Bayesískt stigskipt líkan fyrir daglegan meðalhita - Snæbjörn Helgi Emilsson 1984- (2012)
In this thesis, a Bayesian hierarchical model for daily average temperature is presented. A multivariate normal distribution is selected as the data distribution due to its flexibility and theoretical basis. The linear fit is assumed to be governed by a seasonal effect parameter vector, a linear trend parameter, a long term fluctuation parameter vector and a model constant. The seasonal effect and fluctuations are modeled as independent Gaussian processes which are governed by Gaussian Markov random fields. The covariance matrix of the multivariate normal distribution describes temporal correlation and a seasonally changing variance of the data. A periodic autoregressive (PAR) process is used to model the temporal correlation and regression is used to estimate the parameters. An iterative process is used to update the regression parameters and the Bayesian parameters, since they are dependent on each other. This model allows for future predictions, but is limited to predicting one year ahead. A program based on the model was developed in the R programming language. The program uses the Gibbs sampler, a Markov chain Monte Carlo algorithm, to estimate the parameters of the model by sampling from their conditional distributions. Using the R program the model is applied to observed data from four locations in Iceland over the years 1949 to 2010. These locations are Reykjavík, Akureyri, Dalatangi and Stórhöfði. Based on the model the estimated increase in average temperature over the period is from 0.05 to 0.46°C, depending on location. A prediction was made for the year 2011, which was not a part of the training set. Of the actual temperature values of 2011, only 2.5 to 4.7% of the observations were outside the 95% posterior prediction interval.