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= Announcement =
= Announcement =
* TBA
* 6月14日周三晚6点30分开始，线上习题课。<font size=4 color=red>#腾讯会议：598-944-8767</font>


= Course info =
= Course info =
Line 116: Line 116:


= Assignments =
= Assignments =
*[[概率论与数理统计 (Spring 2023)/Problem Set 1|Problem Set 1]]  请在 2023/3/<strike>15</strike><font color=red>22</font> 上课之前(14:00 UTC+8)提交到 [mailto:pr2023_nju@163.com pr2023_nju@163.com] (文件名为'<font color=red >学号_姓名_A1.pdf</font>'). [[概率论与数理统计 (Spring 2023)/第一次作业提交名单|第一次作业提交名单]].
*[[概率论与数理统计 (Spring 2023)/Problem Set 1|Problem Set 1]]  请在 2023/3/<strike>15</strike><font color=red>22</font> 上课之前(14:00 UTC+8)提交到 [mailto:pr2023_nju@163.com pr2023_nju@163.com] (文件名为'<font color=red >学号_姓名_A1.pdf</font>').  
** [[概率论与数理统计 (Spring 2023)/第一次作业提交名单|第一次作业提交名单]]
*[[概率论与数理统计 (Spring 2023)/Problem Set 2|Problem Set 2]]  请在 2023/4/<strike>12</strike><font color=red>19</font> 上课之前(14:00 UTC+8)提交到 [mailto:pr2023_nju@163.com pr2023_nju@163.com] (文件名为'<font color=red >学号_姓名_A2.pdf</font>').
** [[概率论与数理统计 (Spring 2023)/第二次作业提交名单|第二次作业提交名单]]
*[[概率论与数理统计 (Spring 2023)/Problem Set 3|Problem Set 3]]  请在 2023/5/10 上课之前(14:00 UTC+8)提交到 [mailto:pr2023_nju@163.com pr2023_nju@163.com] (文件名为'<font color=red >学号_姓名_A3.pdf</font>').
** [[概率论与数理统计 (Spring 2023)/第三次作业提交名单|第三次作业提交名单]]
*[[概率论与数理统计 (Spring 2023)/Problem Set 4|Problem Set 4]]  请在 2023/6/<strike>7</strike><font color=red>14</font> (14:00 UTC+8)之前提交到 [mailto:pr2023_nju@163.com pr2023_nju@163.com] (文件名为'<font color=red >学号_姓名_A4.pdf</font>').
** [[概率论与数理统计 (Spring 2023)/第四次作业提交名单|第四次作业提交名单]]


