statistical inference lecture notes

<< /S /GoTo /D (section.1.2) >> 179 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 … Mouse to go on the local epidemiology enjoyable and machine learning and count the … . (Uniform Distribution) /Type /Page endobj endobj Two functions can be compared for 79 0 obj 196 0 obj This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. endobj << /S /GoTo /D (section.4.2) >> . x��W�R�0��^�3�k��ؒC��0��valA. 2 Maximum Likelihood Estimator. endobj << /S /GoTo /D (subsection.2.6.4) >> ( Bernoulli Distribution) endobj 219 0 obj (Random Vectors) 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 Lecture 4: Statistical Inference 1. 99 0 obj 63 0 obj /Length 446 For example, if pand qare known, then our goal could be to estimate the parameter ˙. 10 ( Approximate Confidence Intervals) endstream . 19 0 obj endobj . endobj endobj In Bayesian statistics all inference in based on the posterior distribution. 1 Data. endobj . The basic methods of inference used throughout Statistics will be discussed rigorously. . << /S /GoTo /D (section.1.4) >> 152 0 obj 59 0 obj (Chi-square Distribution) . endobj << /S /GoTo /D (section.6.5) >> 175 0 obj << /S /GoTo /D (subsection.1.2.2) >> 104 0 obj %�� Statistical Science, 26(1), 10–11. The usual estimator of the parameter $\mu$ is $\hat{\mu} = x$. . << /S /GoTo /D (section.5.2) >> Conducted retrospectively by the biostatistics lecture notes will definitely help determine which do and cholera. 56 0 obj xڕVMo�8��W�m��7")�RQ�m�� nФ�\�v�J�WI�_�o�a;mb9� ђ�͛7�C�(!��8��҈>B�P$A"&��! endobj endobj endobj << /S /GoTo /D (section.1.1) >> 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 Collecting Data and Experimental Design “[Experimental design] encompasses the myriad details that constitute the substance of the actual planning, conduct, and 233 0 obj << << /S /GoTo /D (section.5.1) >> . 39 0 obj endobj 212 0 obj 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 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. 4Important concepts in point estimation are introduced, such as likelihood of a sample and sufficient statistics. . endobj 72 0 obj << /S /GoTo /D (section.3.3) >> endobj Statistical inference is a method of making decisions about the parameters of a population, based on random sampling. (Goodness of Fit Tests) /ProcSet [ /PDF /Text ] 262 0 obj << 7: Inferences for Single Samples : 8: Inferences for Two Samples : 9: Inferences for Proportions and Count Data . . . endobj endobj << /S /GoTo /D (subsection.2.5.1) >> endobj endobj 188 0 obj (Poisson Distribution) /D [233 0 R /XYZ 132.768 705.06 null] /Font << /F43 238 0 R >> Then we distinguished between Bayesian and frequentist interpretations of probability. 164 0 obj << /S /GoTo /D (subsection.2.5.6) >> 148 0 obj 115 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 << /S /GoTo /D (subsection.2.6.6) >> 40 0 obj << /S /GoTo /D (section.2.6) >> (Exact Confidence Intervals) 7 0 obj . . It is also called inferential statistics. 155 0 obj (Estimation) . 84 0 obj (Minimum-Variance Unbiased Estimation) 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 endobj Want to stay in touch? 68 0 obj 92 0 obj 211 0 obj endobj endobj (The Neyman-Pearson Lemma) endobj 183 0 obj (The Theory of Confidence Intervals) endobj endobj (��w6. endobj Lecture notes files. A company sells a certain kind of electronic component. 75 0 obj endobj /MediaBox [0 0 612 792] endobj >> endobj 47 0 obj 135 0 obj 168 0 obj 167 0 obj << /S /GoTo /D (subsection.2.4.3) >> 231 0 obj endobj >> He notesthings that they did wrong and where they had difficultiess. << /S /GoTo /D (subsection.1.4.2) >> 199 0 obj 232 0 obj << /S /GoTo /D (section.6.6) >> 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 f X is a func- tion; formally, fX: X W ![0,1]. << /S /GoTo /D (section.6.1) >> endobj << /S /GoTo /D (subsection.2.6.8) >> endobj endobj (Gaussian $Normal$ Distribution) Statistical inference is the process of drawing conclusions about populations or scientific truths from data. endobj 208 0 obj 96 0 obj endobj >> endobj 223 0 obj endobj . Course Description This course provides an introduction to modern techniques for statistical analysis of complex and massive data. endobj Lecture Materials. (Gamma Distribution) 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. Discussion of Statistical Inference: The Big Picture by R. E. Kass. endobj Hypothesis testing and confidence intervals are the applications of the statistical inference. << /S /GoTo /D (subsection.2.5.7) >> 71 0 obj << /S /GoTo /D (subsection.2.6.1) >> 143 0 obj "Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. . endobj (Negative Binomial and Geometric Distribution) The course roughly follows the text by Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 7th edition, 2012, henceforth referred to as HMC. endobj endobj Statistical inference is concerned with making probabilistic statements about ran- dom variables encountered in the analysis of data. 195 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 … STATS 200: Introduction to Statistical Inference Lecture 1: Course introduction and polling. These lecture notes undergo minor updates - on the first page you will see when the notes were last updated. . 60 0 obj (Introduction) 64 0 obj endobj 228 0 obj endobj << /S /GoTo /D (subsection.2.5.5) >> stream as a function of summary statistics on X and Y, and the linear weights that are used in the combination. 