The distribution of mountain permafrost is generally modeled using a combination of statistical techniques and empirical variables. Such models, based on topographic, climatic and geomorphological predictors of permafrost, have been widely used to estimate the spatial distribution of mountain permafrost in North America and Europe. However at present, little knowledge about the distribution and characteristics of mountain permafrost is available for the Andes. In addition, the effects of climate change on slope stability and the hydrological system, and the pressure of mining activities have increased concerns about the knowledge of mountain permafrost in the Andes. In order to model permafrost distribution in the semi-arid Chilean Andes between ~29°S and 32°S, an inventory of rock glaciers is carried out to obtain a variable indicative of the presence and absence of permafrost conditions. Then a Linear Mixed-Effects Model (LMEM) is used to determine the spatial distribution of Mean Annual Air Temperature (MAATs), which is then used as one of the predictors of permafrost occurrence. Later, a Generalized Additive Model (GAM) with a logistic link function is used to predict permafrost occurrence in debris surfaces within the study area. Within the study area, 3575 rock glaciers were inventoried. Of these, 1075 were classified as active, 493 as inactive, 343 as intact and 1664 as relict forms, based on visual interpretation of satellite imagery. Many of the rock glaciers (~60-80%) are situated at positive MAAT, and the number of rock glaciers at negative MAAT greatly decreases from north to south. The results of spatial temperature distribution modeling indicated that the temperature changes by -0.71°C per each 100 m increase in altitude, and that there is a 4°C temperature difference between the northern and southern part of the study area. The altitudinal position of the 0°C MAAT isotherm is situated at ~4250 m a.s.l. in the northern (29°S) section and drops latitudinally to ~4000 m a.s.l. in the southern section (32°S) of the study area. For permafrost modeling purposes, 1911 rock glaciers (active, inactive and intact forms) were categorized into the class indicative of permafrost presence and 1664 (relict forms) as non-permafrost. The predictors MAAT and Potential Incoming Solar Radiation (PISR) and their nonlinear interaction were modeled by the GAM using LOESS smoothing function. A temperature offset term was applied to reduce the overestimation of permafrost occurrence in debris surface areas due to the use of rock glaciers as permafrost proxies. The dependency between the predictor variables shows that a high amount of PISR has a greater effect at positive MAAT levels than in negative ones. The GAM for permafrost distribution achieved an acceptable discrimination capability between permafrost classes (area under the ROC curve ~0.76). Considering a permafrost probability score (PPS) ≥ 0.5 and excluding steep bedrock and glacier surfaces, mountain permafrost can be potentially present in up to about 6.8% (2636 km2) of the study area, whereas with a PPS ≥ 0.75, the potential permafrost area decreases to 2.7% (1051 km2). Areas with the highest PPS are spatially concentrated in the north section of the study area where altitude rises considerably (the Huasco and Elqui watersheds), while permafrost is almost absent in the southern section where the topography is considerably lower (Limarí and Choapa watersheds). This research shows that the potential mountain permafrost distribution can be spatially modeled using topoclimatic information and rock glacier inventories. Furthermore, the results have provided the first local estimation of permafrost distribution in the semi-arid Chilean Andes. The results obtained can be used for local environmental planning and to aid future research in periglacial topics.

The migratory birds stop at different stopover sites during migration. The presence of resources in these stopover sites is essential to regain the energy of these birds. This thesis aims to compare the resource abundance and intake at the two stopover sites: Reda and Wisla river estuaries. How a bird's mass changes during its stay at an estuary is considered as a proxy for the resource abundance of a site. The comparison is made on different subsets, including those which has incomplete data, i.e. next day is not exactly one day after the previous capture. Multiple linear regression, Generalized additive model and Linear mixed effect model are used for analysis. Expectation maximization and an iterative predictive process are implemented to deal with incomplete data. We found that Reda has higher resource abundance and intake as compared to that of Wisla river estuary.

Indiana University-Purdue University Indianapolis (IUPUI) / Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters.