statistics allowing for \r\nbetter accounting of uncertainty. Topics include: \r\nsubjective probability, Bayes rule, prior and posterior \r\ndistributions, conjugate and non-informative \r\npriors, point-wise estimation and credible intervals, \r\nhypothesis testing, introduction to Bayesian \r\ndecision analysis, introduction to empirical Bayes \r\nanalysis, introduction to Markov chain Monte Carlo \r\ntechniques. The course will make use of R statistical \r\nprogramming language for the implementation \r\nof algorithms for extracting information from the \r\nposterior and for the application of the introduced \r\nmethods in a range of Data Science problems.\r\n\nOutcome: Not Provided" . . "Presential"@en . "TRUE" . . "Statistical methods"@en . . "5" . "LEARNING OUTCOMES\nAfter the course, the student will...\n\nlearn to know the basics of statistics and statistical distribution as well as being able to apply the correct distribution.\nunderstand hypotheses testing and different methods for hypotheses testing as well as the strengths and weaknesses of the methods.\nunderstand parameter estimation based on maximum likelihood and least squares methods as well as the strengths and weaknesses of the methods.\nbeing able to apply methods of hypothesis testing and parameter estimation as well as make the correct statistical interpretation.\nbeing familiar with confidence intervals and unfolding.\nCONTENT\nFundamental concepts: experimental errors and their correct interpretation, frequentist & Bayesian interpretation of probability, the most common statistical distributions and their applications.\nMonte Carlo methods: basics of Monte Carlo methods and generation of an arbitrary distribution.\nHypothesis testing: the concept of hypothesis testing, a test statistic, discriminant multivariate analysis, goodness-of-fit tests and ANOVA.\nParameter & error estimation: the concept of parameter estimation, an estimator, the maximum likelihood method and the method of least squares.\nConfidence intervals & Unfolding." . . "Presential"@en . "FALSE" . . "Statistical inverse methods"@en . . "5" . "LEARNING OUTCOMES\nYou will learn\n\nAdvanced statistical methods to describe and analyze research data\nTheory and practice of statistical estimation and testing\nMultivariate methods\nMonte Carlo statistical techniques\nBayesian inference\nStatistical inversion using Markov Chain Monte Carlo methods\nCONTENT\nStatistical inference, linear model, nonlinear model, kernel estimation, multivariate methods, Bayesian inference, Monte Carlo methods, MCMC." . . "Presential"@en . "TRUE" . . "Basic statistics"@en . . "3" . "Contents:\nThe content of the course consists of the following topics:\ndata collection, descriptive statistics, introduction to probability theory;\nintroduction to probability distributions: binomial, normal, and student;\nestimation, testing hypotheses, constructing confidence intervals;\napplication of a binomial test for a population proportion;\napplication of t-tests to standard situations; one sample, two sample, one sample with paired observations;\ncorrelation and Simple linear regression with associated t-tests for coefficients;\nusing statistical software, in particular R-Commander;\nethical issues, as touching upon good statistical practice, will be discussed in class.\nIn the course it will be shown, where these statistical concepts are applied in scientific research. In the tutorials the practical problems are introduced, and a detailed program is given linking the content of the course to the tutorials.\nLearning outcomes:\nAfter successful completion of this course, students are expected to be able to:\n- remember and understand basic ideas of statistical inference and data collection\n- determine and explain the appropriate statistical procedure, given the description of the experiment, the research question, and the type of data\n- carry out the needed analyses for the discussed standard situations and assess the results in terms of the problem\n- perform a hypothesis test for intercept and slope and validate the model assumptions of a simple linear model\n- independently analyze data with the computer software R-Commander" . . "Presential"@en . "TRUE" . . "Advanced statistics"@en . . "6" . "Contents:\nThis course covers several more advanced statistical models and associated designs, and techniques for statistical inference, as relevant to life science studies. The main topics are categorical data, (multiple) regression, analysis of variance (including multiple comparisons), analysis of covariance, and non-parametric tests. The aims of an analysis, the model assumptions, the properties (and limitations) of the models and associated inferential techniques and the interpretation of results in terms of the practical problem will be discussed. Focus will be upon students gaining an understanding of the model ingredients, an (intuitive) understanding of inferential techniques, insight into data structures and implications for choice of model and analysis. Students will be able to perform analysis of data with statistical software, i.e. with R-Studio.