Particle filters are a class of sequential Monte-Carlo methods which are used commonly when estimating various unknowns of the time-varying signals presented in real time, especially when dealing with nonlinearity and non-Gaussianity in BOT applications. This thesis work is designed to perform one such estimate involving tracking a person using the road information available from an IR surveillance video. In this thesis, a parallel custom hardware is implemented in Altera cyclone IV E FPGA device utilizing SIRF type of particle filter. This implementation has accounted how the algorithmic aspects of this sampling based filter relate to possibilities and constraints in a hardware implementation. Using 100MHz clock frequency, the synthesised hardware design can process almost 50 Mparticles/s. Thus, this implementation has resulted in tracking the target, which is defined by a 5-dimensional state variable, using the noisy measurements available from the sensor.

Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials. The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification. A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis. In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

This thesis develops a generalized form of Monte Carlo integration called Resampled Importance Sampling. It is based on the importance resampling sample generation technique. Resampled Importance Sampling can lead to significant variance reduction over standard Monte Carlo integration for common rendering problems. We show how to select the importance resampling parameters for near optimal variance reduction. We also combine RIS with stratification and with Multiple Importance Sampling for further variance reduction. We demonstrate the robustness of this technique on the direct lighting problem and achieve up to a 33% variance reduction over standard techniques. We also suggest using RIS as a default BRDF sampling technique.