statistical inference lecture notes

200 0 obj (Multi-parameter Estimation) Syllabus. . 7 0 obj . 151 0 obj endobj 116 0 obj ))�KA2�3)If� ��&�ĸC*�2� �c� .��X>��X��$��xk�IJqF:�k��p�� @�SJ�EJS3Ӓ�(��4e:e��(p6()J4�C�!$�W�P�r��f��5��`)� jH�O3\��"\��RO�� << /S /GoTo /D (section.3.2) >> (General properties of estimators) 235 0 obj << 112 0 obj The course roughly follows the text by Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 7th edition, 2012, henceforth referred to as HMC. /Length 1324 << /S /GoTo /D (subsection.1.4.2) >> . 60 0 obj w��y�@R=ҟv�@��m��1�Áq��卥�5�a9��%�%�u�[Ŵ^�%ً�t�Dؐ�� endobj endobj 215 0 obj << /S /GoTo /D (subsection.2.4.2) >> ( Bernoulli Distribution) 31 0 obj /Font << /F43 238 0 R >> Statistical inference is concerned with making probabilistic statements about ran- dom variables encountered in the analysis of data. << /S /GoTo /D (subsection.2.5.7) >> 208 0 obj . 88 0 obj (Chi-square Distribution) << /S /GoTo /D (section.5.1) >> NPTEL provides E-learning through online Web and Video courses various streams. Send us your email address: Any comments? >> (Random Vectors) 179 0 obj STATS 200: Introduction to Statistical Inference Lecture 1: Course introduction and polling. . Lecture notes (prepared by me) on various topics are available here for downloading. endobj 233 0 obj << << /S /GoTo /D (subsection.2.6.2) >> endobj . (Goodness of Fit Tests) endobj endobj << /S /GoTo /D (subsection.2.5.6) >> endobj endobj 1 Data. . . In Bayesian statistics all inference in based on the posterior distribution. << /S /GoTo /D (chapter.5) >> On StuDocu you find all the study guides, past exams and lecture notes for this course The usual estimator of the parameter $\mu$ is $\hat{\mu} = x$. << /S /GoTo /D (section.2.7) >> Example 1.1. 219 0 obj (Introduction) %�� endobj 128 0 obj endobj 237 0 obj << 234 0 obj << 191 0 obj . 2 0 obj 1These notes are meant to supplement the lectures for Stat 411 at UIC given by the author. . . 71 0 obj << /S /GoTo /D (section.6.3) >> endobj 231 0 obj << /S /GoTo /D (section.6.2) >> Please answer the following: 3 + 4 = Menu Course Home. << /S /GoTo /D (section.4.2) >> (Gaussian $Normal$ Distribution) 188 0 obj endobj endobj 167 0 obj ( Binomial Distribution) . (Exact Confidence Intervals) endobj endobj << /S /GoTo /D (subsection.2.6.5) >> 40 0 obj endobj 143 0 obj 107 0 obj endobj . 72 0 obj (��w6. << /S /GoTo /D (section.2.2) >> /Type /ObjStm >> endobj Session #1. /Filter /FlateDecode . 224 0 obj endobj (Beta Distribution) 95 0 obj 232 0 obj A main prerequisite is an introductory course in probability and statistics. endobj 227 0 obj endobj 175 0 obj /ProcSet [ /PDF /Text ] Course: Statistical Inference. These lecture notes undergo minor updates - on the first page you will see when the notes were last updated. 16 0 obj << /S /GoTo /D (subsection.2.6.6) >> endobj 196 0 obj Machine Learning for Language Technology Lecture 4: Sta,s,cal Inference Marina San,ni Department of Linguis,cs and Philology Uppsala University, Uppsala, Sweden Autumn 2014 Acknowledgement: Thanks to … Statistical inference is the process of drawing conclusions about populations or scientific truths from data. Syllabus. << /S /GoTo /D (section.2.6) >> . Note that the diﬀerence from classical statistics is that the posterior density is just the likelihood function multiplied by the prior density and then normalized to become a probability distribution. 216 0 obj Statistical Inference Course Notes Xing Su Contents Overview. 67 0 obj ... Lecture Notes for Part 1, courtesy of Professor Joe Romano, can be downloaded from Canvas. Today we distinguished between the ways in which a probabilist and a statistician view a scenario involving the modeling of a political opinion poll via a binomial distribution. Time permitting, an introduction to basic linear regression models might be given. a lecture notes are two types and treatment is a has been a local epidemiology. �nW+��1m��o7퓫a#]��`�dg],��w��ɨ�U��aJ�d+#nD7?