\nLearning outcomes:\nAfter successful completion of this course students are expected to (within the limits of the subjects treated) be able to:\n- translate a research question into a statistical hypothesis: make a plan (type of design or sampling procedure) for the data collection.\n- choose an appropriate model with an understanding of the ingredients of the model in relation to the data;\n- analyse the data (with R-Studio);\n- interpret the results and form conclusions relevant for the actual problem." . . "Presential"@en . "TRUE" . . "Mathematical statistics (part1)"@en . . "3" . "Learning outcomes\nAfter passing the course a student\n· knows how to compute various numerical parameters related to both discrete and continuous random variables;\n· knows basic methods of estimation and testing theory;\n· is able to characterize the entity of an estimate by its properties (unbiasedness, efficiency, consistency);\n· is able to apply the basic methods for deriving estimates (the maximum likelihood, least-squares methods and the method of moments);\n· can construct statistical hypothesis in different situations;\n· is able to construct interval estimates and handle non-normal data;\n· has received training in mathematical statistics that is appropriate for studying field related advanced statistical methods.\nBrief description of content\nIn the part of probability theory, the random events and properties of classical probability are considered. The course covers the theory of random variables and their distributions. In the part of mathematical statistics, the course covers basics of the statistical inference. First, a point estimator, its properties, and methods for finding it are considered. Also, the interval estimation and testing of statistical hypotheses are treated." . . "Presential"@en . "TRUE" . . "Mathematical statistics (part 2)"@en . . "3" . "Learning outcomes\nAfter passing the course a student\n· knows design of modern probability theory;\n· knows the concept of random variables and some most common probability distributions and is able to compute various numerical parameters related to both discrete and continuous random variables;\n· knows basic methods of estimation and testing theory;\n· understands the entity of the estimate and are able to characterize it by the corresponding properties (unbiasedness, efficiency, consistency);\n· knows the basic methods for deriving estimates and are able to apply them (the maximum likelihood, least-squares methods and the method of moments);\n· understand the entity of the hypothesis and are able to construct them in different situations;\n· is able to construct interval estimates and handle non-normal data;\n· has received training in mathematical statistics that is appropriate for studying field related advanced statistical methods.\nBrief description of content\nIn the part of probability theory, the random events and properties of classical probability are considered. The course covers the theory of random variables and their distributions. In the part of mathematical statistics, the course covers basics of the statistical inference. First, a point estimator, its properties, and methods for finding it are considered. Also, the interval estimation and testing of statistical hypotheses are treated." . . "Presential"@en . "FALSE" . . "Time series analysis"@en . . "no data" . "N.A." . . "Presential"@en . "TRUE" . . "Astrostatistics 1-2"@en . . "4" . "Fundamental principles and results of broad ields of staisics applicable to astronomical research. The material is roughly at a level of advanced undergraduate courses in staisics.