We present models and algorithms that can be applied to common problems in analysis of genomic data. These include CNV (Copy Number Variation) detection, local ancestry inference in admixed populations, and haplotype inference in panels of unrelated individuals. Chapter 2 proposes a new algorithm for the Fused Lasso Signal Approximator which was recently been proposed as an alternative to HMM's for CNV detection. Chapter 3 describes new models for local ancestry inference when high density genotype data is available, and our focus is on a higher order Autoregressive Hidden Markov Model (ARHMM). We give solutions to problems that have thus far prevented the use of higher order ARHMM's for this task, and we demonstrate the model on real and simulated data. Finally, in chapter 4 we given an approach for inferring haplotypes from unphased genotype data. We optimize a likelihood closely related to the PHASE model (which is considered one of the most accurate), and we show that the proposed approach is substantially more accurate than recent alternatives. The work in these chapters contributes to common and important tasks in analysis of genomic data for association studies.