Geosteering is the iterative process of navigating the Bottom Hole Assembly (BHA) in a given geological setting in order to achieve pre-specified targets. To guide the directional drilling process, directional survey and logging-while-drilling (LWD) sensor measurements are used to estimate BHA position and the lateral changes of the geological structure. Two types of contemporary geosteering approaches, namely, model-based and stratification-based, are introduced. In the Chapter 1, we formulate the stratification-based approach as a Bayesian optimization procedure: the log from a pilot reference well is used as a stratigraphic signature of the geological structure in a given region; the observed log sequence acquired along the wellbore is projected into the stratigraphic domain given a proposed earth model and directional survey; the pattern similarity between the converted log and the signature is measured by a correlation coefficient; then stochastic searching is performed on the space of all possible earth models to maximize the similarity under constraints of the prior understanding of the drilling process and target formation; finally inference is made based on the samples simulated from the posterior distribution using Stochastic Approximation Monte Carlo (SAMC).

In chapter 2, we propose an efficient non-linear state space model approach to solve the model-based aspect of geosteering. This chapter is an extension to the chapter 1 whose limitations are further addressed here by taking the sequential nature of the acquired sensor measurements into account. For posterior inference of the latent states and model parameters, we apply extended Kalman filter, particle filter with Gibbs and particle filter with Metropolis Hasting. Our proposed methods consistently achieve good performance on synthetic datasets in term of high correlations between the interpreted log and reference log, and provides similar interpretations as the geosteering geologists on real wells. We developed C/C++ based Python packages gs_scpm and gs_smc that are efficient enough to provide accurate steering guidance to the geologists in real-time and those software packages are deployed via https://www.geodesic.ai .

Variable selection, also known as feature selection in the machine learning literature, plays an indispensable role in scientific studies. In many research areas with massive data, finding a subset of representative features that best explain the outcome of interest has become a critical component in any researcher's workflow. In chapter 3, we focus on Bayesian variable selection regression models for count data, and specifically on the negative binomial linear regression model. We address the variable selection problem via spike-and-slab priors. For posterior inference, we review standard MCMC methods and also investigate computationally more efficient variational inference approaches that use data augmentation techniques. We investigate performance of the methods via simulation studies and benchmark datasets. We provide C/C++ code at https://github.com/marinavannucci/snbvbs that help to considerably speed up the variable selection inference process for the negative binomial regression models.