\r\n\r\nSemester 1: Probability; Staisical inference; Probability distribuion funcions; Nonparametric staisics; Data Smoothing;\r\n\r\nSemester 2: Regression; Mulivariate analysis; Clustering, classiicaion; Censored and truncated data; Time series analysis; Spaial point processes;" . . "Presential"@en . "FALSE" . . "Multivariate statistics"@en . . "5" . "We will cover a large fraction of the following multidimensional models: Multidimensional distributions, multiple and partial correlation. The general linear model: Estimation and testing, geometric interpretation. Regression analysis: Estimation and testing, determination of best regression equations, analysis of residuals, prediction intervals, non-linear analysis etc. Multidimensional analysis of variance. Classification: Bayesian classifiers, linear and quadratic discriminant analysis, canonical discriminant analysis. Canonical analysis: Canonical correlation, principal components, factor analysis. Correlation models: Models for random phenomena which vary in time and space. Applications of SAS or R in the above areas." . . "Presential"@en . "FALSE" . . "Statistics for spatial and spatio-temporal data"@en . . "7" . "no data" . . "Presential"@en . "FALSE" . . "Statistical analysis of geographic data"@en . . "3" . "no data" . . "Presential"@en . "TRUE" . . "Statistics"@en . . "6" . "Objectives and Contextualisation\nThe objective of this course is to introduce the basic statistical tools to analyze data arising from experiments or observations, focusing on their correct use and the interpretation of the results.\n\nThe practices with computer of this subject, that are realized with a statistical software package in the computer classroom, are an indispensable part of the course in order to achieve these goals.\n\n\nCompetences\nElectronic Engineering for Telecommunication\nCommunication\nDevelop personal work habits.\nDevelop thinking habits.\nLearn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.\nWork in a team.\nTelecommunication Systems Engineering\nCommunication\nDevelop personal work habits.\nDevelop thinking habits.\nLearn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.\nWork in a team.\nLearning Outcomes\nAnalyse measurements in the area of engineering, using statistical tools to extract and understand information.\nAnalyse measures in the area of engineering, using statistical tools to extract and understand information.\nCommunicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.\nDevelop scientific thinking.\nDevelop the capacity for analysis and synthesis.\nManage available time and resources.\nManage available time and resources. Work in an organised manner.\nPrevent and solve problems.\nReason and model non-deterministic engineering systems or processes using discreet and continuous random variables and their corresponding distributions.\nReason and model non-deterministic systems and processes in engineering using discreet and continuous random variables and their corresponding distributions.\nResolve the mathematical problems that can arise in engineering.\nWork autonomously.\nWork cooperatively.\n\nContent\n1. Descriptive statistics:\n\nTypes of variables and data. Data frames.\nEmpirical experimet associated to a data frame.\nFrequency tables and graphs: histograms and others.\nMeasures of localization. Scattering measures\nCorrelation coefficient and regression line.\nJoint, marginal and conditional data distributions.\n\n2. Introduction to the theory of probability:\n\nBasic properties of probability. Combinatorics.\nConditional probability and independence. Bayes Formula.\nRandom variables. Density and distribution functions.\nExpected value and variance. Moments of a random variable.\nDiscrete distributions: Bernoulli, Binomial, Poisson and others\nContinuous distributions: uniform, exponential, normal and others.\nCentral limit theorem and laws of large numbers.\n\n3. Random vectors and stochastic processes:\n\nJoint, marginal and conditional distributions.\nBivariate normal distribution. Covariance and correlation coefficient.\nFunctions of random variables: distributions khi-square, Rayleigh, Rice.\nConcept of stochastic process. Poisson processes. Markov chains.\n\n4. Statistical Inference:\n\nEstimation and confidence intervals of averages, variances and proportions.\nTests for the expected value and for the proportion.\nComparison tests for expected values and proportions.\nKhi-square tests: goodness of fit, independence and homogeneity." . . "Presential"@en . "TRUE" . . "Linear modeling (incl. f.e.m)"@en . . "3.00" . "Course Contents Learn how to model real life engineering problems using Finite Element Methods.