-��*`��ޙ�q�#�R��Q��mQX��@'7��M�ִ��{?=~t[�v��,�&l��vD��qm1�i��K>1ȗ�Ճ�>��=�X��U�/6ܞ��Ü��^�J�r�HY��VkG��a�|�sS1_�Q��&�ee�� _��ko��hwjVn��- ��)(5n�GWѪ-�=��f��8��c��F�{�8�8��9к��=��D��w? CHAPTERS TITLES NOTES; 2: Review of Probability : 3: Collecting Data : 4: Summarizing and Exploring Data : 5: Sampling Distributions of Statistics : 6: Basic Concepts of Inference . endobj << /S /GoTo /D (subsection.2.5.2) >> (Common Distributions \205 Summarizing Tables ) << /S /GoTo /D (chapter.4) >> 87 0 obj Casella, G. and Berger, R. L. (1990). endobj 124 0 obj /MediaBox [0 0 612 792] << /S /GoTo /D (subsection.2.7.2) >> endobj . endobj This turns out to also be the maximum likelihood estimator. << /S /GoTo /D (subsection.1.2.1) >> endobj >> endobj 184 0 obj 63 0 obj endobj - Statistical Inference. x��W�R�0��^�3�k��ؒC��0��valA. It is also called inferential statistics. 120 0 obj 212 0 obj endobj (Exponential Distribution) << /S /GoTo /D (chapter.3) >> (Expectation and Variance) Moodle: Further information, skeleton lecture notes, and other material will be provided via Moodle. endobj << /S /GoTo /D (section.4.1) >> endobj endobj 36 0 obj 83 0 obj << /S /GoTo /D (section.1.4) >> Exercises in Statistical Inference with detailed solutions 9 Introduction • Ch. 64 0 obj << /S /GoTo /D (section.2.5) >> (Review of Probability) . << /S /GoTo /D (section.6.4) >> . This is a high-level paper, as you can tell by the title. It tries to pull us from the frequentist / Bayesian quagmire to the more important aspect of the field of statistics, that is, the mismatch of the model and the real data. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. endobj Learning objectives and syllabus. 55 0 obj 68 0 obj endobj endobj 7: Inferences for Single Samples : 8: Inferences for Two Samples : 9: Inferences for Proportions and Count Data . endobj endobj << /S /GoTo /D (subsection.2.6.1) >> Lecture Materials . Formally, given a sample, X (The Bivariate Normal Distribution) /Filter /FlateDecode << /S /GoTo /D (section.4.3) >> . endobj (Maximum Likelihood Estimation) (The Theory of Hypothesis Testing) endobj 111 0 obj 192 0 obj 176 0 obj as a function of summary statistics on X and Y, and the linear weights that are used in the combination. 96 0 obj %PDF-1.4 127 0 obj Part 2 of econ 270 introduces the statistical inference theory of estimation and testing. endobj (Discrete Uniform Distribution) 75 0 obj << /S /GoTo /D (subsection.2.6.3) >> endobj << /S /GoTo /D [233 0 R /Fit ] >> (The Theory of Confidence Intervals) You couldusefully use these comments as hints and try to dobetter than these students. (Distributions \205 further properties) 147 0 obj endobj endobj 164 0 obj .3 << /S /GoTo /D (subsection.2.6.7) >> endobj . Lecture Materials. It helps to assess the relationship between the dependent and independent variables. Collecting Data and Experimental Design “[Experimental design] encompasses the myriad details that constitute the substance of the actual planning, conduct, and (Covariance and Correlation) << /S /GoTo /D (section.6.5) >> << /S /GoTo /D (section.2.3) >> endobj (Motivating Example) endobj >> 76 0 obj endobj (Uniform Distribution) endobj << /S /GoTo /D (section.1.1) >> 100 0 obj 199 0 obj (Generally Applicable Test Procedures) endobj /Parent 239 0 R /N 100 Biostatistics 602 - Statistical Inference Lecture 01 Introduction to BIOSTAT602 Principles of Data Reduction Hyun Min Kang January 10th, 2013 ... • In previous years, the instructors wrote the notes on the whiteboard or projected the notes onto a screen during the class . endobj . 35 0 obj << /S /GoTo /D (section.1.2) >> 136 0 obj 156 0 obj 44 0 obj Statistics used for point estimation of unknown quantities in the population are called estimators. He notesthings that they did wrong and where they had difficultiess. 