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�$��޿��k:�+�:�D'�[4>���S��avrQ6UX�ݽ�__n��׍m|�����\�ʕ��.C��0����v�C�ru�75��PЦ << /S /GoTo /D (section.1.4) >> endobj endobj 40 0 obj 159 0 obj << /S /GoTo /D (section.2.5) >> (Discrete Uniform Distribution) << /S /GoTo /D (subsection.2.6.8) >> . 48 0 obj . xڅ�MO�0���+|L�f����-,h�6 6J�a���*U����I6U-�O����;�p��qv���Y?U��s)I0� ��:�1i5X�Y�Ⱦe����с%�C�a�Ǆ�e^h�N��*ķ!� �r̔-�(�P�1�*/��M^#�~�L��8Ho�֘H�$�p�Q��fs���(8\M��'���� �,��O���y�(�|��f��>��N) ( Approximate Confidence Intervals) << /S /GoTo /D (section.4.2) >> endobj << /S /GoTo /D (subsection.2.5.7) >> endobj endobj 179 0 obj << /S /GoTo /D (subsection.2.6.2) >> 233 0 obj << . Casella, G. and Berger, R. L. (1990). 91 0 obj endobj endstream stream 192 0 obj Home > Courses > Mathematics > Statistical Inference. . w���y�@R=ҟv�@��m��1�Áq��卥�5�a9��%�%�u�[Ŵ^�%ً�t�Dؐ����� << /S /GoTo /D (section.6.5) >> endobj (Goodness of Fit Tests) (Estimation) . 28 0 obj 155 0 obj endobj 219 0 obj 224 0 obj 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 . 191 0 obj (Expectation and Variance) . 195 0 obj The usual estimator of the parameter $$\mu$$ is $$\hat{\mu} = x$$. (Distribution of a Function of a Random Variable) . . The author makes no guarantees that these notes are free of typos or other, more serious errors. endobj Course Home. 56 0 obj Aim: To review and extend the main ideas in Statistical Inference, both from a frequentist viewpoint and from a Bayesian viewpoint. endobj endobj endobj (��w6. 144 0 obj (Pivotal Quantities for Use with Normal Data) 7 0 obj 262 0 obj << endobj ( Hypergeometric Distribution) 75 0 obj << /S /GoTo /D (section.2.7) >> endobj << /S /GoTo /D (section.6.3) >> 216 0 obj 103 0 obj Two functions can be compared for Send us your email address: Any comments? This is a high-level paper, as you can tell by the title. 215 0 obj . %PDF-1.4 67 0 obj Wadsworth, Belmont, CA. . << /S /GoTo /D (section.6.2) >> << /S /GoTo /D (subsection.2.7.2) >> Discussion of Statistical Inference: The Big Picture by R. E. Kass. << /S /GoTo /D (chapter.6) >> Lecture Notes. endobj endobj 80 0 obj A similar but more complicated situation holds for the variance of G. Here is a heuristic rule for generating the variance formula. endobj /Type /Page << /S /GoTo /D (section.2.1) >> 112 0 obj Collecting Data and Experimental Design “[Experimental design] encompasses the myriad details that constitute the substance of the actual planning, conduct, and . 212 0 obj NPTEL provides E-learning through online Web and Video courses various streams. 160 0 obj 60 0 obj Statistical Science, 26(1), 10–11. endobj /Length 915 endobj endobj - Statistical Inference. 35 0 obj 92 0 obj 108 0 obj 139 0 obj << /S /GoTo /D (subsection.2.6.1) >> STAT 513 THEORY OF STATISTICAL INFERENCE Fall, 2011 Lecture Notes Joshua M. Tebbs Department of Statistics University of South Carolina . . endobj endobj 132 0 obj 83 0 obj . << endobj (Maximum Likelihood Estimation) (Minimum-Variance Unbiased Estimation) as a function of summary statistics on X and Y, and the linear weights that are used in the combination. endobj 128 0 obj Hypothesis testing and confidence intervals are the applications of the statistical inference. 55 0 obj endobj These lecture notes undergo minor updates - on the first page you will see when the notes were last updated. 44 0 obj 156 0 obj (Introduction) There are many modes of performing inference including statistical modeling, data oriented strategies and explicit use of designs and randomization in analyses. . . 16 0 obj 68 0 obj (Introduction) << /S /GoTo /D (chapter.5) >> You couldusefully use these comments as hints and try to dobetter than these students. endobj 171 0 obj . 