\nComputational methods in structural analysis are of prime importance in industry as tools to assess the efficiency and\nperformance of structures in the field of aerospace, mechanical, civil and biomedical engineering. A combination of theoretical\nand practical knowledge in finite element analysis are valuable skills needed to address such problems in industry. To efficiently\nmodel a real life engineering problem using finite element analysis and predict its future behaviour, an engineer must possess a\nstrong theoretical understanding of the finite element method (FEM) along with the understanding of the importance of\nverification and validation of such computational models.\nStudy Goals At the end of this course students are able to:\n1. Explain the different steps in a finite element analysis and apply them to practical engineering problems\n2. Explain and apply basic principles behind finite element analysis (i.e., minimum total potential energy and weighted residual\nfunction)\n3. Develop and implement 1D (bar, truss, beam and frame) and 2D (triangular and rectangular) elements in a finite element set-up\n4. Use and interpret results from 1D and 2D elements in commercial finite element software\n5. Explain and perform verification and validation of results obtained using finite element principles" . . "Presential"@en . "TRUE" . . "Non-linear modeling (using f.e.m.)"@en . . "3.00" . "Course Contents Learn how to model non-linear structural/solid mechanics problems using Finite Element Method (FEM).\nComputational methods, particularly FEM, are important tools to assess the efficiency and performance of materials & structures\nin the field of aerospace, mechanical, civil and biomedical engineering. Reduced performance and failure of materials &\nstructures are mostly due to the effects of different nonlinearities such as buckling, yielding, damage and fracture. A combination\nof theoretical and practical knowledge in non-linear FEM are valuable skills needed to address such problems in industry and\nacademia.\nUpon finishing this course, you will have the skill set needed to solve various non-linear structural/solid mechanics problems\nusing FEM. Both the theoretical and the practical aspects will be covered. A free FEM package will be used for practical\napplications.\nStudy Goals - be able to explain the theories of non-linear FEM and use them to perform analytical work\n- be able to apply non-linear FEM to solve practical engineering problems\n- be able to identify and employ efficient modelling techniques" . . "Online"@en . "TRUE" . . "Statistics applied to science and engineering"@en . . "6.0" . "### Working language\n\nEnglish\n_Note: Note that the working language will be English, and students can always ask questions in Portuguese._\n\n### Goals\n\n1\\. Enable the student for regression analysis involving continuous or discrete responses (generalized linear models)\ntwo\\. Implement statistical analyzes in suitable software\n3\\. Promoting a critical spirit in a data analysis process (data collection, modelling, interpretation of results, ...)\n\n### Learning outcomes and skills\n\nAt the end of the curricular unit, it is intended that students:\na) acquire knowledge about the organized collection of information\nb) learn statistical techniques and models commonly used in data processing\nc) know how to correctly choose the statistical models learned for concrete problems\nd) know how to apply and implement the models studied in R\ne) acquire a critical spirit and ability to interpret the results obtained.\n\n### Working mode\n\nIn person\n\n### Prerequisites (prior knowledge) and co-requisites (concurrent knowledge)\n\nPrior knowledge of random variables and probability distributions, sample statistics, confidence intervals and hypothesis testing is required. These are the usual contents of an introductory curricular unit to Probability and Statistics in higher education. A brief review of this matter will be carried out.\n\n### Program\n\n0\\. Brief review of inference-based techniques. statistics - confidence intervals and hypothesis tests\n1- Introduction to programming language in software environment **R.**\ntwo\\. Pearson correlation and Spearman correlation.\n3\\. Simple linear regression.\n4\\. Multiple linear regression. Model, parameter estimation, hypothesis tests for coefficients, confidence intervals, prediction intervals, determination coefficient, multicollinearity, model selection methods, model comparison, diagnosis.\n5\\*. Analysis of variance - ANOVA: 1 and 2 factors.\n6\\*. Generalized linear models. Logistic regression.