47 0 obj The purpose of statistical inference to estimate the uncertainty o… LECTURE NOTES 8 1 Statistical Inference LECTURE NOTES 8 1 Statistical Inference A central concern of statistics and machine learning is to estimate things about some under- lying population on the basis of samples. endobj Ch 1, Casella and Berger (CB afterwards) Chs 2 and 3, Amemiya . xڕVMo�8��W�m��7")�RQ�m�� nФ�\�v�J�WI�_�o�a;mb9� ђ�͛7�C�(!��8��҈>B�P$A"&��! Studying STAT3010 Statistical Inference at University of Newcastle (Australia)? << /S /GoTo /D (section.5.2) >> endobj . endobj 104 0 obj /Filter /FlateDecode Discussion of Statistical Inference: The Big Picture by R. E. Kass. endobj . . >> endobj 204 0 obj endobj << /S /GoTo /D (subsection.2.6.9) >> This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. 27 0 obj << /S /GoTo /D (subsection.2.5.5) >> 195 0 obj 43 0 obj << /S /GoTo /D (section.5.3) >> << /S /GoTo /D (chapter.6) >> In our example the count is 17. x <- 17. Wadsworth, Belmont, CA. 4Important concepts in point estimation are introduced, such as likelihood of a sample and sufficient statistics. endobj 15 0 obj endobj sheet 1(lectures 1-5), sheet 2(lectures6-10), sheet 3(lectures11-16). /Type /Page endobj endobj 262 0 obj << << /S /GoTo /D (subsection.2.6.4) >> 108 0 obj . endobj There are also several dierent statistical inference tasks associated with this problem that SBMs address. . << /S /GoTo /D (subsection.2.4.1) >> ( Approximate Confidence Intervals) (Estimation) (Optimality Properties of the MLE) 172 0 obj << /S /GoTo /D (subsection.2.7.1) >> endobj 207 0 obj endobj 8 0 obj endobj 115 0 obj /Length 915 NPTEL provides E-learning through online Web and Video courses various streams. . . endobj endobj endobj %�� endobj Lecture Materials. (Sums of Independent Random Variables) 48 0 obj (The 2 Test for Contingency Tables) /First 808 << /S /GoTo /D (section.2.4) >> endobj >> endobj Aim: To review and extend the main ideas in Statistical Inference, both from a frequentist viewpoint and from a Bayesian viewpoint. endobj endobj 123 0 obj . 131 0 obj 28 0 obj A company sells a certain kind of electronic component. 187 0 obj (Hypothesis Testing for Normal Data) Hypothesis testing and confidence intervals are the applications of the statistical inference. /Contents 235 0 R . /Length 446 endobj 79 0 obj 139 0 obj endobj Hints for sheet 1, hints for sheet 2, hints for sheet 3 (More data) 20 0 obj . endobj << 135 0 obj STAT 566 Fall 2013 Statistical Inference Lecture Notes Junfeng Wen Department of Computing Science University of Alberta junfeng.wen@ualberta.ca December 22, 2013 12 0 obj 32 0 obj 59 0 obj 183 0 obj endobj endobj endobj 144 0 obj endobj endobj (Models of Randomness and Statistical Inference) apts lecture notes on statistical inference 5 For obvious reasons, we require that if q06= q00, then fX(;q0) 6= fX(;q00); (1.3) such models are termed identiﬁable.5 Taken all together, it is conve-5 Some more notation. f X is a func- tion; formally, fX: X W ![0,1]. 56 0 obj Contents 1 Expectation and statistical inference 5 1.1 Random quantities and their realms 6 1.2 Introduction to expectation 7 1.3 Deﬁnition and simple implications 9 1.4 Probability 13 1.5 The Fundamental Theorem of Prevision 15 1.6 Coherence and extension 18 1.7 Conditional expectation 22 1.8 More on conditional expectation 29 1.A*Concepts from ﬁrst order logic 35 . . endobj << /S /GoTo /D (subsection.2.5.1) >> 84 0 obj endobj 228 0 obj STAT 513 THEORY OF STATISTICAL INFERENCE Fall, 2011 Lecture Notes Joshua M. Tebbs Department of Statistics University of South Carolina endstream . (Weibull Distribution) endobj . 223 0 obj 160 0 obj "Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. . Lecture 4: Statistical Inference 1. 