Gaussian Process Regression Analysis For Daily Maximum Temperature

Functional data is a data which is manifested in the form of function. Functional data analysis plays an important role in modern data processing and statistical anal-ysis. In the modeling process, The Gaussian process which is an important Bayesian machine learning method has many advantages. For example, it needs less parameters and easy convergence, it is suitable for many types of kernel functions and it can be a good deal with the problem of high dimensionality, small samples, and nonlinear rela-tionships. Therefore, it will play a very good effect to apply the Gaussian function into the functional data analysis. Data daily maximum temperature as a meteorological data is a typical functional data. Based on the Gaussian process, this article improves the Gaussian process, and then utilizes the improved model to analyze the multi-region daily maximum temperature, and then discuss the fitting and forecasting effect by dif-ferent Gaussian process model. At last, through empirical analyze the daily maximum temperature of air data, we verify that in terms of analyzing the multi-region daily maximum temperature, the model in this article has an efficient predictive.The subject matter of this master’s thesis is as follows:The first chapter introduces the research background and research status of func-tional data which include the data daily temperature analysis, and the basic concept of Gaussian process. In addition to this, it gives the relevant knowledge of basis function, data preprocessing and Gaussian process regression.The chapter two utilizes the Gaussian process function regression model (GPFR) to forecast the daily maximum temperature. Based on the Gaussian process function regression model, the article utilizes three different predictive mode which is called ran-dom prediction and extension prediction and multi-step prediction to empirical analyze the summer daily maximum temperature of ten cities. Then compared with the usual Gaussian process regression and the linear function regression model. The results show that in different predictive mode, GPFR model prediction error is smaller and more accurate. So GPFR model is applicable to the meteorological functional data including data daily temperature.On the basis of the second chapter, the third chapter will further improve the GPFR model and let GPFR model become Gaussian process function regression model with fixed effect (eGPFR). This chapter further adds three kinds of temperature fore-casting factors as barometric pressure and rainfall and location, then utilizes eGPFR model to analyze and forecast the summer daily maximum temperature of ten cities. Then compared with the GPFR model and LFR model. The results show that in terms of predicting the various cities’ daily maximum temperature, the rmse of eGPFR model is only 1.7933, significantly lower than the root mean square error of GPFR model and LFR model. Then in estimating the mean trend, eGPFR model has a better effect and it improve the accuracy of forecasting daily maximum temperature.The forth chapter we applied Functional principal component analysis to Gaussian process. Because of the increasing number of cities and years, the dimension also has increased and the covariance structure has been more complex. So we use Nystrom method to simplify the calculation precess of covariance function, then use functional principal component analysis method predict the daily maximum temperature. We can find that this method can reduce the algorithm complexity, and also have a good prediction.The fifth chapter introduces the advantages of apply the model in this article in forecasting the daily maximum temperature, and then leads to further outlook.