\n\\*Only one subject will be studied, from 5. to 6.\n\n### Mandatory Bibliography\n\nRita Gaio; Notes written by the teacher\n\n### Complementary Bibliography\n\nISBN: 1-58488-029-5\nISBN: 0-387-95475-9\nISBN: 978-0-521-86116-8\nISBN: 0-387-95187-3\nISBN: 0-387-95284-5\nISBN: 1-58488-325-1\nISBN: 0-387-98218-3\nJulian Faraway; Linear Models with R, Taylor and Francis, 2009. ISBN: 1584884258\nJulian Faraway; Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Chapman & Hall/CRC Texts in Statistical Science, 2006. ISBN: 158488424X\n\n### Teaching methods and learning activities\n\nTheoretical-practical classes with different examples of application of techniques and statistical models presented in a computational laboratory. The software used is R.\n\n### Software\n\nR Project\n\n### Key words\n\nPhysical Sciences > Mathematics > Statistics\n\n### Type of evaluation\n\nDistributed evaluation with final exam\n\n### Assessment Components\n\nTest: 37.50%\nWritten work: 25.00%\nExam: 37.50%\n\n**Total:**: 100.00\n\n### Occupation Components\n\nSelf-study: 110.00 hours\nFrequency of classes: 42.00 hours\nWritten work: 10.00 hours\n\n**Total:**: 162.00\n\n### Get Frequency\n\nThere is no lack of frequency.\n\n### Final classification calculation formula\n\n1\\. The work consists of a written report and an oral presentation. Carrying out the work is optional.\n \ntwo\\. The grade of the work cannot be improved.\n \n3\\. The evaluation of the normal season will include the classification of two tests (T1 and T2), each with a quotation of 10 points. The T2 test will take place on the day designated for the exam of the normal season.\n \n4\\. The evaluation of the appeal period will only include a final exam, which will focus on all the contents of the curricular unit. The classifications of the T1 and T2 tests will not be considered here.\n \n5\\. Evaluation formula in the **regular season**: There are two evaluation formulas, depending on whether or not the curricular unit's work/project is delivered.\n \na) For students who **turn in work**:\na1) T1+T2: weight of 13 or 15 (in 20); work: weight of 7 or 5 (in 20)\nOf the two evaluation components, the one in which the student had the best rating (on a scale of 0-20) has, for that student, the maximum weight indicated above. The worst component has, for that student, the minimum weight indicated above.\na2) In order to pass, the student must obtain a classification greater than 20% in each of the components (tests and work).\n \nb) For students who **do not turn in the work**:\nIn this case, only the test scores count; however, the student's final classification will never be higher than 16, even with a higher grade in the tests.\n \n6\\. Evaluation formula in **appeal season**: There are two evaluation formulas, depending on the delivery or not of the work/curricular unit project.\n \na) For students who **turn in work**:\na1) resource exam: weight of 13 or 15 (out of 20); work: weight of 7 or 5 (in 20)\nOf the two evaluation components, the one in which the student had the best rating (on a scale of 0-20) has, for that student, the maximum weight indicated above. The worst component has, for that student, the minimum weight indicated above.\na2) In order to pass, the student must obtain a classification greater than 20% in each of the components (exam and work).\n \nb) For students who **do not turn in the work**:\nIn this case, only the exam score counts; however, the final classification of the student will never exceed 16 points, even if he/she has a higher grade in the exam.\n\nMore information at: https://sigarra.up.pt/fcup/pt/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=479406" . . "Presential"@en . "TRUE" . . "Model Identification and data fitting"@en . . "6.0" . "This course is devoted to the various practical and theoretical aspects which involve the estimation (the identification) of a mathematical model within a given model class, starting from a record of observed measurement data (input-output data). First, we address distance measures, norms, and criterion functions. Then we discuss the prediction error identification of linear regression models, with special emphasis on the various interpretations of such models (deterministic, stochastic with Gaussian white noise and maximum likelihood estimation, stochastic in a Bayesian estimation context) and on numerical implementation aspects (recursion, numerical complexity, numerical conditioning and square root filtering). Next, we study identification within the important class of auto-regressive dynamical models, to which the Levinson algorithm applies. Other related topics receiving attention are identifiability, model reduction and model approximation. Some techniques for the estimation of linear dynamical i/o-systems are illustrated with the system identification toolbox in Matlab.