1Stat 35, UCLA, Ivo Dinov Slide 1UCLA STAT 35Applied Computational and InteractiveProbabilityzInstructor: Ivo Dinov, Asst. Prof. In Statistics and NeurologyzTeaching Assistant: Anwar KhanUniversity of California, Los Angeles, Winter 2005http://www.stat.ucla.edu/~dinov/Stat 35, UCLA, Ivo DinovSlide 2Course OrganizationSoftware: No specific software is required. SYSTAT, R, SOCR resource, etc.Course Description, Class homepage, online supplements, VOH’s, etc.http://www.stat.ucla.edu/~dinov/courses_students.htmlStat 35, UCLA, Ivo Dinov Slide 3What is Statistics? A practical examplezDemography: Uncertain population forecastsby Nico Keilman, Wolfgang Lutz, et al., Nature 412, 490 - 491 (2001) zTraditional population forecasts made by statistical agencies do not quantify uncertainty. But demographers and statisticians have developed methods to calculate probabilistic forecasts. zThe demographic future of any human population is uncertain, but some of the many possible trajectoriesare more probable than others. So, forecast demographics of a population, e.g., sizeby 2100, should include two elements: a range of possible outcomes, and a probability attached to that range. Stat 35, UCLA, Ivo Dinov Slide 4What is Statistics?zTogether, ranges/probabilities constitute a prediction interval for the population. There are trade-offs between greater certainty (higher odds) and better precision (narrower intervals). Why?zFor instance, the next table shows an estimate that the odds are 4 to 1 (an 80% chance) that the world's population, now at 6.1 billion, will be in the range [5.6 : 12.1] billion in the year 2100. Odds of 19 to 1 (a 95% chance) result in a widerinterval: [4.3 : 14.4] billion.Stat 35, UCLA, Ivo Dinov Slide 5What is Statistics?Stat 35, UCLA, Ivo Dinov Slide 6What is Statistics?Largeview2Stat 35, UCLA, Ivo Dinov Slide 7What is Statistics?zDemography: Uncertain population forecastsby Nico Keilman, Nature 412, ,2001zTraditional population forecastsmade by statistical agencies do not quantify uncertainty. But lately demographers and statisticians have developed methods to calculate probabilistic forecasts. zProportion of population over 60yrs.Stat 35, UCLA, Ivo Dinov Slide 8What is Statistics?Stat 35, UCLA, Ivo Dinov Slide 9What is Statistics?zThere is concern about the accuracy of population forecasts, in part because the rapid fall in fertility in Western countries in the 1970s came as a surprise. Forecasts made in those years predicted birth rates that were up to 80% too high. zThe rapid reduction in mortality after the Second World War was also not foreseen; life-expectancy forecasts were too low by 1–2 years; and the predicted number of elderly, particularly the oldest people, was far too low.Stat 35, UCLA, Ivo Dinov Slide 10What is Statistics?zSo, during the 1990s, researchers developed methods for making probabilistic population forecasts, the aim of which is to calculate prediction intervals for every variable of interest. Examples include population forecasts for the USA, AU, DE, FIN and the Netherlands; these forecasts comprised prediction intervals for variablessuch as age structure, average number of children per woman, immigration flow, disease epidemics. zWe need accurate probabilistic population forecasts for the whole world, and its 13 large division regions (see Table). The conclusionis that there is an estimated 85% chance that the world's population will stop growing before 2100. Accurate?Stat 35, UCLA, Ivo Dinov Slide 11What is Statistics?zThere are three main methods of probabilistic forecasting:time-series extrapolation; expert judgement; and extrapolation of historical forecast errors.zTime-series methods rely on statistical models that are fitted to historical data. These methods, however, seldom give an accurate description of the past. If many of the historical facts remain unexplained, time-series methods result in excessively wide prediction intervals when used for long-term forecasting.zExpert judgement is subjective, and historic-extrapolation alone may be near-sighted.Stat 35, UCLA, Ivo Dinov Slide 12Intro & Descriptive StatszVariation in datazData DistributionszStationary and (dynamic) non-stationary processeszCauses of Variation3Stat 35, UCLA, Ivo DinovSlide 13Newtonian science vs. chaotic sciencezArticle by Robert May, Nature, vol. 411, June 21, 2001zScience we encounter at schools deals with crisp certainties(e.g., prediction of planetary orbits, the periodic table as a descriptor of all elements, equations describing area, volume, velocity, position, etc.)zAs soon as uncertainty comes in the picture it shakes the foundation of the deterministic science, because only probabilistic statements can be made in describing a phenomenon (e.g., roulette wheels, chaotic dynamic weather predictions, Geiger counter, earthquakes, etc.)zWhat is then science all about – describing absolutely certain events and laws alone, or describing more general phenomena in terms of their behavior and chance of occurring? Or may be both!Stat 35, UCLA, Ivo DinovSlide 1450 60 70 80 90Samples of 20 peopleSamples of 500 peopleSample percentageTarget: True populationpercentage = 69%Figure 1.1.1Comparing percentages from 10 different surveys each of20 people with those from 10 surveys each of500 people (all surveys from same population).From Chance Encounters by C.J. Wild and G.A.F. Seber, © John Wiley & Sons, 2000.Variation in sample percentagesPoll: Do you consider yourselfoverweight? 1010We are getting closer toThe population mean, asis this a coincidence?∞→nStat 35, UCLA, Ivo DinovSlide 15Experiments vs. observational studiesfor comparing the effects of treatmentsz In an Experiment experimenter determines which units receive which treatments. (ideally using some form of random allocation)z Observational study – useful when can’t design a controlled randomized study compare units that happen to have received each of the treatments Ideal for describing relationshipsbetween different characteristics in a population. often useful for identifying possible causes of effects, but cannot reliably establish causation.z Only properly designed and executed experimentscan reliably demonstrate causation.Stat 35, UCLA, Ivo DinovSlide 16The Subject of Statisticsz Statistics is concerned with the process of finding out about the world and how it operates - in the face of variation and uncertaintyz by collecting and analyzing, making sense(interpreting) of