统计学简史与数据科学(中南财经大学)ppt课件.ppt
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1、统计学简史与数据科学,袁卫 2016.12.10 中南财经政法大学,英国培根: 读史可以明智(Histories make men wise)德国斯勒兹: 统计是静态的历史, 历史是动态的统计. (Statistics is the state history while history is the dynamic statistics).,一、早期源头(Early Beginnings)二、数学基础 (Mathematical Foundations)三、现代发展 (Modern Era),一、早期源头(公元前450年至15世纪),均值的使用,450 bc Hippias of Elis
2、uses the average value of the length of a kings reign (the mean) to work out the date of the first Olympic Games, some 300 years before his time.希皮亚斯(Hippias), 出生于希腊伯罗奔尼撒(Peloponnesus)西北部的埃利斯(Elis), 与柏拉图(Plato)是同时代的人,历史上第一位数学史家。他在公元前450年用以前每个国王执政时间长短的均值推算出首届奥运会是距当时300多年前的公元前776年举办的。,431 bc Attackers
3、 besieging Plataea in the Peloponnesian war calculate the height of the wall by counting the number of bricks. The count was repeated several times by different soldiers. The most frequent value (the mode) was taken to be the most likely. Multiplying it by the height of one brick allowed them to cal
4、culate the length of the ladders needed to scale the walls.公元前431年希腊伯罗奔尼撒战争中雅典人让士兵数城墙砖的层数,取士兵数据的众数乘以每块砖的厚度推算城墙的高度,用以计算云梯所需长度。,众数的使用,400 bc In the Indian epic the Mahabharata, King Rtuparna estimates the number of fruit and leaves (2095 fruit and 50 000 000 leaves) on two great branches of a vibhitak
5、a tree by counting the number on a single twig, then multiplying by the number of twigs. The estimate is found to be very close to the actual number. This is the first recorded example of sampling “but this knowledge is kept secret”, says the account.公元前400年,印度史诗摩诃婆罗多(Mahabharata)中国王利用只计算两个大树枝上的果实和叶
6、子数量乘上树枝的数量估算整棵树果实和叶子的数量,这是已知最早的抽样推断。,抽样推断,AD 2 Chinese census under the Han dynasty finds 57.67 million people in 12.36 million households the first census from which data survives, andstill considered by scholars to have been accurate公元2年, 中国汉代进行了人口普查,结果是1236万家庭,5767万人口。记载的数据被认为是相当准确的。,普查,AD 7 Cens
7、us by Quirinus, governor of the Roman province of Judea, is mentioned in Lukes Gospel as causing Joseph and Mary to travel to Bethlehem to be taxed.路加福音记载,公元7年,意大利罗马省省长奎里努斯实施了普查,导致约瑟夫和玛丽前往约瑟夫祖籍大卫家族所在的伯利恒申报户籍.,普查,840 Islamic mathematician Al-Kindi uses frequency analysis the most common symbols in a
8、coded message will stand for the most common letters to break secret codes. Al-Kindi also introduces Arabic numerals to Europe.公元840年,伊斯兰数学家金迪利用最常用符号和最常用字符破解伊斯兰密码,他还将阿拉伯数字介绍到欧洲。,频数分析,10th century The earliest known graph, in a commentary on a book by Cicero, shows the movements of the planets throug
9、h the zodiac. It is apparently intended for use in monastery schools.公元10世纪,意大利西塞罗书中最早使用了曲线,描述黄道带中行星运动的轨迹,也是修道院最早使用的图表曲线。,曲线,1069 Domesday Book: survey for William the Conqueror of farms, villages and livestock in his new kingdom the start of official statistics in England.1069年最终税册:英王征服者威廉一世做的调查,对新
10、王国村庄和牲畜进行调查,这是英国官方统计最早的记录(英格兰约150万人,90%是农民)。,官方统计,1150 Trial of the Pyx, an annual test of the purityof coins from the Royal Mint, begins. Coins aredrawn at random, in fixed proportions to the number minted. It continues to this day.公元1150年,英国皇家制币厂开始硬币纯度和质量的年度检验。通过随机样本进行等比例抽样检验,延续至今。,随机抽样,1188 Geral
11、d of Wales completed the first population census of Wales.公元1188年,英国威尔士的杰拉尔德完成了威尔士第一次人口普查。,人口普查,1303 A Chinese diagram entitled “The Old Method Chart of the Seven Multiplying Squares” shows the binomial coefficients up to the eighth power the numbers that are fundamental to the mathematics of probab
12、ility, and that appeared five hundred years later in the west as Pascals triangle.公元1303年中国“杨辉(1261)三角形”(贾宪更早)给出二项分布系数8次幂,奠定概率论的数学基础,而帕斯卡(1662)三角形是500年之后才出现。,二项式系数,1346 Giovanni Villanis Nuova Cronica gives statistical information on the population and trade of Florence.公元1346年,意大利佛罗伦斯当时的历史学家佐凡尼微拉尼(
