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Mountain meadows in the western USA are experiencing increased rates of conifer encroachment due to climate change and land management practices. Past research has focused on conifer removal as a meadow restoration strategy, but there has been limited work on conifer transpiration in a pre-restoration state. Meadow restoration by conifer removal has the primary goal of recovering sufficient growing season soil moisture necessary for endemic, herbaceous meadow vegetation. Therefore, conifer water use represents an important hydrologic output toward evaluating the efficacy of this active management approach. This study quantified and evaluated transpiration of encroached conifers in a mountain meadow using sap flow prior to restoration by tree removal. We report results of lodgepole pine transpiration estimates for an approximate 1-year period and an evaluation of key environmental variables influencing water use during a dry growing season. The study was conducted at Rock Creek Meadow (RCM) in the southern Cascade Range near Chester, CA, USA. Sap flow data were collected in a sample of lodgepole pine and scaled on a per-plot basis to the larger meadow using tree survey data within a stratified random sampling design (simple scaling). These estimates were compared to a MODIS evapotranspiration (ET) estimate for the meadow. The 1-year period for transpiration estimates overlapped each of the 2019 and 2020 growing seasons partially. The response of lodgepole pine transpiration to solar radiation, air temperature, vapor pressure deficit, and volumetric soil water content was investigated by calibrating a modified Jarvis-Stewart (MJS) model to hourly sap flow data collected during the 2020 growing season, which experienced below average antecedent winter precipitation. The model was validated using spatially different sap flow data in the meadow from the 2021 growing season, also part of a dry year. Calibration and validation were completed using a MCMC approach via the DREAM(ZS) algorithm and a generalized likelihood (GL) function, enabling model parameter and total uncertainty assessment. We also used the model to inform transpiration scaling for the calibration period in select plots in the meadow, which allowed comparison with simple scaling transpiration estimates. Average total lodgepole pine transpiration at RCM was estimated between 220.57 ± 25.28 and 393.39 ± 45.65 mm for the entire campaign (mid-July 2019 to mid-August 2020) and between 100.22 ± 11.49 and 178.75 ± 20.74 mm for the 2020 partial growing season (April to mid-August). The magnitude and seasonal timing were similar to MODIS ET. The model showed good agreement between observed and predicted sap velocity for the 2020 partial growing season (RMSE = 1.25 cm h-1), with meteorological variables modulating early growing season sap flow and volumetric soil water content decline imposing transpiration decrease in the late growing season. The model validation performed similarly to calibration in terms of performance metrics and the influence of meteorological variables. The consistency of the declining volumetric soil water content effect during the late growing season between periods could not be evaluated due to an abridged validation period. Overall, the implementation GL-DREAM(ZS) showed promise for future use in MJS models. Lastly, the model derived transpiration estimates for the 2020 partial growing season showed some of the potential utility in using the MJS model to scale sap flow at the study locale. It also highlights some of the key limitations of this approach as it is executed in the present study.

Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.

In this masterthesis I have rewied basic approaches to volatility estimating. These approaches are based on classical and Bayesian statistics. I have applied the volatility models for the purpose of volatility forecasting of a different foreign exchange (EURUSD, GBPUSD and CZKEUR) in the different period (from a second period to a day period). I formulate the models EWMA, GARCH, EGARCH, IGARCH, GJRGARCH, jump diffuison with constant volatility and jump diffusion model with stochastic volatility. I also proposed an MCMC algorithm in order to estimate the Bayesian models. All the models we estimated as univariate models. I compared the models according to Mincer Zarnowitz regression. The most successfull model is the jump diffusion model with a stochastic volatility. On the second place they were the GJR- GARCH model and the jump diffusion model with a constant volatility. But the jump diffusion model with a constat volatilit provided much more overvalued results.The rest of the models were even worse. From the rest the IGARCH model is the best but provided undervalued results. All these findings correspond with R squared coefficient.

This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field.

This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field.

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This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field. / Science, Faculty of / Statistics, Department of / Graduate

Ce travail de recherche propose une solution aux problèmes inverses probabilistes avec des outils de la statistique bayésienne. Le problème inverse considéré est d'estimer la distribution d'une variable aléatoire non observée X à partir d'observations bruitées Y suivant un modèle physique coûteux H. En général, de tels problèmes inverses sont rencontrés dans le traitement des incertitudes. Le cadre bayésien nous permet de prendre en compte les connaissances préalables d'experts en particulier lorsque peu de données sont disponibles. Un algorithme de Metropolis-Hastings-within-Gibbs est proposé pour approcher la distribution a posteriori des paramètres de X avec un processus d'augmentation des données. A cause d'un nombre élevé d'appels, la fonction coûteuse H est remplacée par un émulateur de krigeage (métamodèle). Cette approche implique plusieurs erreurs de natures différentes et, dans ce travail,nous nous attachons à estimer et réduire l'impact de ces erreurs. Le critère DAC a été proposé pour évaluer la pertinence du plan d'expérience (design) et le choix de la loi apriori, en tenant compte des observations. Une autre contribution est la construction du design adaptatif adapté à notre objectif particulier dans le cadre bayésien. La méthodologie principale présentée dans ce travail a été appliquée à un cas d'étude en ingénierie hydraulique. / This thesis provides a probabilistic solution to inverse problems through Bayesian techniques.The inverse problem considered here is to estimate the distribution of a non-observed random variable X from some noisy observed data Y explained by a time-consuming physical model H. In general, such inverse problems are encountered when treating uncertainty in industrial applications. Bayesian inference is favored as it accounts for prior expert knowledge on Xin a small sample size setting. A Metropolis-Hastings-within-Gibbs algorithm is proposed to compute the posterior distribution of the parameters of X through a data augmentation process. Since it requires a high number of calls to the expensive function H, the modelis replaced by a kriging meta-model. This approach involves several errors of different natures and we focus on measuring and reducing the possible impact of those errors. A DAC criterion has been proposed to assess the relevance of the numerical design of experiments and the prior assumption, taking into account the observed data. Another contribution is the construction of adaptive designs of experiments adapted to our particular purpose in the Bayesian framework. The main methodology presented in this thesis has been applied to areal hydraulic engineering case-study.