statistical decision theory lecture notes

8. 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. /FormType 1 x��XKo7��W�:,��"�Ҡ�:P m�V~ � ;.��ΐ;$WZ�q즵�ˏ3�y��+�9l�{��Q�x�`�)�e�+.�cw[v�89`z��ݝ�v�ῒJ�Ju��? The course roughly follows the text by Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 7th edition, 2012, henceforth referred to as HMC. (2004). Bayesians view statistical inference as a problem in belief dynamics , of using evidence about a phenomenon to … /FormType 1 << endstream << endobj In statistical decision theory, we formalize good and bad results with a loss function. Bayes Decision Theory Prof. Alan Yuille Spring 2014 Outline 1.Bayes ... Bayes decision theory is the ideal decision procedure { but in practice it can be di cult to apply because of the limitations described in the next subsection. Bayesian testing, Bayes factor. if ~y >> /Type /XObject G. x��Zݓ۶�_��5��7�N�ɹM&I[�:M��'�N�%�LR��. � /Matrix [1 0 0 1 0 0] /Length 1298 << stream stream .��c� 7� W)P��o&hq� The Bayesian revolution in statistics—where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine—is here to stay. Some of the material in these notes will be published by Cambridge University Press as Statistical Machine Learning: A Gentle Primer by Rui M. Castro and Robert D. Nowak. Topics I Loss function I Risk ... (note anything that we can’t read, ... decisions. /Subtype /Form 44 0 obj !d��$SZs%��ذ[ܲ�9�� YnY��EQ��d 7x��B��b N� [� g0l��&+8A@�$�p@cl�Qe�*4�[5 gL:�V+� � #��N�ō�k��t. My sincere gratitude to the students at University of Illinois who tookECE598YWin Spring 2016 and contributed to scribing the initial version of the lecture notes. 3. 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 … 1.1 The Risk Function 3. /BBox [0 0 362.835 3.985] These notes provide an introduction to the fun bits of quantum field theory, in particular those topics related to topology and strong coupling. Erich L. Lehmann and George Casella, Theory of point estimation. 2 Basic Elements of Statistical Decision Theory 1. x��P(�� 1 Decision Theory Suppose we want to estimate a parameter using data Xn = (X 1;:::;X n). 2DI70 - Statistical Learning Theory Lecture Notes Rui Castro April 3, 2018. What is the best possible estimator b= b(X 1;:::;X n) of ? The mean of Xis written /Filter /FlateDecode /Type /XObject 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 … 16 0 obj /FormType 1 }��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 stream >> x��P(�� 2 Basic Elements of Statistical Decision Theory 1. >> Decision theory as the name would imply is concerned with the process of making decisions. %PDF-1.5 /Matrix [1 0 0 1 0 0] Wiley, 1950. Please be patient with the Windows machine.... 2. Bayesian Methods and Modern Statistics: STA 360/601 Lecture 3 1. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. Information theory and an extension of the maximum likelihood principle. /Matrix [1 0 0 1 0 0] /Subtype /Form 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). 2. Bayesian decision theory provides a unified and intuitively appealing approach to drawing inferences from observations and making rational, informed decisions. 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. STAT 619 STAT 619, Statistical Decision Theory Spring 2009. /Resources 14 0 R Comparison with classical hypothesis testing. 2. 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. The accompanying textbook for the course is Keener’s R��'�c��db��r��.��:+�? /Matrix [1 0 0 1 0 0] The extension to statistical decision theory includes decision making in the presence of statistical knowledge which provides some information where there is uncertainty. 1These notes are meant to supplement the lectures for Stat 411 at UIC given by the author. /Filter /FlateDecode Objective: g( ), e.g., inference on the entropy of distribution P . /Resources 19 0 R 13 0 obj The observations, based on which decisions are to … The Bayesian choice: from decision-theoretic foundations to computational implementation. /Filter /FlateDecode Signal processing, machine learning, and statistics all revolve around extracting useful information from signals and data. 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. Lecture 2. 3 0 obj stream /Length 15 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. Bayes estimators, Bayes risk. Abraham Wald, Statistical decision functions. 18 0 obj %�� 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. Springer Ver-lag, chapter 2. 