= Lectures =
= Lectures =
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# [http://tcs.nju.edu.cn/slides/prob2023/ProbSpace.pdf 概率空间]
# [http://tcs.nju.edu.cn/slides/prob2023/ProbSpace.pdf 概率空间]
#* 阅读：'''[BT] 第1章''' 或 '''[GS] Chapter 1'''
#* 阅读：'''[BT] 第1章''' 或 '''[GS] Chapter 1'''
#* Example for total probability: [[概率论与数理统计 (Spring 2023)/Polynomial identity testing| Polynomial identity testing]]
#* Example for '''chain rule''': [[概率论与数理统计 (Spring 2023)/Karger's min-cut algorithm| Karger's min-cut algorithm]]
#* Example for chain rule: [[概率论与数理统计 (Spring 2023)/Karger's min-cut algorithm| Karger's min-cut algorithm]]
#* Example for '''total probability''': [[概率论与数理统计 (Spring 2023)/Polynomial identity testing| Polynomial identity testing]]
# [http://tcs.nju.edu.cn/slides/prob2023/RandVar.pdf 随机变量]
#* 阅读：'''[BT] 第2章''' 或 '''[GS] Chapter 2, Sections 3.1~3.5, 3.7'''
#* 阅读：'''[MU] Chapter 2'''
#* the [http://tcs.nju.edu.cn/slides/prob2023/discrete-pmf.nb '''Mathematica notebook file'''] for the PMFs of basic discrete distributions
#* [https://www.bilibili.com/video/BV1ta411A7fp/ 高尔顿板（Galton board）视频] 和 [https://en.wikipedia.org/wiki/Galton_board 维基百科页面]
#* [[概率论与数理统计 (Spring 2023)/Average-case analysis of QuickSort|Average-case analysis of '''''QuickSort''''']]
# [http://tcs.nju.edu.cn/slides/prob2023/Deviation.pdf 矩与偏差]
#* 阅读：'''[MU] Chapter 3'''
#* 阅读：'''[BT] 章节 2.4, 4.2, 4.3, 5.1''' 或 '''[GS] Sections 3.3, 3.6, 7.3'''
#* [[概率论与数理统计 (Spring 2023)/Two-point sampling|Two-point sampling]]
#* [[概率论与数理统计 (Spring 2023)/Threshold of k-clique in random graph|Threshold of <math>k</math>-clique in random graph]]
#* [[概率论与数理统计 (Spring 2023)/Weierstrass Approximation Theorem|Weierstrass approximation]]
# [http://tcs.nju.edu.cn/slides/prob2023/Continuous.pdf 连续分布]
#* 阅读：'''[BT] 第3章, 和4.1节''' 或 '''[GS] Chapter 4'''
#* 阅读：'''[MU] Chapters 8, 9'''
#* [https://measure.axler.net/MIRA.pdf Measure, Integration & Real Analysis] by Sheldon Axler
# [http://tcs.nju.edu.cn/slides/prob2023/Convergence.pdf 极限定理]
#* 阅读：'''[BT] 第5章'''
#* 阅读：'''[GS] Sections 5.7~5.10, 7.1~7.5'''
# [http://tcs.nju.edu.cn/slides/prob2023/Concentration.pdf 测度集中]
#* 阅读：'''[MU] Chapters 4''' and '''Sections 13.1, 13.4~13.5'''
#* 阅读：'''[GS] Sections 5.11, 12.1~12.3, 7.8~7.9'''
#* [[概率论与数理统计 (Spring 2023)/Hoeffding's lemma|Hoeffding's lemma]]
#* [[概率论与数理统计 (Spring 2023)/Entropy and volume of Hamming balls|Entropy and volume of Hamming balls]]
# [http://tcs.nju.edu.cn/slides/prob2023/Process.pdf 随机过程]
#* 阅读：'''[BT] 第6章, 第7章'''
#* 阅读：'''[MU]  Chapters 7, Sections 13.1~13.3''' or '''[GS] Chapters 6, Sections 12.4~12.5'''
#* [[概率论与数理统计 (Spring 2023)/OST and applications|OST and applications]]
# [[Media:Stat01.pdf | 统计与贝叶斯推断]], [[Media:Stat02-2023.pdf | 经典统计推断]]
#* 阅读：'''[BT] 第8章, 第9章'''