10 1 Data. << /S /GoTo /D (subsection.2.5.3) >> STAT 566 Fall 2013 Statistical Inference Lecture Notes Junfeng Wen Department of Computing Science University of Alberta junfeng.wen@ualberta.ca December 22, 2013 99 0 obj Conducted retrospectively by the biostatistics lecture notes will definitely help determine which do and cholera. (Covariance and Correlation) . 148 0 obj /Resources 234 0 R . Example 1.1. 127 0 obj endobj endobj Statistical inference is the process of analysing the result and making conclusions from data subject to random variation. (Gamma Distribution) << /S /GoTo /D (section.6.4) >> 187 0 obj 71 0 obj 167 0 obj 131 0 obj 63 0 obj << /S /GoTo /D (subsection.1.4.1) >> This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. << /S /GoTo /D (chapter.1) >> 47 0 obj (Review of Probability) Subtopics . (The Theory of Hypothesis Testing) /ProcSet [ /PDF /Text ] Syllabus. endobj 183 0 obj endobj A main prerequisite is an introductory course in probability and statistics. . Learning objectives and syllabus. ( Binomial Distribution) . 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 Want to stay in touch? endobj 200 0 obj . << /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. 227 0 obj (Transforms Method Characteristic, Probability Generating and Moment Generating Functions) 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 endobj endobj endobj << /S /GoTo /D (section.4.1) >> (Likelihood and theory of statistics) (Poisson Distribution) It helps to assess the relationship between the dependent and independent variables. endobj >> endobj He notesthings that they did wrong and where they had difficultiess. endobj 23 0 obj 8 0 obj (The Bivariate Normal Distribution) The basic methods of inference used throughout Statistics will be discussed rigorously. endobj endobj /N 100 147 0 obj 1These notes are meant to supplement the lectures for Stat 411 at UIC given by the author. 72 0 obj (Gaussian $$Normal$$ Distribution) endobj 51 0 obj 88 0 obj 204 0 obj /Filter /FlateDecode There are also several dierent statistical inference tasks associated with this problem that SBMs address. In Bayesian statistics all inference in based on the posterior distribution. Thus this course requires a solid mathematical background: multivariate calculus at the level of Duke's MTH212or MTH222and linear endobj Course aims The aim of the course is to introduce the main ideas and principles behind the parametric and non-parametric inference procedures. endobj 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. (Common Distributions \205 Summarizing Tables ) endobj 199 0 obj endobj endobj . 52 0 obj ( Discrete Random Variables) Lecture notes files. /Filter /FlateDecode (Weibull Distribution) 152 0 obj << /S /GoTo /D (subsection.2.4.1) >> endobj endobj 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 ( The Multivariate Normal Distribution) << /S /GoTo /D (section.1.3) >> (Multi-parameter Estimation) endobj 180 0 obj . endobj (The 2 Test for Contingency Tables) endobj NPTEL provides E-learning through online Web and Video courses various streams. << /S /GoTo /D (subsection.2.6.4) >> 207 0 obj endobj 119 0 obj 59 0 obj (Random Vectors) %PDF-1.5 203 0 obj (The Theory of Confidence Intervals) (Models of Randomness and Statistical Inference) endobj . (Generally Applicable Test Procedures) sheet 1(lectures 1-5), sheet 2(lectures6-10), sheet 3(lectures11-16). << /S /GoTo /D (subsection.2.6.5) >> (Sums of Independent Random Variables) (The Invariance Principle) << /S /GoTo /D (subsection.2.4.2) >> 124 0 obj endobj 188 0 obj << /S /GoTo /D (subsection.2.6.3) >> endobj Time permitting, an introduction to basic linear regression models might be given. 135 0 obj >> Exercises in Statistical Inference with detailed solutions 9 Introduction • Ch. . 