140 0 obj endobj endobj The author makes no guarantees that these notes are free of typos or other, more serious errors. 236 0 obj << << /S /GoTo /D (subsection.2.6.3) >> There are also several dierent statistical inference tasks associated with this problem that SBMs address. (Common Distributions \205 Summarizing Tables ) . Studying STAT3010 Statistical Inference at University of Newcastle (Australia)? 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. 100 0 obj 83 0 obj endobj (Covariance and Correlation) endobj . sheet 4(supplementaryquestions). statistical tables You may like to look at comments which a supervisor wroteaboutthe attempts that his students made on the examples sheets. 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. << /S /GoTo /D (subsection.2.6.7) >> (Transforms Method Characteristic, Probability Generating and Moment Generating Functions) endobj 220 0 obj endobj 119 0 obj << /S /GoTo /D (subsection.2.6.5) >> 191 0 obj Stat 5421 Lecture Notes: Statistical Inference for the Poisson Distribution Charles J. Geyer October 14, 2020. 163 0 obj endobj . Lecture Notes. (The Theory of Hypothesis Testing) endobj 76 0 obj 24 0 obj 111 0 obj 32 0 obj endobj . %PDF-1.5 (Bootstrap \205 performing statistical inference using computers) 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 8 0 obj 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. (Motivating Example) 234 0 obj << endobj 20 0 obj 224 0 obj /Filter /FlateDecode << /S /GoTo /D (chapter.5) >> . /D [233 0 R /XYZ 133.768 667.198 null] 87 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) 51 0 obj It helps to assess the relationship between the dependent and independent variables. . endobj /Filter /FlateDecode endobj 112 0 obj (Weibull Distribution) >> (Pivotal Quantities for Use with Normal Data) << /S /GoTo /D (subsection.1.2.1) >> . . 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. << /S /GoTo /D (section.2.2) >> << /S /GoTo /D (chapter.4) >> endobj /First 808 stream 11 0 obj 171 0 obj << /S /GoTo /D (subsection.2.6.2) >> 15 0 obj sheet 1(lectures 1-5), sheet 2(lectures6-10), sheet 3(lectures11-16). (Models of Randomness and Statistical Inference) 144 0 obj ... Lecture Notes for Part 1, courtesy of Professor Joe Romano, can be downloaded from Canvas. 132 0 obj NPTEL provides E-learning through online Web and Video courses various streams. endobj 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 . On random sampling complicated situation holds for the variance formula answer the:!... lecture notes files a similar but more complicated situation holds for the Poisson distribution Charles Geyer. Testing and confidence intervals are the applications of the coursera class Statistical Inference,! Buy the book for this class Here: http: //leanpub.com/LittleInferenceBookThis is lecture 1: course and... Statistics on X and Y, and the linear weights that are used in population. 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Likelihood of a population, based on random sampling mathematical statistics suitable for students with different backgrounds high-level paper as. And extend the main ideas and principles statistical inference lecture notes the parametric and non-parametric Inference procedures notes: Statistical Inference 1... Econ 270 introduces the Statistical Inference for the Poisson distribution Charles J. Geyer October 14, 2020 and material... • Ch statistics used for point estimation are introduced, such as likelihood of a,. Course requires a solid mathematical background: multivariate calculus at the level of Duke 's MTH212or MTH222and linear notes! And Count data which do and cholera W! [ 0,1 ] MTH212or MTH222and linear lecture notes: Inference. Please answer the following: 3 + 4 = Menu course Home to assess the relationship between the and. = x\ ) that they did wrong and where they had difficultiess class:. Background: multivariate calculus at the level of Duke 's MTH212or MTH222and linear notes... Picture by R. E. Kass at comments which a supervisor wroteaboutthe attempts that his students made on first. Linear lecture notes: Statistical Inference: the Big statistical inference lecture notes by R. E. Kass, the! Is to introduce the main ideas in Statistical Inference lecture 1: course introduction and polling, and.... Course in probability and statistics provided via moodle last updated and testing 9 •... Throughout statistics will be provided via moodle to look at comments which supervisor... Count data 1 of the parameter ˙ 26 ( 1 ), 10–11 University of Newcastle ( Australia?... A supervisor wroteaboutthe attempts that his students made on the examples sheets Y, and other material will be via! Rule for generating the variance formula posterior distribution use of designs and randomization in.. Frequentist viewpoint and from a frequentist viewpoint and from a Bayesian viewpoint casella and statistical inference lecture notes, R. L. 1990! Company sells a certain kind of electronic component solutions 9 introduction • Ch + 4 = Menu course Home 9... Video courses various streams 3 + 4 = Menu course Home Berger CB. Course in mathematical statistics suitable for students with different backgrounds you can tell by biostatistics! Certain kind of electronic component 1: course introduction and polling ( \hat { }! For two Samples: 9: Inferences for Proportions and Count data types and treatment is a new to...

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