澳洲统计模型STAT2011课程作业辅导

　　澳洲统计模型STAT2011课程作业辅导如果您打算主修数学，计算机科学或物理学，或者在悉尼大学攻读工程课程，则需要对HSC Mathematics Extension 1(3单元)有很好的了解。

　　如果您已经完成并对HSC数学有了很好的了解，并希望参加一门假定具有HSC数学扩展1知识的课程，那么扩展1桥梁课程就是为您准备的。内容将涵盖我们在数学扩展1中选择的主题相信对学生最有利。有关内容的详细信息，请单击此处。

　　统计模型STAT2011课程详情

　　学生收到UAC的录取通知后 ，扩展1衔接课程将于2020年2月3日星期一开始。该课程将以两种形式提供：日间课程和夜校。每个课程包括12个两个小时的课程。

　　班级规模很小，因此学生可以得到最大程度的个人关注。在衔接课程中，预计学生每天至少要花费两个小时进行私人学习和家庭作业。

　　尽管该课程是专门为帮助学生注册悉尼大学第一年主流数学课程而设计的，但计划注册其他机构的学生也可以参加。请注意，衔接课程没有考试。

　　费用

　　任一课程的费用均为435美元。费用包括商品及服务税(GST)和小班授课的24小时学费，一本带简短笔记的练习本，以及每天在数学学习中心多花两个小时的机会，那里可以提供个人帮助。填写报名表(请参阅下文)时，必须使用信用卡(仅万事达卡或Visa卡)支付费用。报名和付款的截止日期为2020年1月30日(星期四)午夜。

　　日期和时间

　　课程日期天时报

　　扩展1

　　(白天)2月3日星期一至2月18日星期二周一至周五上午10点至中午12点

　　分机1

　　(晚上)2月3日星期一至2月20日星期四周一至周四下午6点至晚上8点

　　去哪儿

　　所有学生应于2020年2月3日星期一来到悉尼大学新法学院附楼研讨会440室。新法学院附楼在化学学院对面的东部大街主校区。440室位于4楼。

　　白天的学生将从上午9:30开始分配课程，晚上的学生将从下午5:30开始分配课程。请确保您在课程于上午10:00(白天)和下午6:00(晚上)开始之前及时到达以完成此过程。

　　入学条件

　　大学保留在课程开始之前或期间更改衔接课程安排，取消或终止课程或拒绝法律允许的任何注册的权利。如果任何课程的入学人数不足，大学保留向学生提供选择其他安排或退款的权利。

　　如果您提前注册并支付衔接课程费用，但后来却发现自己无法参加该课程，只要您在开课日期前至少一周告知我们，您的费用将退还(减去25美元的管理费)。我们的联系方式如下。请注意，大学对个人情况或工作承诺的任何变化不承担任何责任。

　　隐私声明：数学学习中心和悉尼大学数学与统计学院需要您在注册表中提供的信息，以管理您的注册和参加衔接课程。未经您的明确同意，除非法律要求，否则任何个人信息都不会在大学之外泄露。