= Concepts =
= Concepts =
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* [https://en.wikipedia.org/wiki/Independence_(probability_theory) Independence]  
* [https://en.wikipedia.org/wiki/Independence_(probability_theory) Independence]  
** [https://en.wikipedia.org/wiki/Pairwise_independence Pairwise independence]
** [https://en.wikipedia.org/wiki/Pairwise_independence Pairwise independence]
* [https://en.wikipedia.org/wiki/Random_variable Random variable]
** [https://en.wikipedia.org/wiki/Cumulative_distribution_function Cumulative distribution function]
** [https://en.wikipedia.org/wiki/Probability_mass_function Probability mass function]
** [https://en.wikipedia.org/wiki/Probability_density_function Probability density function]
* [https://en.wikipedia.org/wiki/Multivariate_random_variable Random vector]
** [https://en.wikipedia.org/wiki/Joint_probability_distribution Joint probability distribution]
** [https://en.wikipedia.org/wiki/Conditional_probability_distribution Conditional probability distribution]
** [https://en.wikipedia.org/wiki/Marginal_distribution Marginal distribution]
* Some '''discrete''' probability distributions
** [https://en.wikipedia.org/wiki/Bernoulli_trial Bernoulli trial] and [https://en.wikipedia.org/wiki/Bernoulli_distribution Bernoulli distribution]
** [https://en.wikipedia.org/wiki/Discrete_uniform_distribution Discrete uniform distribution]
** [https://en.wikipedia.org/wiki/Binomial_distribution Binomial distribution]
** [https://en.wikipedia.org/wiki/Geometric_distribution Geometric distribution]
** [https://en.wikipedia.org/wiki/Negative_binomial_distribution Negative binomial distribution]
** [https://en.wikipedia.org/wiki/Hypergeometric_distribution Hypergeometric distribution]
** [https://en.wikipedia.org/wiki/Poisson_distribution Poisson distribution]
** and [https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions others]
* Balls into bins model
** [https://en.wikipedia.org/wiki/Multinomial_distribution Multinomial distribution]
** [https://en.wikipedia.org/wiki/Birthday_problem Birthday problem]
** [https://en.wikipedia.org/wiki/Coupon_collector%27s_problem Coupon collector]
** [https://en.wikipedia.org/wiki/Balls_into_bins_problem Occupancy problem]
* Random graphs
** [https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model Erdős–Rényi random graph model]
** [https://en.wikipedia.org/wiki/Galton%E2%80%93Watson_process Galton–Watson branching process]
* [https://en.wikipedia.org/wiki/Expected_value Expectation]
** [https://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician Law of the unconscious statistician, ''LOTUS'']
** [https://dlsun.github.io/probability/linearity.html Linearity of expectation]
** [https://en.wikipedia.org/wiki/Conditional_expectation Conditional expectation]
** [https://en.wikipedia.org/wiki/Law_of_total_expectation Law of total expectation]
* [https://en.wikipedia.org/wiki/Markov%27s_inequality Markov's inequality]
* [https://en.wikipedia.org/wiki/Chebyshev%27s_inequality Chebyshev's inequality]
* [https://en.wikipedia.org/wiki/Moment_(mathematics) Moment] related
** [https://en.wikipedia.org/wiki/Central_moment Central moment]
** [https://en.wikipedia.org/wiki/Variance Variance]
** [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation]
** [https://en.wikipedia.org/wiki/Covariance Covariance]
** [https://en.wikipedia.org/wiki/Correlation Correlation]
** [https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation Correlation does not imply causation]
** [https://en.wikipedia.org/wiki/Skewness Skewness]
** [https://en.wikipedia.org/wiki/Kurtosis Kurtosis]
*[https://en.wikipedia.org/wiki/Probability_density_function Probability density function]
** [https://en.wikipedia.org/wiki/Probability_distribution#Absolutely_continuous_probability_distribution Continuous probability distribution]
**[https://en.wikipedia.org/wiki/Conditional_probability_distribution#Conditional_continuous_distributions Conditional continuous distributions]
**[https://en.wikipedia.org/wiki/Convolution_of_probability_distributions Convolution of probability distributions] and [https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions List of convolutions of probability distributions]
* [https://en.wikipedia.org/wiki/Measure_(mathematics) Measure]
