The course roughly follows the text by Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 7th edition, 2012, henceforth referred to as HMC. /FormType 1 /Matrix [1 0 0 1 0 0] << Springer Ver-lag, chapter 2. theory of statistical decision functions (Wald 1950)" Akaike, H. 1973. >> 2. LECTURE NOTES ON STATISTICAL INFERENCE KRZYSZTOF PODGORSKI´ Department of Mathematics and Statistics University of Limerick, Ireland November 23, 2009 !d���$SZs%��ذ[ܲ�9�� �����YnY��EQ��d 7x��B��b N� [� g0l��&+8A@�$�p@cl�Qe�*4�[5 gL:�V+� � #������N�ō�k���t. Bayesian Methods and Modern Statistics: STA 360/601 Lecture 3 1. /Type /XObject 2DI70 - Statistical Learning Theory Lecture Notes Rui Castro April 3, 2018. x��Zݓ۶�_��5��7�N�ɹM&I[�:M��'�N�%�LR���. 2. Statistical Learning Theory vs Classical Statistics • In this course, we are concerned with results that apply to large classes of distributions P, such as the set of all joint distributions on X ×Y. Bayesian decision theory provides a unified and intuitively appealing approach to drawing inferences from observations and making rational, informed decisions. >> Lecture 2: Statistical Decision Theory (Part I) Wenbin Lu Department of Statistics North Carolina State University Fall 2019 Wenbin Lu (NCSU) Data Mining and Machine Learning Fall 2019 1 / 35. Instructors: Harrison H. Zhou. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. ... Statistical Field Theory. /Type /XObject >> The mean of Xis written Objective: g( ), e.g., inference on the entropy of distribution P . (2004). /Subtype /Form Olivier Bousquet, St ephane Boucheron, G abor Lugosi (2004) \Introduction to Statistical Learning Theory". /Length 1298 endstream The accompanying textbook for the course is Keener’s ... 10 Decision Trees and Classi cation95 /FormType 1 Erich L. Lehmann and George Casella, Theory of point estimation. The focus is on decision under risk and under uncertainty, with relatively little on social choice. /Filter /FlateDecode Statistical Decision Theory From APTS Lecture Notes on Statistical Inference, Jonathan Rougier, Copyright © University of Bristol 2015. endobj These are notes for a basic class in decision theory. endobj Lecture Notes on Bayesian Estimation and Classification M´ario A. T. Figueiredo, Instituto de Telecomunicac¸˜oes, and Instituto Superior T´ecnico ... 1.2 Statistical Decision Theory 9 • Formal model of the observations. /Type /XObject 1763 1774 1922 1931 1934 1949 1954 1961 Perry Williams Statistical Decision Theory 7 / 50 Outline of This Note Part I: Statistics Decision Theory (from Statistical Perspectives - \Estimation") loss and risk MSE and bias-variance tradeo Lecture notes on: Information-theoretic methods for high-dimensional statistics* Yihong Wu January 14, 2020 * Work in progress and apologies for many mistakes. stream Lecture 2. /BBox [0 0 8 8] /Length 15 Information Theory (from slides of Tom Carter, June 2011) \Information" from observing the occurrence of an event:= #bits needed to encode the probability of the event p= log. /Length 2953 /Resources 21 0 R Please be patient with the Windows machine.... 2. 3. The elements of decision theory are quite logical and even perhaps intuitive. 2 Basic Elements of Statistical Decision Theory 1. What is the best possible estimator b= b(X 1;:::;X n) of ? Lecture notes on statistical decision theory Econ 2110, fall 2013 Maximilian Kasy March 10, 2014 These lecture notes are roughly based on Robert, C. (2007). Note the important identity Var(X) = E[X2] E[X]2: (1.6) There is a special notation that is in standard use. /Filter /FlateDecode x���P(�� �� Signal processing, machine learning, and statistics all revolve around extracting useful information from signals and data. %���� /Subtype /Form Objective: g( ), e.g., inference on the entropy of distribution P . .