Title Bout: MLE vs. MoM Opponents: R.A. Fisher and Karl Pearson

Title Bout: MLE vs. MoM Opponents: R.A. Fisher and Karl Pearson

Title Bout: MLE vs. MoM Opponents: R.A. Fisher and Karl Pearson By Lada Kyj and Galen Papkov Rice University - STAT 600 September 27, 2004 Outline Short Biographies Journal rage Criterion

Method of Moments Maximum Likelihood MLE vs. MoM Issues Whos who? R.A. Fisher (Born February 17, 1890 in London, England)

Superstitious fact Studied mathematics and astronomy at Cambridge (also interested in biology) Rejected from enlisting in the military for WWI due to poor eyesight Introduced concepts such as randomization, likelihood, and ANOVA Karl Pearson (born March 27, 1857 in London, England)

Attended Cambridge Had various interests Mathematics, physics, metaphysics, law, etc Contributed to regression analysis and developed the correlation coefficient and the chi-square test.

Is characterized as trying to use large samples to deduce correlations in the data whereas Fisher used small samples to determine causes. Journal Rage Began in 1917 when Pearson claimed that Fisher had failed to distinguish likelihood from inverse probability in a paper he wrote in 1915 Feud continued for many years Fire of feud fed by injustice

It would be fair to say that both showed hatred towards the other. Criteria of Consistency A statistic is consistent if, when it is calculated from the population, it is equal to the population parameter. PROBLEM! Many statistics for the same parameter can be

consistent. Criteria of Efficiency A statistic is efficient if, when derived from a large sample, it tends to a normal distribution with minimum variance. Relates to estimation accuracy PROBLEM! This criterion is still incomplete since different methods of calculation may tend to agreement for

large samples, but not for finite samples. Criteria of Sufficiency A statistic is sufficient when no other statistic which can be calculated from the same sample provides any additional information per the value of the parameter to be estimated. Relates to information Method of Moments Developed

by Pearson in 1894 Method: k = E[Xk] 1 = E[X] = Xbar (sample mean) Satisfies consistency Example The

Cauchy distribution is a great example that portrays the limitations of the MoM. A few outliers appear to dominate the value of the mean. Cannot use MoM, go to MLE Maximum Likelihood Estimation Developed by Fisher

Officially called maximum likelihood estimation in 1921 The likelihood of a parameter is proportional to the probability of the data. Method: Obtain L(x;) Take first derivative, set = 0, solve for

Conditions for Determining Maximum First order conditions: Second order conditions: (Hessian is negative definite) Maximum Likelihood Estimation (cont.) Criterion:

Consistency Efficiency Sufficiency poor proof! Asymptotically normal and invariant Led to the development of the factorization theorem.

Is used as an efficiency yardstick for other estimators, such as the method of moments. MLE vs. MoM MoM is easy to use for normal curves. Mean is the best statistic for locating this curve MLE:

Evaluating and maximizing likelihood function is often challenging Difficult to write down complete statistical model of the joint distribution of the data More robust Greater efficiency Issues Neither are great for exploratory data

analysis since the underlying distribution must be known. MLE is believed to be sufficient (an acceptable proof has not been derived) References http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fisher.html http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pearson.html

Aldrich, John (1997). R.A. Fisher and the Making of Maximum Likelihood 1912-1922. Statistical Science, Vol. 12, No. 3, p. 162-176. Fisher, R. A. (1921a). On the mathematical foundations of theoretical statistics. P

Recently Viewed Presentations

  • HAVS - Impacto

    HAVS - Impacto

    The hazardous effects of occupational exposure to HAV have been discussed in hundreds of studies as far back as 1911. The composite of vibration-induced signs and symptoms referred to as Hand-Arm Vibration Syndrome includes episodic numbness; tingling and blanching of...
  • List of Acupuncture Points English Names --- Lung

    List of Acupuncture Points English Names --- Lung

    List of Acupuncture Points English Names --- Lung Channel (手太陰肺經) Central Palace (中府) Cloud Gate (云门) Sky Palace (天府) Guardian White (侠白) Foot Marsh (尺泽) Greatest Hole (孔最) Narrow Defile (列缺) Channel Gutter (经渠) Supreme Abyss (太渊) Fish Divide (鱼际)...
  • Creative Teaching Methods - iTeenChallenge

    Creative Teaching Methods - iTeenChallenge

    Creative Teaching Methods * MOVING BEYOND LECTURE TO CREATIVE DISCIPLESHIP TRAINING 10-2009 iTeenChallenge Course T506.05 What are the 3 biggest… Problems Needs Challenges you face as a teacher? 10-2009 * iTeenChallenge Course T506.05 Creative teachers are not a small group...
  • Ders 6 - Akademik Bilişim

    Ders 6 - Akademik Bilişim

    Bilimsel araştırma alanlarını temsil etmek üzere seçilir Bilimsel Dergiler Bilimsel iletişime katkı sağlayan yazarlar Bu yazarların ürettiği eserler Oeuvre: Belli bir yazara ait yayın grubu (White, 2003-pearson r) Atıf dizinlerinde yazar isimleri yazarların çalışmalarının bir alt grubuna karşılık gelir (McCain,...
  • LACMTA Celebrates Black History Month African Americans in

    LACMTA Celebrates Black History Month African Americans in

    oard Chair Yvonne Brathwaite Burke. March. 29, 2012, nominated. by. President. Barack. Obam. a. to . serve as Director of the Amtrak. Board of. Directors. •1967-1972 California State Assemblymember, 63rd District •1972-1978 California's First Black Congresswoman •1979-1980 Los Angeles County...
  • Muscle Contractions, Fatigue & Names

    Muscle Contractions, Fatigue & Names

    Isotonic contractions "same tone" Myofilaments are able to slide past each other during contractions. The muscle shortens, tension rises. Walking, running, lifting an object. 9/17/2018. SAP2b. Constant tension on muscles as muscle shortens. Muscle changes length. 2 types: Concentric-muscle shortens....
  • Anatomy & Physiology Chapter 7: Skeletal System

    Anatomy & Physiology Chapter 7: Skeletal System

    The organs of the skeletal system include the bones and structures that connect bones to other structures including ligaments, tendons, and cartilages. ... Epiphyseal line = remnant of epiphyseal disc/plate. a. cartilage at the junction of the diaphysis and epiphyses...
  • AAIBS Conference Prince Alfred College 19th April 2009

    AAIBS Conference Prince Alfred College 19th April 2009

    PDHPE. New Staff Induction (annually) Aims of today's presentation. Today we hope to give you: ... Stand alone. Teacher directed learning. Transdisciplinary approach to teaching and learning. Inquiry pedagogy. Central Idea for the day.