** [https://en.wikipedia.org/wiki/Borel_set Borel set]
** [https://en.wikipedia.org/wiki/Lebesgue_integration Lebesgue integration]
** [https://en.wikipedia.org/wiki/Measurable_function Measurable function]
** [https://en.wikipedia.org/wiki/Cantor_set Cantor set]
** [https://en.wikipedia.org/wiki/Non-measurable_set Non-measurable set]
* Some '''continuous''' probability distributions
** [https://en.wikipedia.org/wiki/Continuous_uniform_distribution Continuous uniform distribution]
** [https://en.wikipedia.org/wiki/Exponential_distribution Exponential distribution] and [https://en.wikipedia.org/wiki/Poisson_point_process Poisson point process]
** [https://en.wikipedia.org/wiki/Normal_distribution Normal (Gaussion) distribution]
*** [https://en.wikipedia.org/wiki/Gaussian_function Gaussian function] and [https://en.wikipedia.org/wiki/Gaussian_integral Gaussian integral]
*** [https://en.wikipedia.org/wiki/Standard_normal_table Standard normal table]
*** [https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule 68–95–99.7 rule]
*** [https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables Sum of normally distributed random variables]
*** [https://en.wikipedia.org/wiki/Multivariate_normal_distribution Multivariate normal distribution]
** [https://en.wikipedia.org/wiki/Chi-squared_distribution Chi-squared distribution]
** [https://en.wikipedia.org/wiki/Gamma_distribution Gamma distribution] and [https://en.wikipedia.org/wiki/Gamma_function Gamma function]
** [https://en.wikipedia.org/wiki/Beta_distribution Beta distribution] and [https://en.wikipedia.org/wiki/Beta_function Beta function]
** [https://en.wikipedia.org/wiki/Cauchy_distribution Cauchy distribution]
** and [https://en.wikipedia.org/wiki/List_of_probability_distributions#Absolutely_continuous_distributions others]
* [https://en.wikipedia.org/wiki/Inverse_transform_sampling Inverse transform sampling]
* [https://en.wikipedia.org/wiki/Stochastic_dominance Stochastic dominance] and [https://en.wikipedia.org/wiki/Coupling_(probability) Coupling]
* [https://en.wikipedia.org/wiki/Moment-generating_function Moment-generating function]
* [https://en.wikipedia.org/wiki/Convergence_of_random_variables Convergence of random variables]
** [https://en.wikipedia.org/wiki/Pointwise_convergence Pointwise convergence]
** [https://en.wikipedia.org/wiki/Convergence_of_measures#Weak_convergence_of_measures Weak convergence of measures]
** [https://en.wikipedia.org/wiki/Convergence_in_measure Convergence in measure]
** [https://en.wikipedia.org/wiki/Skorokhod%27s_representation_theorem Skorokhod's representation theorem]
** [https://en.wikipedia.org/wiki/Continuous_mapping_theorem Continuous mapping theorem]
* [https://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli_lemma Borel–Cantelli lemma] and [https://en.wikipedia.org/wiki/Zero%E2%80%93one_law zero-one laws]
* [https://en.wikipedia.org/wiki/Law_of_large_numbers Law of large numbers]
* [https://en.wikipedia.org/wiki/Central_limit_theorem Central limit theorem]
** [https://en.wikipedia.org/wiki/De_Moivre%E2%80%93Laplace_theorem De Moivre–Laplace theorem]
** [https://en.wikipedia.org/wiki/Berry%E2%80%93Esseen_theorem Berry–Esseen theorem]
* [https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory) Characteristic function]
** [https://en.wikipedia.org/wiki/Lévy%27s_continuity_theorem Lévy's continuity theorem]
* Concentration of measures:
** [https://en.wikipedia.org/wiki/Moment-generating_function Moment-generating function]
** [https://en.wikipedia.org/wiki/Chernoff_bound Chernoff bound]
** [https://en.wikipedia.org/wiki/Hoeffding%27s_inequality Hoeffding's bound]
** [https://en.wikipedia.org/wiki/Doob_martingale#McDiarmid's_inequality McDiarmid's inequality]
** [https://en.wikipedia.org/wiki/Doob_martingale Doob martingale] and [https://en.wikipedia.org/wiki/Azuma%27s_inequality Azuma's inequality]
** [https://en.wikipedia.org/wiki/Sub-Gaussian_distribution Sub-Gaussian distribution]
* [https://en.wikipedia.org/wiki/Stochastic_process Stochastic process]
* [https://en.wikipedia.org/wiki/Stopping_time Stopping time]
* [https://en.wikipedia.org/wiki/Martingale_(probability_theory) Martingale]
** [https://en.wikipedia.org/wiki/Optional_stopping_theorem Optional stopping theorem]
* [https://en.wikipedia.org/wiki/Wald%27s_equation Wald's equation]
* [https://en.wikipedia.org/wiki/Markov_chain Markov chain]
** [https://en.wikipedia.org/wiki/Markov_property Markov property] and [https://en.wikipedia.org/wiki/Memorylessness memorylessness]
** [https://en.wikipedia.org/wiki/Stochastic_matrix Stochastic matrix]
** [https://en.wikipedia.org/wiki/Stationary_distribution Stationary distribution]