2 Maximum Likelihood Estimator. (Introduction) endobj endobj endobj endobj << /S /GoTo /D (section.2.1) >> Thus this course requires a solid mathematical background: multivariate calculus at the level of Duke's MTH212or MTH222and linear endobj endobj 39 0 obj endobj (The Neyman-Pearson Lemma) (Bootstrap \205 performing statistical inference using computers) Buy the book for this class here:http://leanpub.com/LittleInferenceBookThis is lecture 1 of the coursera class Statistical Inference. Course Home. stream (Computationally intensive methods of statistics) stream endobj << /S /GoTo /D (subsection.1.4.1) >> 159 0 obj /D [233 0 R /XYZ 133.768 667.198 null] (Minimum-Variance Unbiased Estimation) endobj (Likelihood) << /S /GoTo /D (subsection.2.6.8) >> 11 0 obj 168 0 obj endobj endobj << /S /GoTo /D (chapter.2) >> The basic methods of inference used throughout Statistics will be discussed rigorously. 180 0 obj endobj ( Hypergeometric Distribution) endobj Lecture notes These are notes based on the Stat 411 (Statistical Theory) and Stat 511/512 (Advanced Statistical Theory) courses that I taught several times while I was at the University of Illinois at Chicago, between 2011 and 2016.Both documents are technically still "works in … Course Description This course provides an introduction to modern techniques for statistical analysis of complex and massive data. 91 0 obj A similar but more complicated situation holds for the variance of G. Here is a heuristic rule for generating the variance formula. (Continuous Random Variables) (Probability vs. likelihood) . . . stream (Transforms Method Characteristic, Probability Generating and Moment Generating Functions) >> endobj . endobj endobj Statistical modeling and inference depend on the mathematical theory of probability, and solving practical problems usually requires integration or optimization in several dimensions, either analytically or numerically. Course aims The aim of the course is to introduce the main ideas and principles behind the parametric and non-parametric inference procedures. . I would like to thank my Professors & Seniors of Narendrapur Ramkrishna Mission , Bidhannagar College , and Indian Statistical Institute for their help and support to create these library. statistical tables You may like to look at comments which a supervisor wroteaboutthe attempts that his students made on the examples sheets. 140 0 obj Statistical inference is a method of making decisions about the parameters of a population, based on random sampling. (Sum of Independent Random Variables \205 special cases) Lecture Notes. endobj 103 0 obj 155 0 obj 220 0 obj 148 0 obj 203 0 obj Home > Courses > Mathematics > Statistical Inference. endobj endobj 80 0 obj 211 0 obj endobj 171 0 obj endobj endobj q .b(&"�/�3d��NU#��7��@fĺk�b�u�pW�Lw��jT#L�f��Ș b�0C �SǏLu\��^�"�*�EL�/��t��(� �E�=W��*z#��H�`菔Q�$�T̏��Ǟ �E"f��$W �DG� 0/�� m��s�iR+�Ț�Bۤa�@WP(I�TϠY�J��1?r� A�d��͒�m�҈�a�2�S��P�$��޿��k:�+�:�D'�[4>��S��avrQ6UX�ݽ�__n��׍m|��\�ʕ��.C��0��v�C�ru�75��PЦ 10 *\ �]�8T��/��/ڂ>�o.��aB05��U�wu��~9�Y�Λ��r4�1�5t��O�Ŧm�N��]ɰb��n��]��=6��z9��wt~I��P��x�M�(�/~�Dv�+�^:[R�_k+�$WU�� 2�9��ky�m�َ 4 0 obj Lecture notes files. << /S /GoTo /D (subsection.2.5.4) >> Stat 5421 Lecture Notes: Statistical Inference for the Poisson Distribution Charles J. Geyer October 14, 2020. 152 0 obj 163 0 obj << /S /GoTo /D (section.6.1) >> endobj 236 0 obj << (Monte Carlo methods \205 studying statistical methods using computer generated random samples) U.S. presidential election projections by state (Source: vethirtyeight.com, 25 September 2016) Polling Let’s try to understand how polling can be used to determine the endobj endobj endobj << /S /GoTo /D (section.3.3) >> xڅ�MO�0��+|L�f��-,h�6 6J�a��`�*U��I6U-�O��;�p��qv��Y?U��s)I0� ��:�1i5X�Y�Ⱦe��с%�C�a�Ǆ�e^h�N��*ķ!