13、GiovanniVillani)在著作NuovaCronica中纪录了人口和贸易的统计信息。,人口与贸易统计,二、数学基础(16世纪至19世纪末),1560 Gerolamo Cardano calculates probabilitiesof different dice throws for gamblers.公元1560年,意大利文艺复兴科学家吉罗拉莫卡尔达诺计算出掷骰子的各种概率。,概率初步,1570 Astronomer Tycho Brahe uses the arithmeticmean to reduce errors in his estimates of the locat
14、ions of stars and planets.公元1570年,丹麦天文学家第谷布拉赫在估计星球的位置和运行时使用算术平均数减少误差。,均值与误差,1644 Michael van Langren draws the first known graph of statistical data that shows the size of possible errors. It is of different estimates of the distance between Toledo and Rome.公元1644年,荷兰天文学家Michael van Langren 用统计数据画出第
15、一张误差图,用不同方法估计从西班牙托莱多到意大利罗马的距离。,误差图,1654 Pascal and Fermat correspond about dividing stakes in gambling games and together create the mathematical theory of probability.公元1654年法国帕斯卡和费马通过对赌博中如何下注等问题通信的研究共同创立了概率的数学理论。,概率数学基础,1657 Huygenss On Reasoning in Games of Chance is the first book on probability
16、 theory.He also invented the pendulum clock.公元1657年,荷兰科学家惠更斯完成“机会游戏的推理”一书,这是第一本概率理论的书,他还是摆钟的发明者。,首本概率著作,1663 John Graunt uses parish records to estimate the population of London.公元1663年,英国约翰 格朗特利用伦敦教区的洗礼、弥撒等数据分析并估计伦敦的人口, 并首次给出新生婴儿性别比52:48。,人口统计,1693 Edmund Halley prepares the first mortality tables
17、statistically relating death rates to age the foundation of life insurance. He also drew a stylised map of the path of a solar eclipse over England one of the first data visualisation maps.1693年,英国哈雷制作了第一张分年龄的死亡率表,为人寿保险奠定了基础。他还画出日食经过英国的路线图,这也是数据的第一张可视化地图。,首张死亡率表,1713 Jacob Bernoullis Ars conjectandi
18、 derives the law of large numbers the more often you repeat an experiment, the more accurately you can predict the result.1713年,瑞士科学家伯努利在猜测术一书中提出大数定律,即实验次数越多,预测结果就越准确。,大数定律,1728 Voltaire and his mathematician friend de la Condamine spot that a Paris bond lottery is offering more in prize money than
19、the total cost of the tickets; they corner the market and win themselves a fortune.公元1728年法国伏尔泰和他的数学家朋友拉.孔达明计算出巴黎债券彩票的奖金总额高于购买的成本,于是他们垄断了彩票市场, 并获得收益.,博彩统计,1749 Gottfried Achenwall coins the word “statistics” (in German, Statistik); he means the information you need to run a nation state.公元1749年德国阿亨瓦
20、尔创造了德文词汇 “Statistik”, 即 “statistics”。他定义“统计”为治理国家所需要的信息。,德文“统计”词汇的出现,1757 Casanova becomes a trustee of, and may have had a hand in devising, the French national lottery.1757年法国卡萨诺瓦成为法国国家彩票的受托人,发明了彩票。,国家彩票业出现,1761 The Rev. Thomas Bayes proves Bayestheorem the cornerstone of conditional probability a
21、nd the testing of beliefs and hypotheses.1761年英国贝叶斯证明了贝叶斯定理,奠定了条件概率的基础,检验信念和假设。,贝叶斯定理,1786 William Playfair introduces graphs and barcharts to show economic data.1786年英国爱丁堡William Playfair 首次用图表反映经济数据变化。,经济数据图表,1789 Gilbert White and other clergymen-naturalists keep records of temperatures, dates of
22、 first snowdrops and cuckoos, etc; the data is later useful for study of climate change.1789年英国吉尔伯特.怀特和其他牧师博物学家记录温度变化、首次降雪时间以及变化情况等。数据被用来研究气候变化。,气候统计,1790 First US census, taken by men on horseback directed by Thomas Jefferson, counts 3.9 million Americans.1790年美国在第三任总统托马斯.杰斐逊总统指导下进行了首次人口普查,结果为390万人
23、口。,美国首次人口普查,1791 First use of the word “statistics” in English, by Sir John Sinclair in his Statistical Account of Scotland.1791年英国约翰.辛克莱在他“苏格兰统计账户”中首次使用英文词“统计”Statistics.,英文“统计”词汇的出现,1805 Adrien-Marie Legendre introduces the method of least squares for fitting a curve to a given set of observations
24、.1805年法国数学家勒让德首次使用最小二乘法利用数据去拟合曲线。,最小二乘法,1808 Gauss, with contributions from Laplace,derives the normal distribution the bell-shaped curve fundamental to the study of variation and error.1808年德国高斯和拉普拉斯一起得到正态分布,即钟形曲线,奠定了误差研究的基础。,正态分布,1833 The British Association for the Advancement of Science sets up
25、a statistics section. Thomas Malthus, who analysed population growth, andCharles Babbage are members. It later becomes the Royal Statistical Society.1833年,英国高等科学协会建立了统计分会,分析人口增长的托马斯.马尔萨斯和查尔斯巴贝奇都是会员,这个分会后来成为英国皇家统计学会。,英国统计学会,1835 Belgian Adolphe Quetelets Treatise on Man introduces social science stat
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