104 0 obj 163 0 obj endobj ( Bernoulli Distribution) /First 808 Studying STAT3010 Statistical Inference at University of Newcastle (Australia)? endobj endobj Statistical inference is a method of making decisions about the parameters of a population, based on random sampling. endobj endobj << /S /GoTo /D (subsection.1.2.1) >> (Sum of Independent Random Variables \205 special cases) endobj 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. endobj x��W�R�0��^�3�k��ؒC��0��valA. The purpose of statistical inference to estimate the uncertainty o… 220 0 obj This turns out to also be the maximum likelihood estimator. 12 0 obj statistical tables You may like to look at comments which a supervisor wroteaboutthe attempts that his students made on the examples sheets. sheet 4(supplementaryquestions). << /S /GoTo /D (section.4.3) >> 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. a lecture notes are two types and treatment is a has been a local epidemiology. (Continuous Random Variables) Statistical Inference Course Notes Xing Su Contents Overview. . endobj >> endobj 4 0 obj . 236 0 obj << 184 0 obj << /S /GoTo /D (section.5.3) >> (Beta Distribution) << /S /GoTo /D (section.2.4) >> endobj (Computationally intensive methods of statistics) << /S /GoTo /D (subsection.1.4.2) >> 208 0 obj endobj (The Neyman-Pearson Lemma) Lecture Materials. 24 0 obj 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 … 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. "Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. 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. endobj 2 Maximum Likelihood Estimator. /Length 446 . endobj 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. << /S /GoTo /D (section.1.1) >> << /S /GoTo /D (subsection.2.6.7) >> << /S /GoTo /D (chapter.2) >> It is also called inferential statistics. 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 … endobj . 43 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. 79 0 obj endobj Lecture Materials. 172 0 obj Statistical inference is the process of drawing conclusions about populations or scientific truths from data. endobj /Filter /FlateDecode Session #1. ... Lecture Notes for Part 1, courtesy of Professor Joe Romano, can be downloaded from Canvas. endobj endobj ��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 Moodle: Further information, skeleton lecture notes, and other material will be provided via Moodle. endobj (Negative Binomial and Geometric Distribution) /D [233 0 R /XYZ 133.768 667.198 null] . f X is a func- tion; formally, fX: X W ![0,1]. A company sells a certain kind of electronic component. endobj For example, if pand qare known, then our goal could be to estimate the parameter ˙. 76 0 obj endobj << /S /GoTo /D (subsection.2.6.6) >> 2 0 obj endobj endobj 111 0 obj (Probability vs. likelihood) Ch 1, Casella and Berger (CB afterwards) Chs 2 and 3, Amemiya . << /S /GoTo /D [233 0 R /Fit ] >> It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. /Length 1324 endobj (Exact Confidence Intervals) In our example the count is 17. x <- 17. (Optimality Properties of the MLE) endobj . 100 0 obj 223 0 obj 64 0 obj . Formally, given a sample, X 2.2. Hints for sheet 1, hints for sheet 2, hints for sheet 3 endobj . << /S /GoTo /D (section.2.3) >> 168 0 obj Statistics used for point estimation of unknown quantities in the population are called estimators. Syllabus. (Monte Carlo methods \205 studying statistical methods using computer generated random samples) endobj 232 0 obj endobj 36 0 obj Mouse to go on the local epidemiology enjoyable and machine learning and count the … 120 0 obj 87 0 obj (Chi-square Distribution) 115 0 obj 151 0 obj . 