���c� 7� W)P����o&hq� Bayesians view statistical inference as a problem in belief dynamics , of using evidence about a phenomenon to … Lecture Notes on Advanced Statistical Theory1 Ryan Martin Department of Statistics North Carolina State University www4.stat.ncsu.edu/~rmartin January 3, 2017 1These notes were written to supplement the lectures for the Stat 511 course given by the author at the University of Illinois Chicago. endobj /Resources 19 0 R In contrast to parametric problems, we will not (often) assume that P comes from a small (e.g., finite-dimensional) space, P ∈ {Pθ: θ ∈ Θ}. 3. /Filter /FlateDecode In statistical decision theory, we formalize good and bad results with a loss function. << Bayes Decision Theory Prof. Alan Yuille Spring 2014 Outline 1.Bayes ... Bayes decision theory is the ideal decision procedure { but in practice it can be di cult to apply because of the limitations described in the next subsection. << :��0�f�0b��-�O��R�V��YI�5��r;���7��O���]�CP:SL��)�LJb�,^\>y��ʙ%^�]^�h ��a��.W�7����|� /~����V}����(�����������v����r��ӗ&��KC5 ����[����K�D�W�y��SVR�P5��p��c�H��hc��1U�g��x݃�[m��.�q˺��] �\����[�D҅�����b2�0��p���/Z�G��wu���J��bL`��W��AJ����ebM�J"�� �|wϫ��:��ث�K�V�l&-��A ߢ�4/�u�.�Y� ��:��Ü���՜u��/h��e���R(���� STAT 619 STAT 619, Statistical Decision Theory Spring 2009. Least favourable Bayesian answers. 2. p: E.g., a coin ip from a fair coin contains 1 bit of information. Gauge Theory. Probability Theory and Statistics With a view towards the natural sciences Lecture notes Niels Richard Hansen Department of Mathematical Sciences University of Copenhagen November 2010. Data: X˘P , where Xis a random variable observed for some parameter value . endstream David Tong: Lectures on Theoretical Physics Classical Mechanics. Data: X˘P , where Xis a random variable observed for some parameter value . /Subtype /Form << R��'�c��db��r����.��:+�? << � << >> /BBox [0 0 16 16] stream The extension to statistical decision theory includes decision making in the presence of statistical knowledge which provides some information where there is uncertainty. The Bayesian choice: from decision-theoretic foundations to computational implementation. 16 0 obj %PDF-1.5 Information theory and an extension of the maximum likelihood principle. }����l��[�[0*-��b ����]��P!�}���.����2�sL�>����P��v�j7w�ר�۾�z�䘴W��A�vA���Q�n\V��z�`��r�z7�eV&���-u�,���������ơ�p Bayesian testing, Bayes factor. 18 0 obj This set of lecture notes explores some of the (many) connections relating information theory, statistics, computation, and learning. stream /Subtype /Form endstream Lecture7 IntroductiontoStatisticalDecisionTheory I-HsiangWang DepartmentofElectricalEngineering NationalTaiwanUniversity ihwang@ntu.edu.tw December20,2016 /Type /XObject 1.1 The Risk Function >> /Matrix [1 0 0 1 0 0] x���P(�� �� w{��ϯ�j�ny��n0n�߶�-�(����l~�ϯ�j]m�����f5ȼ������XPJ�T��ᘲ؁$x�U��2߂+�:����$8��)b57>�#��8�D܈�A���EBD��i�m���'���ժ��]��m�a�O������`�p��{ᙂ���Q��]yE-�Ҥ�C}�8��~�}���w!��j���>�U���?�C�ڭM�c 쏘q���ݪG��77��:`[�V�*љ,��T���)#TkH4�F�+�o�6�|Hl�� Some of the material in these notes will be published by Cambridge University Press as Statistical Machine Learning: A Gentle Primer by Rui M. Castro and Robert D. Nowak. stream The observations, based on which decisions are to … /Matrix [1 0 0 1 0 0] Note that a general decision rule may be randomized, i.e., for any realization of X= x, (x) produces an action a2Afollowing the probability 1Some readings: 1. Poisson approximation or Poissonization is a well-known technique widely used in probability theory, statistics and theoretical computer science, and the current treatment is essentially taken from Brown et al. 44 0 obj /Length 15 /Resources 14 0 R Part 3: Decision-theoretic approach: { Chapter 10: Bayesian inference as a decision problem. Course material: https://github.com/DrWaleedAYousef/Teaching x���P(�� �� (Robert is very passionately Bayesian - read critically!) 