Probabilistic programming languages (PPLs) provide users with an interface to write probabilistic models and leave the statistical inference to the compiler and runtime systems. Ideally, the purpose of PPLs is to provide a seamless inference interface that makes the model and the inference parts modular. Yet, the structure of the user-defined model affects inference accuracy and execution time. Users can utilize certain structures, such as conjugate prior relations or tree structures within a given model, to improve inference efficiency; however, manually utilizing these structures in a model is time-consuming and error-prone. Especially as the PPL's expressiveness increases, the models may become too complex to rewrite. This thesis tackles the problems related to the automation of optimizations, improving the execution time and the accuracy of the inference based on the structure of the model. Further, it aims to make these optimizations expressive enough to handle complex models written in universal PPLs. 

The scope of this thesis is to optimize Bayesian inference in universal PPLs. The three contributions presented propose automated optimization approaches to improving the inference accuracy and execution time while preserving the expressiveness of the optimized program. The first contribution considers dynamic delayed sampling, a runtime algorithm to reduce inference variance through analytical relationships between random variables. We develop a compile-time version of the delayed sampling algorithm to reduce execution overhead. The second contribution regards the design and implementation of dynamic delayed sampling in a statically typed universal PPL, Miking CorePPL. Integrating delayed sampling into a statically typed PPL requires introducing additional constructs to the language. The third contribution is related to the forward pass of belief propagation algorithm, an efficient inference algorithm on tree graphs. We propose an approach automating this forward pass of belief propagation in statically typed universal PPLs to optimize likelihood calculations by utilizing the tree structures in a model. We evaluate the proposed approaches on real-world problems, such as topic modeling and phylogenetic problems.

This thesis investigates the effect of Soil-Structure Interaction (SSI) on the dynamic response of railway bridges with integrated retaining walls, referred to as end shield bridges, numerically and experimentally. The research aims to determine how surrounding soils influence the dynamic behavior of the system and their impact on high-speed train passage. The effect of uncertainties related to soil properties is examined, and simplified modeling techniques for incorporating SSI in the analysis of railway bridges are proposed. For this purpose, four railway bridges with end shields, including two single-span and two three-span structures, are equipped with numerous accelerometers and excited using a hydraulic actuator across various frequencies and load amplitudes.

In Paper I, a simplified 2D beam model of a three-span railway bridge, considering SSI only at the end shields, is presented. The effects of neglecting the backfill soil and removing the cantilever sections during high-speed train passage are investigated. It is shown that excluding the backfill soil leads to a significant increase in the acceleration response of the bridge due to the impact load effects of the train, and an acceptable alternative to not modeling the soil is to remove the cantilever parts of the bridge.

In Paper II, the impact of surrounding soils on the dynamic behavior of the same three-span railway bridge is studied in depth. A full 3D model of the railway bridge-soil system is created in the FE software and calibrated to the experimental data using the Frequency Response Functions (FRFs) at each sensor location. To assess the dynamic effect of surrounding soils, different models without soil components are created. It is observed that excluding soil can lead to a significant shift in the natural frequencies of the structure, particularly for higher modes, and a substantial increase in FRF amplitude.~Furthermore, high-speed train passage analysis indicates that removing soil can dramatically enhance the resonance response of the bridge.

In Pape III, simplified 3D solid and 2D beam modeling alternatives for end shield bridges are proposed. In the simplified 3D solid model, the influence of the backfill soil is introduced through distributed springs and dashpots derived from simple equations. In the simplified 2D beam model, the dynamic effect of the backfill soil is derived from the impedance functions of the soil medium. The performance of these simplified models is then compared to the calibrated 3D models in terms of the modal properties of the first bending mode and the maximum acceleration response during high-speed train passage. The results show that the simplified models closely align with the calibrated models, proving to be simple and efficient alternatives for practical use in bridge design.