\n\nPrerequisites\nLinear Algebra, Mathematical Modelling, Probability and Statistics.\n\nRecommended reading\nL. Ljung, System Identification: Theory for the User (2nd ed.), Prentice-Hall, 1999.\nT. Soderstrom and P. Stoica, System Identification, Prentice-Hall, 1989.\n\nMore information at: https://curriculum.maastrichtuniversity.nl/meta/463537/model-identification-and-data-fitting" . . "Presential"@en . "TRUE" . . "Mathematical and statistical techniques"@en . . "6.0" . "Learning objectives\n\n \n\nReferring to knowledge\n\n\nGet acquainted with fundamental results of probability theory and statistics. Understand their relevance to important issues in experimental and theoretical physics.\nUnderstand the power and limitations of Monte-Carlo methods, in particular when applied to physical contexts\nDevelop comprehensive skills on the topic, ranging from the ability to write code to perform computations on specific data to the ability to prove easy mathematical statements in order to solve theoretical issues.\nGet acquainted with the techniques for data analysis and the basic concepts of data mining. Specifically, to code in Python to implement the analysis and to use a variety of software tools for data mining, including Neural Networks.\n \n\n \n\nTeaching blocks\n\n \n\n1. The concept of probability\n1.1. Conditional probability and Bayes theorem\n\n1.2. Frequentists versus Bayesians\n\n2. Random variables\n2.1. Mean, variance and moments\n\n2.2. Change of variables\n\n2.3. Examples of one-dimensional p.d.f’s\n\n2.4. Distributions of more than one random variable\n\n2.5. Examples of n-dimensional p.d.f’s\n\n2.6. Reproducibility\n\n2.7. Some theorems of probability theory\n\n3. Monte Carlo\n3.1. Random generation of uniform numbers\n\n3.2. Generation of different p.d.f.\n\n3.3. The inverse transformation method\n\n3.4. The composition method\n\n3.5. Von Neumann’s method\n\n3.6. Stratified sampling method\n\n3.7. Events with weight\n\n3.8. Monte Carlo integration\n\n3.9. Markov chains\n\n4. Statistical inference\n4.1. Non-parametric estimation\n\n4.2. Parametric estimation\n\n4.3. Confidence intervals\n\n4.4. Fisher Information\n\n4.5. Sufficient statistics\n\n4.6. Cramer-Rao inequality\n\n4.7. Construction of estimators\n\n4.8. The maximum likelihood method\n\n4.9. The minimum chi2 method\n\n5. Statistical tests\n5.1. Hypothesis test\n\n5.2. Significance test\n\n5.3. Decision theory\n\n6. Advanced topics\n6.1. Feldman-Cousins criterion for confidence intervals\n\n6.2. The sPlot method\n\n6.3. The sFit method\n\n7. Multivariate analysis and statistical treatment techniques\n7.1. Introduction to multivariate data analysis\n\n7.2. Data analysis and representation; Statistical distances.\n\n7.3. Principal component analysis\n\n7.4. Clustering\n\n7.5. Discriminant analysis\n\n7.6. Non-parametric methods of estimation of a probability density function\n\n7.7. Hands-on exercises\n\n8. Neural Networks\n8.1. Basic concepts of Artificial Neural Networks\n\n8.2. Design, training and use of Neural Networks\n\n8.3. Self Organizing maps\n\n8.4. Hands-on exercises\n\n9. Data mining\n9.1. Introduction to data mining: basic concepts\n\n9.2. Combination of data analysis techniques to implement a data mining procedure\n\n9.3. Complementary topics: Big data, artificial intelligence, cloud computing\n\n \n\n \n\nOfficial assessment of learning outcomes\n\n \n\nThere is no exam for this subject. Instead, 6 problem-solving assignments are set during the course. Grading is based on the assessment of the reports submitted.\n\n \n\n \n\nExamination-based assessment\n\nRepeat assessment: students have to repeat and resubmit the 6 problem-solving assignments following the instructions from the lecturers. Once the assignments have been assessed, students take an oral exam on their contents. If this exam is successfully passed, the final grade is calculated from the marks of the assignments; otherwise, the subject is graded as failed.\n\n \n\n \n\n \n\nReading and study resources\n\nCheck availability in Cercabib\n\nBook\n\nDeGroot, Morris H. Probability and statistics. 