2 Basic Elements of Statistical Decision Theory 1. Decision theory divides decisions into three categories that include Decisions under certainty; where a manager has far too much information to choose the best alternative, Decisions under conflict; where a manager has to anticipate moves and countermoves of one or more competitors and lastly, Decisions under uncertainty; where a manager has to dig-up a lot of data to make sense of what is going on and … Email: huibin.zhou@yale.edu TA: Peisi Yan Email: peisi.yan@yale.edu Class Time and Place: M&W 2:30-3:45pm in Room 107, 24 Hillhouse Ave Course Description: Shrinkage estimation and its connection to minimaxity, admissibility, Bayes, empirical Bayes, and hierarchical Bayes. x��XKo7��W�:,����"�Ҡ�:P m�V~ � ;.���ΐ;$WZ�q즵�ˏ3�y��+�9l�{��Q�x�`�)�e�+.�cw[v�89`z�����ݝ�v�ῒJ�Ju��? Note, Bayes Decision Theory (and Machine Learning) can also be used if ~yis a vector-valued. �k���g� _:�_z�H{��pcp~�nu�f�Y�uU��uU�a�l��U[w�����#��n���4mݯ�]�����#7CB�b[}���Q���[��}�`;���A�wઘ�SB΋M�6�Zl0C��������_gO�{���ƍ;�=����XP�����Y�=_�9+ֵ���7�p�n�x����x���Dɏ����! Lectures on Statistics William G. Faris December 1, 2003. ii. >> /Length 15 /Filter /FlateDecode If the event has probability 1, we get no information from the occurrence of the event. 20 0 obj Deci-sion theoretic framework: point estimation, loss function, deci-sion rules. Statistical Decision Theory – Page 4 tons of fertilizer (Figure 2). It combines the sampling information (data) with a knowledge of the consequences of our decisions. The Bayesian revolution in statistics—where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine—is here to stay. %���� /Filter /FlateDecode Lecture note for Stat 231: Pattern Recognition and Machine Learning Tasks subjects Features x Observables X Decision Inner belief w control sensors selecting Informative features statistical inference risk/cost minimization In Bayesian decision theory, we are concerned with the last three steps in … 2. Statistical Experiment: A family of probability measures P= fP : 2 g, where is a parameter and P is a probability distribution indexed by the parameter. G. Decision theory provides a framework for answering this question. %PDF-1.5 3. endobj /Filter /FlateDecode Wiley, 1950. Statistical Decision Theory Statistical decision theory is concerned with the problem of making decisions. Abraham Wald, Statistical decision functions. I.e. stream /BBox [0 0 5669.291 8] x���P(�� �� /Length 15 So the starting point of this chapter is a family of distributions for Lawrence D. Brown (2000) \An Essay on Statistical Decision Theory". /Matrix [1 0 0 1 0 0] Decision theory, in statistics, a set of quantitative methods for reaching optimal decisions.A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action, with their consequences. /FormType 1 /BBox [0 0 362.835 3.985] Statistical Experiment: A family of probability measures P= fP : 2 g, where is a parameter and P is a probability distribution indexed by the parameter. if ~y Comparison with classical hypothesis testing. Lindley’s paradox. If, in fact, fertilizer demands that year was 5,000 tons, he would receive the maximum absolute gross profit of $30,000 (5,000 tons x … 1These notes are meant to supplement the lectures for Stat 411 at UIC given by the author. 2. /FormType 1 The author makes no guarantees that these notes are free of typos or other, more serious errors. Decision theory as the name would imply is concerned with the process of making decisions. These notes provide an introduction to the fun bits of quantum field theory, in particular those topics related to topology and strong coupling. Bayes estimators, Bayes risk. 8. Stat293 class notes Statistical Learning: Algorithms and Theory Sayan Mukherjee LECTURE 1 Course preliminaries and overview •Course summary Theproblem ofsupervisedlearningwill be developedin the framework of statistical learning theory. Topics I Loss function I Risk ... 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