Latest revision as of 07:44, 27 February 2024

概率论与数理统计
Probability Theory
& Mathematical Statistics
Instructor
尹一通
Email yinyt@nju.edu.cn
office 计算机系 804
刘景铖
Email liu@nju.edu.cn
office 计算机系 516
Class
Class meeting

Wednesday, 2pm-4pm
Friday (双), 2pm-4pm

仙II-403
Office hour Thursday, 2pm-4pm
计算机系 804（尹一通）
计算机系 516（刘景铖）
Textbook
概率导论（第2版·修订版）
Dimitri P. Bertsekas and John N. Tsitsiklis
郑忠国 童行伟 译；人民邮电出版社 (2022)
Probability and Random Processes (4E)
Geoffrey Grimmett and David Stirzaker
Oxford University Press (2020)
Probability and Computing (2E)
Michael Mitzenmacher and Eli Upfal
Cambridge University Press (2017)
v · d · e

This is the webpage for the Probability Theory and Mathematical Statistics (概率论与数理统计) class of Spring 2023. Students who take this class should check this page periodically for content updates and new announcements.

Announcement

  • 6月14日周三晚6点30分开始，线上习题课。#腾讯会议：598-944-8767

Course info

  • Instructor :
  • QQ群: 598724033（申请加入需提供姓名、院系、学号）

Syllabus

课程内容分为三大部分：

  • 经典概率论：概率空间、随机变量及其数字特征、多维与连续随机变量、极限定理等内容
  • 概率与计算：测度集中现象 (concentration of measure)、概率法 (the probabilistic method)、离散随机过程的相关专题
  • 数理统计：参数估计、假设检验、贝叶斯估计、线性回归等统计推断等概念

对于第一和第二部分，要求清楚掌握基本概念，深刻理解关键的现象与规律以及背后的原理，并可以灵活运用所学方法求解相关问题。对于第三部分，要求熟悉数理统计的若干基本概念，以及典型的统计模型和统计推断问题。

经过本课程的训练，力求使学生能够熟悉掌握概率的语言，并会利用概率思维来理解客观世界并对其建模，以及驾驭概率的数学工具来分析和求解专业问题。

教材与参考书 Course Materials

  • [BT] 概率导论（第2版·修订版），[美]伯特瑟卡斯（Dimitri P.Bertsekas）[美]齐齐克利斯（John N.Tsitsiklis）著，郑忠国 童行伟 译，人民邮电出版社（2022）。
  • [GS] Probability and Random Processes, by Geoffrey Grimmett and David Stirzaker; Oxford University Press; 4th edition (2020).
  • [MU] Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis, by Michael Mitzenmacher, Eli Upfal; Cambridge University Press; 2nd edition (2017).

成绩 Grading Policy

  • 课程成绩：本课程将会有若干次作业和一次期末考试。最终成绩将由平时作业成绩和期末考试成绩综合得出。
  • 迟交：如果有特殊的理由，无法按时完成作业，请提前联系授课老师，给出正当理由。否则迟交的作业将不被接受。

学术诚信 Academic Integrity

学术诚信是所有从事学术活动的学生和学者最基本的职业道德底线，本课程将不遗余力的维护学术诚信规范，违反这一底线的行为将不会被容忍。

作业完成的原则：署你名字的工作必须是你个人的贡献。在完成作业的过程中，允许讨论，前提是讨论的所有参与者均处于同等完成度。但关键想法的执行、以及作业文本的写作必须独立完成，并在作业中致谢（acknowledge）所有参与讨论的人。符合规则的讨论与致谢将不会影响得分。不允许其他任何形式的合作——尤其是与已经完成作业的同学“讨论”。

本课程将对剽窃行为采取零容忍的态度。在完成作业过程中，对他人工作（出版物、互联网资料、其他人的作业等）直接的文本抄袭和对关键思想、关键元素的抄袭，按照 ACM Policy on Plagiarism的解释，都将视为剽窃。剽窃者成绩将被取消。如果发现互相抄袭行为， 抄袭和被抄袭双方的成绩都将被取消。因此请主动防止自己的作业被他人抄袭。

学术诚信影响学生个人的品行，也关乎整个教育系统的正常运转。为了一点分数而做出学术不端的行为，不仅使自己沦为一个欺骗者，也使他人的诚实努力失去意义。让我们一起努力维护一个诚信的环境。

Assignments

Lectures

  1. 课程简介
  2. 概率空间
  3. 随机变量
  4. 矩与偏差
  5. 连续分布
  6. 极限定理
    • 阅读：[BT] 第5章
    • 阅读：[GS] Sections 5.7~5.10, 7.1~7.5
  7. 测度集中
  8. 随机过程
    • 阅读：[BT] 第6章, 第7章
    • 阅读：[MU] Chapters 7, Sections 13.1~13.3 or [GS] Chapters 6, Sections 12.4~12.5
    • OST and applications
  9. 统计与贝叶斯推断, 经典统计推断
    • 阅读：[BT] 第8章, 第9章

Concepts

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