4th ed. Boston : Pearson Education, cop. 2012 Enllaç\n\n2a ed Enllaç\n\nFeller, William. An introduction to probability theory and Its applications, 2nd ed. New York : Wiley, 1972. v. 2 Enllaç\n\n\nhttps://cercabib.ub.edu/discovery/search?vid=34CSUC_UB:VU1&search_scope=MyInst_and_CI&query=any,contains,b1536375* Enllaç\n\nWitten, I. H. ; Frank, Eibe ; Hall, Mark A. Data mining : a practical machine learning tools. 4th ed. Burlington, [etc.] : Morgan Kaufman, cop. 2017 Enllaç\n\n\nhttps://cercabib.ub.edu/discovery/search?vid=34CSUC_UB:VU1&search_scope=MyInst_and_CI&query=any,contains,b1727639* Enllaç\n\nLandau, David P ; Binder, K. A guide to Monte Carlo simulations in statistical physics. 4a ed. Cambridge : Cambridge University Press, cop. 2015 Enllaç\n\n\nData Mining: Practical Machine Learning Tools and Techniques; Ian H. , Witten, Eibe Frank, Mark A. Hall, Christopher Pal; Ed. Morgan Kauffmann, ISBN 978-0128042915\n\n\nVideo, DVD and film\n\nNeural Networks: Zero to Hero: youtube series on Neural Networks\n\nhttps://www.youtube.com/playlist?list=PLAqhIrjkxbuWI23v9cThsA9GvCAUhRvKZ Enllaç\n\nArticle\n\nWeinzierl, Stephan. \"Introduction to Monte Carlo method\", a: http://arxiv.org/abs/hep-ph/0006269 Enllaç\n\n \tConferences\n\nWeb page\n\nScientific computing tools for Python: https://www.scipy.org/about.html \n\nIntroduction to Probability for Data Science: https://probability4datascience.com/\n\nMore information at: http://grad.ub.edu/grad3/plae/AccesInformePDInfes?curs=2023&assig=568423&ens=M0D0B&recurs=pladocent&n2=1&idioma=ENG" . . "Presential"@en . "TRUE" . . "Statistical techniques"@en . . "20.0" . "Recommended Prerequisites\nBefore taking this module it is advised that you should have passed:\nor 2 of Level 8 modules in Bio/Env/Geog\nGEO1PE\nBIO1CB\nENV1GE\nBIO2IP\nGEO2EI\nENV2LE\nor 2 of Level 8 modules in Bio/Env/Geog\nLandscape Evolution (ENVU2LV)\nPeople and the Environment (GEOU1PP)\nGlobal Environmental Issues (GEOU2GE)\nIntroduction to Cell Biology (BIOU1CE)\nBuilding Planet Earth (ENVU1BP)\nIntroduction to Physiology (BIOU2PH)\nProhibited Combinations\nYou may not take this module if you have previously passed:\nStatistical Techniques (SCI4T4)\nModule Description\nStatistical techniques are fundamental for addressing quantitative questions and making inferences from data. Consequently, statistical tools are indispensable for addressing questions across the natural and social sciences. \n\nIn this module, you’ll learn the following important skills for working with environmental and biological datasets: \n\nHow to manipulate datasets and characterise their statistical properties. \nUnderstanding and applying null hypothesis testing. \nApplying the correct statistical test to data using statistical software. \nInterpreting the results of statistical tests to make conclusions about scientific problems. \nBy developing an understanding of statistics, you will become better able to critically evaluate the scientific literature and conduct scientific research. Because literacy in statistics and a proficiency in using statistical software is critical for addressing all data-driven investigations, the skills that you learn in this module will be broadly relevant to solving a broad range of important problems. The UN has defined 17 Sustainable Development Goals (SDGs), which set out the world's roadmap to ending poverty, reducing inequality, and protecting the planet by 2030. Addressing any of these SDGs will rely on some data collection and analysis, meaning that the skills you learn in this module are potentially relevant for all of them. \n\nLocation/Method of Study\nStirling/On Campus, UK\nStirling\n\nModule Objectives\nThis module is designed to familiarise you with:Statistical analysis and associated computing software to implement it.Hypothesis testing.Basic statistical techniques that are used in analysing data.Applications of statistical techniques to a range of environmental and biological data sets and problems.Describing and reporting statistical analysis in report writingAnswering unseen questions about statistical problems in a time-limited context\n\nAdditional Costs\nThere are no additional costs associated with this Module.\n\nCore Learning Outcomes\nOn successful completion of the module, you should be able to:\n\nmanipulate datasets and characterise their statistical properties;\ndemonstrate an understanding of null hypothesis testing;\nchoose and apply the correct statistical test to unseen data using statistical software;\ninterpret the results of statistical tests in order to generate conclusive statements on scientific problems.