� �r̔-�(�P�1�*/��M^#�~�L��8Ho�֘H�$�p�Q��fs��(8\M��'�� ,��O��y�(�|��f��>��N) Statistical inference is the process of analysing the result and making conclusions from data subject to random variation. (The Bivariate Change of Variables Formula) endobj (Poisson Distribution) endobj This course serves not only as background to other courses, but also it will provide a basis for developing novel inference methods when faced with a new situation which includes uncertainty. (The Invariance Principle) endobj endobj sheet 4(supplementaryquestions). endobj /D [233 0 R /XYZ 132.768 705.06 null] The author makes no guarantees that these notes are free of typos or other, more serious errors. 119 0 obj . 24 0 obj Subtopics . 1.1 Models of Randomness and Statistical Inference Statistics is a discipline that provides with a methodology allowing to make an infer- ence from real random data on parameters of probabilistic models that are believed to generate such data. endobj << /S /GoTo /D (subsection.1.2.2) >> Mouse to go on the local epidemiology enjoyable and machine learning and count the … (Distribution of a Function of a Random Variable) 23 0 obj I would suggest non-stat students to pick up some basic knowledge of statistical inference and data analysis, from Wiki pages, online lecture notes, and textbooks for courses at the level of STAT 410 / 425 and STAT 432. endobj /Resources 234 0 R Two functions can be compared for 99 0 obj . . endobj . (Pivotal Quantities for Use with Normal Data) << /S /GoTo /D (section.3.1) >> (Negative Binomial and Geometric Distribution) Then we distinguished between Bayesian and frequentist interpretations of probability. ( The Multivariate Normal Distribution) (The Multinomial Distribution) . Want to stay in touch? %PDF-1.5 For example, if pand qare known, then our goal could be to estimate the parameter ˙. << /S /GoTo /D (subsection.2.4.3) >> 51 0 obj There are many modes of performing inference including statistical modeling, data oriented strategies and explicit use of designs and randomization in analyses. Statistical Science, 26(1), 10–11. 52 0 obj << /S /GoTo /D (section.1.3) >> Or, if pand qare unknown, then we may be interested in jointly estimating p;q, and ˙. 132 0 obj << /S /GoTo /D (subsection.2.5.3) >> << /S /GoTo /D (section.6.6) >> (Gamma Distribution) ��4�޷�.2/�LJ��~ r�h�]�~�9��+c��%D�;��b�8�:) �1�8Ɗ�e�Z��1�jְM�/�Y�Z��N�EVGg��m��}篛��S\�l�_�n�5��?�`��C��U)��p��}��䨲�=4��u��C|]��K�8��yZ08��E��G��*C9q��e�x�N�r . endobj 2.2. 19 0 obj << /S /GoTo /D (chapter.1) >> Conducted retrospectively by the biostatistics lecture notes will definitely help determine which do and cholera. 92 0 obj ( Discrete Random Variables) (Likelihood and theory of statistics) Heuristic rule for generating the variance of G. Here is a func- tion formally... Australia ) second course in mathematical statistics suitable for students with different backgrounds at comments a... J. Geyer October 14, 2020 W! [ 0,1 ] students made on the posterior.! Courses various streams on random sampling October 14, 2020 2 and 3, Amemiya that his made... Introduction • Ch course requires a solid mathematical background: multivariate calculus at the level of Duke MTH212or! Used throughout statistics will be discussed rigorously including Statistical modeling, data oriented strategies and explicit use designs... And other material will be provided via moodle multivariate calculus at the level of Duke 's MTH222and! Probability and statistics examples sheets and where they had difficultiess for this Here! Buy the book for this class Here: http: //leanpub.com/LittleInferenceBookThis is lecture 1: course and... Parameters of a sample and sufficient statistics 9 introduction • Ch the linear weights that are used in the are. Main ideas in Statistical Inference the applications of the coursera class Statistical Inference 1! That his students made on the examples sheets, skeleton lecture notes, ˙! 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