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MATH2740: Environmental Statistics

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MATH2740: Environmental Statistics MATH2740: Environmental Statistics Lecturer: Andrew J. Baczkowski – room 11-13 – email: [email protected] Regularly updated information about the module is available on the internet at: http://www.maths.leeds.ac.uk/∼sta6ajb/math2715/math2740.html Module objective: To introduce statistical concepts and models for analysing data of an envi- ronmental nature: (a) analyse data of a spatial nature, (b) analyse models when applied to the analysis of categorical data arising from observational studies. Provisional detailed syllabus: 1. Types of data. 2. Spatial point patterns: contagious distributions. 3. Quadrant analysis: testing for non-randomness. 4. Distance methods: nearest neighbour analysis. 5. Spatial autocorrelation: join count statistics; testing hypotheses of spatial correlation. 6. Categorical data analysis: log-linear models; goodness of fit; three-dimensional tables; model selection. Booklist: No one book will be useful. References will be given for each lecture. Some useful textbooks include: Cressie, N.A.C. (1993) Statistics for Spatial Data. New York: Wiley. Diggle, P.J. (1983) Statistical Analysis of Spatial Point Patterns. London: Academic Press. Ripley, B.D. (1981) Spatial Statistics. New York: Wiley. Upton, G.J.G. and Fingleton, B. (1985) Spatial Data Analysis by Example. Volume I: Point Pattern and Quantitative Data. Wiley, Chichester. Agresti, A. (2002) Categorical Data Analysis. New Jersey: Wiley. Attendance: Attendance sheets will be circulated in each lecture for you to sign. Assessment: 80% of marks for two hour examination at end of semester and 20% of marks for continuous assessment comprising the exercise sheets and practicals. Examination paper: The examination paper will be in two parts. Part A will consist of twenty questions. Half will be multiple choice questions worth two marks each and half will require a short answer worth two marks each. Part B will have three longer questions. You have to answer all questions from part A and all questions from part B. Exercise sheets for MATH2740: A new exercise sheet will be commenced every week or so. You will usually have a fortnight to discuss each in the examples classes before handing them in to be marked. Solution sheets will be handed out in a later handout. 1 MATH2740 lecture topics 1. Types of data. Point location data, distance measurements, quadrat data, quantitative spatial data, contingency tables. 2. Spatial point pattern I. Types of point pattern, point processes, Poisson process. 3. Spatial point pattern II. Contagious distributions, Neyman type A distribution, negative binomial distribution, fitting negative binomial distribution to data. 4. Quadrat Analysis I. Analysis of quadrat data, Poisson process, index of dispersion, testing complete spatial randomness, other dispersion indices. 5. Quadrat Analysis II. Choice of quadrat size, quadrat variance methods, Greig-Smith ap- proach, two-term local variance method. 6. Distance Methods I. Point-object and object-object distances, distribution of point-object distances for a Poisson process, Rayleigh distribution, Clark-Evans test of randomness. 7. Distance Methods II. Distribution of squared distance, testing randomness, Skellam-Moore test, Mountford’s test of randomness. 8. Distance Methods III. Introduction, F -distribution, intensity estimation, testing randomness, Hopkins test of randomness, Byth and Ripley test of randomness. 9. Spatial Autocorrelation I. Two colour maps, spatial autocorrelation, join count statistics. 10. Spatial Autocorrelation II. Testing spatial autocorrelation I, moments of join count statistics, testing spatial autocorrelation II. 11. Spatial Autocorrelation III. Problems with testing spatial autocorrelation, general weights, regression residuals, other measures of spatial autocorrelation. 12. Categorical Data Analysis I. Introduction, the 2× 2 table, multinomial model for 2× 2 table, product binomial model for 2 × 2 table, tables with both margins fixed. 13. Categorical Data Analysis II. The r × c table, multinomial model for r × c table, product multinomial model for 2 × 2 table, Poisson count model for r × c table. 14. Multiplicative Models for Contingency Tables. Example, multiplicative independence model for 2×2 table., multiplicative saturated model, multiplicative saturated model for 2×2 table, the odds ratio. 15. Log-linear Models for r×c Contingency Table. Saturated model for r×c table, independence model for r × c table, other models for r × c table, the log-linear model using R, parameter interpretation for r × c model. 16. Testing Goodness-of-Fit for Log-linear Models. Pearson chi-squared test, likelihood ratio chi-squared test, examples, model notation, model selection, analysis using R. 17. 23 Contingency Tables. Log-linear models for 23 table, examples. 18. Model Selection in 33 Contingency Tables. Informal model selection using odds ratio, model selection, use of saturated model, use of likelihood ratio chi-squared test statistic, examples. 19. Log-linear Models with Four or More Factors. Examples. 20. Further Topics in Categorical Data Analysis. Types of study, sampling models, empty cells, Simpson’s paradox. 2.
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