1 AN INTRODUCTION

2 POWER SPECTRUM ESTIMATORS
2.1 The Quadratic Maximum Likelihood Estimator
2.2 Inverting the Pixel Covariance Matrix
2.3 Forming the Fisher Matrix
2.4 Review of the Pseudo- $C_{\ell}$ Estimator

3 METHODOLOGY
3.1 Theory Power Spectrum
3.2 Survey Geometry
3.3 Pseudo $C_{\ell}$ Implementation

4 RESULTS
4.1 Benchmark Against Existing Estimators
4.2 Accuracy of Numerical Fisher Matrix
4.3 Comparing $C_{\ell}$ Variances of QML to Pseudo- $C_{\ell}$
4.4 Cosmological Parameter Inference
4.5 Non-Gaussian Maps

5 CONCLUSIONS