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UNIVERSITY OF ST ANDREWS Statistics Seminars - Martinmas 1999 ____________________________________________________________ MONDAY 27 SEPTEMBER Professor Walter ZUCCHINI (Georg-August-Universitaet, Goettingen) "An overview and applications of hidden Markov models for time series" MONDAY 4 OCTOBER Dr Song CHEN (La Trobe University, Australia) "Non-parametric Horvitz-Thompson Estimators in Mark Recapture or Line Transect Surveys" MONDAY 15 NOVEMBER Mr Rob KEMPTON (BioSS, Edinburgh) "Fitting the Design to the Model: Repeated Measures with Carryover" ____________________________________________________________ All seminars start at 4 p.m., tea being available from 3.40 p.m. Visitors will be very welcome. All the seminars will be held in Lecture Theatre B, Mathematical Institute. Further information from: Dr I B J Goudie (email: [log in to unmask]) SEMINAR ABSTRACTS Professor Walter ZUCCHINI (Georg-August-Universitaet, Goettingen) "An overview and applications of hidden Markov models for time series" The components and some properties of a simple hidden Markov model will be outlined. It is shown how such models can be fitted to univariate time series, such as binomial or Poisson counts, and how they can be used for forecasting. It is illustrated how the simple models can be modified and extended to describe more complex types of time series (for example categorical, multinomial and other multivariate data) and how trends, seasonal fluctuations and covariates other than time can be incorporated in the models. Examples of applications will be used to illustrate the methodology. Dr Song CHEN (La Trobe University, Australia) "Non-parametric Horvitz-Thompson Estimators in Mark Recapture or Line Transect Surveys" We develop a new estimator of population size when data come from a two-stage mark recapture experiment or an independent observer line transect survey and at least one continuous covariate for each detection is measured. The new estimator has two features: (i) detection probabilities are estimated non-parametrically by kernel smoothing of redetections, (ii) population size is estimated with a Horvitz-Thompson type estimator. Expressions for asymptotic bias and variance are developed. We provide an illustration on some real data. Mr Rob KEMPTON (BioSS, Edinburgh) "Fitting the Design to the Model: Repeated Measures with Carryover" Trials with animals or humans often involve applying a sequence of treatments to each subject. This allows treatments to be adequately replicated when the number of subjects is limited for ethical or cost reasons. Treatment differences will also be estimated more precisely when based on responses from the same subject, rather than the more variable comparison between subjects. However, treatment responses from sequential measurements are prone to distortion from context effects, in particular, the sequence order (or period) in which the treatment is applied and carryover from preceding treatments. These effects need to be taken account in design and analysis. We review and extend recommendations for repeated measures designs based on an additive model where responses are the sum of effects for subject, period, treatment and carryover from the immediately previous treatment. We then develop new results for a non-linear model in which the carryover from a treatment is proportional to its direct effect. Neighbour balanced designs are shown to be optimal, but the form of balance depends on the sign and magnitude of carryover. The implications for the design of taste panel experiments are discussed. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%