      Statistical Models STAT2011 Lecturer: Michael Stewart (Carslaw 818) Semester 1, 2017 Unit of Study Outline This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random variable models, like the binomial, Poisson and geometric, and continuous models, including the normal and exponential, will be studied. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. All students are expected to attend 3 lectures, 1 tutorial and 1 computer class per week. All room numbers are for the Carslaw building. • Lectures: Monday, Tuesday and Wednesday in 175. • Tutorials: Wednesday 2pm (453); Thursday 2pm (451,729/30,354) from week 2. • Computer classes: Wednesday 3pm (705/6); Thursday 3pm (610/1,705/6,729/30) from week 2. For statistical computing we shall be using the RStudio graphical interface (freely available from rstudio.com) to the R statistical computing environment (freely available from r-project.org) for generating reports using the LATEX typesetting system (freely available from latex-project.org). Students are encouraged to install these three pieces of free, open source and cross-platform software on their own machines. Electronic communication Please send all emails to STAT2011@sydney.edu.au. Messages sent to any other address may not be responded to. Please include your name and student number in all communication and/or send from your official university email address. Assessment breakdown 1. Written examination: 65% 2. Quizzes (held in tutorial classes in weeks 4, 7 and 10): 15% 1 3. Computer test (held in the week 13 computer class): 10% 4. Weekly computer work (weeks 2–12): 10% Learning Outcomes 1. Construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models. such as probabilities, expectations and variances. 2. Fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters. 3. Compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates. 4. Assess the goodness of fit (as appropriate) of a fitted model. 5. [D] Apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory. 6. [HD] Prove certain mathematical results (e.g. inequalities, limiting results) used in the course. Approximately equal weight will be applied to each of these 6 outcomes in the overall assessment breakdown. A student will need to reach a basic level of competency in all of outcomes 1 to 4 to receive a passing grade. Certain tutorial exercises concerning material in outcomes 1 to 4 will go beyond “basic”; these will be marked with a star? . Tutorial exercises concerning outcomes 5 and 6 will be marked with D or HD as appropriate. Lecture schedule There are 3 lectures in each of the 13 weeks of semester (none are lost to public holidays) giving 39 lectures. Of these, 37 are scheduled with new material, the last two are left as review lectures. A draft schedule appears below with (a), (b) and (c) corresponding to Monday, Tuesday and Wednesday respectively. Lecture notes and other resources will be available at sydney.edu.au/science/maths/STAT2011. 1. (a) Introduction; overview; classical probability; revision; examples. (b) Simple/classical random variables; prob distribution; expectation; probability as expectation. (c) computational shortcut for expectation; functions of random variables; linear functions; variance; computational shortcut for E[g(X)]. 2. (a) Considering two random varibles at once; computational shortcut for E[g(X, Y )]. (b) Independence; V ar(X + Y ); covariance/correlation. (c) Combining experiments independently; urn models; sampling with replacement; models for each observation. 2 3. (a) E(X¯), V ar(X¯), E(S 2 ); binary case: full probability distribution of sum/mean. (b) Convergence in probability; Chebyshev’s inequality. (c) Proof of Chebyshev’s inequality using Markov’s inequality. 4. (a) Sampling without replacement; binary case: hypergeometric distribution including E(·) and V ar(·); E(·) and V ar(·) in the general case. (b) Serial No. model; order statistics. (c) Waiting time urn model; mean, variance; St Petersburg “paradox”. 5. (a) Assessing goodness of fit; Saxony data. (b) General binomial mixture models; two instances. (c) Conditional distributions; conditional expectation and variance formulae. 6. (a) ESTIMATION; modelling paradigm; measures of uncertainty. (b) Examples of unbiased estimators. (c) Biased estimators; Jensen’s inequality; waiting times example. 7. (a) Large sample approxmation to MSE; bootstrap methods. (b) Proof of convergence in probability of the secant gradient ratio. (c) Comparing estimators in the B(2, p) (genetics) example. 8. (a) The Cauchy-Schwartz inequality; Cramer-Rao lower bound; minimum variance unbiased estimators. (b) The method of maximum likelihood. Binomial example. (c) More maximum likelihood examples. 9. (a) Beyond classical probability; Poisson ; Geometric. (b) Negative binomial distribution. (c) Streams of events; Poisson counts; exponential waiting times. 10. (a) Cumulative distribution functions; probability density functions. (b) Continuous maximum likelihood; estimating exponential rate. (c) Gamma: integer shape; positive shape. 11. (a) Uniform distribution: limit of a single draw from Serial no. model. (b) Uniform sample as limit of Serial number model; order statistics; beta distribution. (c) Transforming from the uniform; large-sample approximations for general order statistics 12. (a) Graphical study of distributions of sums: (negative-)binomial, Poisson, gamma. (b) The normal distribution. The Central Limit Theorem. (c) Estimating a normal mean and variance. 13. (a) Assessing goodness of fit to the normal distribution; qq-plots; location/scale models. (b) Review of important examples. (c) Review of important examples. 3 Materials and Resources • Lecture notes, tutorial and computer exercises and other materials will be made available via the course webpage: sydney.edu.au/science/maths/STAT2011 • There is no formal textbook for the course, however the following references may be useful: – Statistics by David Freedman, Robert Pisani and Roger Purves (any edition). Possibly the best statistics textbook around, it emphasises concepts more than mathematics (it is designed for students without calculus). It used to be used in the now dormant unit STAT1021 General Statistical Methods (for Arts students) so several copies should be in the library. – An Introduction to Mathematical Statistics and Its Applications (any edition) by Richard J. Larsen and Morris L. Marx. This used to be a text for the course, it does not cover all of the current content, however it should be useful for basic concepts and procedures – there should be several copies in the library. – Mathematical Statistics and Data Analysis by John Rice. This is the text for STAT2911, is quite advanced but does cover some topics not covered by the Larsen and Marx book. – The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith. This elementary, fun book does a very good job of explaining tricky statistical concepts in an effective and entertaining way; very highly recommended (and quite inexpensive). Michael Stewart March 2017.