1Stat 13, UCLA, Ivo DinovSlide 1UCLA STAT 13Introduction toStatistical Methods for the Life and Health SciencesInstructor: Ivo Dinov, Asst. Prof. of Statistics and NeurologyTeaching Assistants:Brandi Shanata & Tiffany HeadUniversity of California, Los Angeles, Fall 2007http://www.stat.ucla.edu/~dinov/courses_students.htmlStat 13, UCLA, Ivo DinovSlide 2Administrativez The book for this course -- Statistics for the Life Sciences, by Samuels & Witmer, 3rdedition, 2003. Homework will be primarily assigned from the text You are responsible for keeping up with reading Some chapters will be covered by reading onlyStat 13, UCLA, Ivo DinovSlide 3UCLA STAT 13to just hear is to forgetto see is to rememberto do it yourself is to understand …(… to listen in class is to … comprehend …)Stat 13, UCLA, Ivo DinovSlide 4What is Statistics? A practical exampleModeling the Spread of the Flu VirusGoals: Quantify long-range dissemination of infectious diseases (e.g., flu virus)Methods: Use influenza-related mortality data to analyze the between-state progression of inter-pandemic influenza in the United States over the past 30 years. Results: Outbreaks show hierarchical spatial spread evidenced by higher pair-wise synchrony between more populous states. Seasons with higher influenza mortality are associated with higher disease transmission and more rapid spread than are mild level mortality/transmission.Cécile Viboud, Ottar Bjørnstad, David Smith, Lone Simonsen, Mark Miller, Bryan GrenfellSynchrony, Waves, and Spatial Hierarchies in the Spread of InfluenzaScience 21 April 2006: Vol. 312. no. 5772, pp. 447 – 451 DOI: 10.1126/science.1125237Stat 13, UCLA, Ivo DinovSlide 5What is Statistics? A practical exampleModeling the Spread of the Flu VirusWeekly epidemics: (A) Death rates from pneumonia and influenza (P&I) per 100,000 population on a log10 scale. (B & C) Death rates in excess attributed to influenza in the United States (B) and by state as a color intensity plot (C). Vertical RED bands correspond to synchronized epidemics.Stat 13, UCLA, Ivo DinovSlide 6What is Statistics? A practical examplehttp://www.sciencemag.org/cgi/content/full/312/5772/447?maxtoshow=&HITS=20&hits=20&RESULTFORMAT=&andorexacttitle=or&andorexacttitleabs=or&fulltext=confidence+interval&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&fdate=7/1/2005&tdate=9/30/2006&resourcetype=HWCIT2Stat 13, UCLA, Ivo DinovSlide 7What is Statistics? A practical exampleModeling the Spread of the Flu VirusInfluenza spread and workflows. (A) Gray dotsrepresent the observed phase synchrony in influenza epidemics (yaxis) plotted against the total number of individuals commuting between each pair of states (x axis, log10 scale). Superimposed is the best fit statistical model(spline, blue curve) and 95% confidence intervals (CI). Stat 13, UCLA, Ivo DinovSlide 8What is Statistics? A practical exampleStat 13, UCLA, Ivo DinovSlide 9What is Statistics? A practical exampleParameter estimates for the piecewise gravity model fitted to U.S. workflow data by county. Models are fitted separately for distances above and below 119 km. d is the Euclidian distance between the population centers of two counties; t1, t2, and ρrepresent dependence of dispersal workflows on the population size of the donor (resident county) and recipient (work county) and the distancebetween them, respectively. A total of 3,109 counties in 49 continental U.S. states are used, yielding 161,710 pairs of counties with nonzero flow of workers. Why?0.29 ± (0.003) 3.05 ± (0.012) ρ: distance (km) 0.14 ± (0.001) 0.64± (0.004) population of work county (recipient), t20.24 ± (0.001) 0.30± (0.004) ??? (meaning)population of residence county (donor), t1d=Distances > 119 kmd=Distance < 119 kmPoint Estimates (Standard Error)ParameterStat 13, UCLA, Ivo DinovSlide 10What is Statistics? A practical exampleModeling the Spread of the Flu VirusSimulated spread of influenza by a gravity model based on work movements, for epidemics originating in California or Wyoming. Stat 13, UCLA, Ivo DinovSlide 11What is Statistics? A practical exampleLast Example: % of Assets invested in Equities Stat 13, UCLA, Ivo DinovSlide 12Statistics Examplez What do you think of when you hear “statistics”?z Definition: Statistics is the science of acquiring & understanding data and making decisions in the face of variability and uncertainty.z To utilize statistics we need to understand: how the data was collected why it was collected how to analyze and interpret the data Appropriately!3Stat 13, 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, momentum, etc.)zAs soon as uncertainty comes in the picture it shakes the foundation of the deterministic sciences, 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 13, UCLA, Ivo DinovSlide 14Variation in sample percentages50 60 70 80 90Samples of 20 peopleSamples of 500 peopleSample percentageTarget: True populationpercentage = 69%Poll: Do you consider yourselfoverweight? 1010We are getting closer toThe population mean, asis this a coincidence?∞→nComparing percentages from 10 different surveys each of20 people with those from 10 surveys each of500 people (all surveys from same population).Stat 13, UCLA, Ivo DinovSlide 15Statistics ExampleExample: A plant ecologist measured the growth response of cotton grass (cm) to four different fertilizer treatments in Northern Alaska. For each treatment, five small 4 ft2 plots were selected, all within the particular field of interest.None N(nitrogen) N + P (phosphorus) N+P+K(potassium)NWhat points seem important from this description?Stat 13, UCLA, Ivo DinovSlide 16Statistics ExampleExample (cont’): The data obtained from this experiment were: Fertilizer Plot Index None Nitrogen Nitrogen + Phosphorous Nitrogen + Phosphorous + Potassium 1 10 58 63 68 2 6 45 43 47 3 11 55
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