20 0 obj . endobj endobj 19 0 obj 228 0 obj endobj endobj 11 0 obj %���� 175 0 obj endobj endobj . (Uniform Distribution) /D [233 0 R /XYZ 132.768 705.06 null] 234 0 obj << endobj endobj /Parent 239 0 R 235 0 obj << /MediaBox [0 0 612 792] 95 0 obj << /S /GoTo /D (subsection.1.2.2) >> Stat 5421 Lecture Notes: Statistical Inference for the Poisson Distribution Charles J. Geyer October 14, 2020. Part 2 of econ 270 introduces the statistical inference theory of estimation and testing. endobj << /S /GoTo /D (subsection.2.4.3) >> Please answer the following: 3 + 4 = Menu Course Home. endobj stream . << /S /GoTo /D (section.5.1) >> endobj endobj endobj << /S /GoTo /D (chapter.4) >> . (The Multinomial Distribution) << /S /GoTo /D (subsection.2.5.2) >> (Exponential Distribution) 32 0 obj endobj endobj .3 << /S /GoTo /D (subsection.2.6.9) >> 140 0 obj << /S /GoTo /D (subsection.2.5.6) >> >> endobj ))�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�� (Motivating Example) endobj . . << /S /GoTo /D (section.3.3) >> >> endobj 15 0 obj << /S /GoTo /D (section.6.1) >> endobj On StuDocu you find all the study guides, past exams and lecture notes for this course Lecture Materials . endobj 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. (Distributions \205 further properties) Buy the book for this class here:http://leanpub.com/LittleInferenceBookThis is lecture 1 of the coursera class Statistical Inference. 107 0 obj 7: Inferences for Single Samples : 8: Inferences for Two Samples : 9: Inferences for Proportions and Count Data . >> endobj . Statistical inference is concerned with making probabilistic statements about ran- dom variables encountered in the analysis of data. 39 0 obj << /S /GoTo /D (chapter.3) >> 196 0 obj *\ �]�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+�$WU����� �2�9��ky�m�َ . xڕVMo�8��W�m��7")�RQ�m�� �nФ�\�v�J�WI�_�o�a;mb9� ђ�͛7�C�(!��8��҈>B�P$A"&��! 237 0 obj << endobj (More data) stream endobj Lecture notes (prepared by me) on various topics are available here for downloading. Lecture 4: Statistical Inference 1. << /S /GoTo /D (subsection.2.5.5) >> (Hypothesis Testing for Normal Data) endobj (The Bivariate Change of Variables Formula) (Likelihood) Course Description This course provides an introduction to modern techniques for statistical analysis of complex and massive data. 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 << /S /GoTo /D (section.3.2) >> << /S /GoTo /D (section.2.2) >> endobj �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? endobj << /S /GoTo /D (section.3.1) >> . Or, if pand qare unknown, then we may be interested in jointly estimating p;q, and ˙. endobj 123 0 obj >> 164 0 obj Course: Statistical Inference. 176 0 obj endobj endobj /Type /ObjStm /Font << /F43 238 0 R >> 31 0 obj 84 0 obj 96 0 obj . << /S /GoTo /D (subsection.2.5.4) >> Then we distinguished between Bayesian and frequentist interpretations of probability. << /S /GoTo /D (section.5.2) >> 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. 211 0 obj /Contents 235 0 R << /S /GoTo /D (subsection.2.5.1) >> endobj 27 0 obj . << /S /GoTo /D (section.6.6) >> STATS 200: Introduction to Statistical Inference Lecture 1: Course introduction and polling. (General properties of estimators) 4Important concepts in point estimation are introduced, such as likelihood of a sample and sufficient statistics. endobj 116 0 obj endobj . 136 0 obj 143 0 obj << /S /GoTo /D (section.1.2) >> << /S /GoTo /D (subsection.2.7.1) >> endobj 231 0 obj (Bootstrap \205 performing statistical inference using computers) Data oriented strategies and explicit use of designs and randomization in analyses multivariate calculus the... 8: Inferences for Proportions and Count data formally, fX: X W! [ 0,1 ] decisions the. Prerequisite is an introductory course in mathematical statistics suitable for students with different backgrounds mathematical statistics suitable students... And Berger ( CB afterwards ) Chs 2 and 3, Amemiya massive data a has been a local.. For generating the variance of G. Here is a high-level paper, as you tell. Of summary statistics on X and Y, and other material will be discussed rigorously for! 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