\nIntroductory Reading and Preparatory Work\nLab workbook: http://bradduthie.github.io/SCIU4T4\n\nDelivery\nDirected Study\t15 hours\tLarge group presentation or talk on a particular topic\nDirected Study\t33 hours\tA session involving the development and practical application of a particular skill or technique\nDirected Study\t36 hours\tA meeting involving one-to-one or small group supervision, feedback or detailed discussion on a particular topic or project, online or in person\nDirected Study\t24 hours\tAssessment activity that takes place within a scheduled session, usually conducted under some form of examination or test conditions\nTotal Study Time\t200 hours\t\nAttendance Requirements\nYour engagement with learning materials and activities and attendance at scheduled live sessions and other events is extremely important. Full engagement in your studies will enable you to get the most out of the course and help you perform at your best when it comes to assessment.\n\nWe expect you to engage with all aspects of this module and with your programme of study. You should:\n\n· Engage with all module materials, activities, and online timetabled teaching sessions\n· Actively participate in discussions and practical activities\n· Prepare in advance of live sessions by undertaking the required reading and/or other forms of preparation\n· Submit coursework/assessments by the due time and date\n· Complete class tests and examinations at the specified time and date\n· Make your module co-ordinator aware at the earliest opportunity if you experience problems which may impact on your engagement\n· Inform the University of absence from study (planned or unplanned), e.g. illness, emergency as outlined at http://www.stir.ac.uk/registry/studentinformation/absence\n· Respond to e-mails from your personal tutor, module co-ordinator or programme director and attend meetings if requested.\n· Engage with in-sessional English language classes (if applicable)\nWe will monitor these aspects throughout each semester to check that you are fully participating and that you are coping well with your studies. Some activities may be prescribed, failure to engage with 2/3 of prescribed activities will result in your module grade being capped at the pass mark (40 for Undergraduate modules, 50 for Postgraduate modules).\n\nAssessment\n% of final\ngrade\tLearning\nOutcomes\nClass Test\t0\t1\nClass Test\t25\t2\nClass Test\t25\t2\nExam (Canvas - on campus)\t50\t1,2,3,4\nCoursework: 50%\nExamination: 50%\n\n\nMore information at: https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=SCIU4T4&_gl=1*1l7ziqq*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzNzg0My4wLjAuMA.." . . "Presential"@en . "TRUE" . . "Practical statistics"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=MATU9D2&_gl=1*kjdomz*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzOTA0NS4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Statistics using r (sciu7sr)"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=SCIU7SR&_gl=1*18l5y8i*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzOTg3Ny4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Statistics using r (sciu7sr)"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=SCIU7SR&_gl=1*g5o1ly*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjA0MDA2Ni4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Statistics, error theory and least squares method"@en . . "5" . "Descriptive statistics. Concept, rules and properties of probability. Conditional probability, independence of events, Bayes theorem. Distributions of random variables. Expected value and variance. Basic distributions and applications. Bivariate distributions, independence of random variables. Central limit theorem. Sampling distributions. Point estimation, confidence intervals and statistical hypothesis testing. Linear model: estimation and testing of parameters, coefficient of determination, prediction. Χ2 – goodness of fit test, probability plotting. Contingency tables. Applications using computer packages. Introduction to adjustment theory, principle of Least Squares. Estimation of a single variable from direct measurements (equally and unequally weighted). Multidimensional variables. Variance-Covariance propagation. Bivariate normal distribution, error ellipse. Least Squares adjustments by the methods of observation and condition equations. Estimation of Variance-Covariance matrices. Geodetic applications." . . "Presential"@en . "TRUE" .