1763 1774 1922 1931 1934 1949 1954 1961 Perry Williams Statistical Decision Theory 7 / 50 endstream /Length 15 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. /Length 15 /Resources 21 0 R /Type /XObject 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. Instructors: Harrison H. Zhou. Gauge Theory. 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}. Outline of This Note Part I: Statistics Decision Theory (from Statistical Perspectives - \Estimation") loss and risk MSE and bias-variance tradeo Deci-sion theoretic framework: point estimation, loss function, deci-sion rules. endobj /Subtype /Form These are notes for a basic class in decision theory. Note, Bayes Decision Theory (and Machine Learning) can also be used if ~yis a vector-valued. %�� Lecture Notes 14 36-705 We continue with our discussion of decision theory. The elements of decision theory are quite logical and even perhaps intuitive. /Filter /FlateDecode << theory of statistical decision functions (Wald 1950)" Akaike, H. 1973. /BBox [0 0 5669.291 8] /Resources 17 0 R /Length 15 x��P(�� This set of lecture notes explores some of the (many) connections relating information theory, statistics, computation, and learning. Least favourable Bayesian answers. 3. Data: X˘P , where Xis a random variable observed for some parameter value . The focus is on decision under risk and under uncertainty, with relatively little on social choice. 2. << >> endstream Statistical Decision Theory Statistical decision theory is concerned with the problem of making decisions. /BBox [0 0 8 8] stream /Filter /FlateDecode :��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(�� Statistical Decision Theory – Page 4 tons of fertilizer (Figure 2). >> endobj Note the important identity Var(X) = E[X2] E[X]2: (1.6) There is a special notation that is in standard use. Course material: https://github.com/DrWaleedAYousef/Teaching endobj 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�� Decision theory provides a framework for answering this question. /Subtype /Form %PDF-1.5 LECTURE NOTES ON STATISTICAL INFERENCE KRZYSZTOF PODGORSKI´ Department of Mathematics and Statistics University of Limerick, Ireland November 23, 2009 Part 3: Decision-theoretic approach: { Chapter 10: Bayesian inference as a decision problem. >> Data: X˘P , where Xis a random variable observed for some parameter value . If the event has probability 1, we get no information from the occurrence of the event. Lawrence D. Brown (2000) \An Essay on Statistical Decision Theory". endstream 2. p: E.g., a coin ip from a fair coin contains 1 bit of information. ... Statistical Field Theory. /BBox [0 0 16 16] /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 … Lectures on Statistics William G. Faris December 1, 2003. ii. << David Tong: Lectures on Theoretical Physics Classical Mechanics. The author makes no guarantees that these notes are free of typos or other, more serious errors. �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��! 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. It combines the sampling information (data) with a knowledge of the consequences of our decisions. /Type /XObject Objective: g( ), e.g., inference on the entropy of distribution P . Lindley’s paradox. stream /FormType 1 Lecture7 IntroductiontoStatisticalDecisionTheory I-HsiangWang DepartmentofElectricalEngineering NationalTaiwanUniversity ihwang@ntu.edu.tw December20,2016 Olivier Bousquet, St ephane Boucheron, G abor Lugosi (2004) \Introduction to Statistical Learning Theory". Statistical Decision Theory From APTS Lecture Notes on Statistical Inference, Jonathan Rougier, Copyright © University of Bristol 2015. /Length 2953 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. (Robert is very passionately Bayesian - read critically!) x��P(�� 20 0 obj The basic premise of Statistical Decision Theory is that we want to make inferences about the parameter of a family of distributions. So the starting point of this chapter is a family of distributions for 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. 2. 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. I.e. 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. Lecture notes on: Information-theoretic methods for high-dimensional statistics* Yihong Wu January 14, 2020 * Work in progress and apologies for many mistakes. ... 10 Decision Trees and Classi cation95