statistical decision theory lecture notes

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

statistical decision theory lecture notes

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