## Statistical Methods in Astronomy-Lecture 1: Numerical Techniques

1. Examples of Techniques you might use:
• Fitting
• Interpolating / Extrapolating
• Smoothing
• Derivatives / Integrals
• Solutions to equations
• Books:
• Bevington & Robinson: Data Reduction and Error Analysis for Physical Sciences (McGraw-Hill)
• Press et al, Numerical Receipes in Fortran and C (Cambridge)
2. Differentiation / Integration
• Differentiation
• Differential Equations
• Integration (Trapezoidal, Simpsons Rule)
3. Roots to Non-Linear Equations
• Trial and Error on an Interval
• Newton-Raphson
4. Exact data fitting
• Polynomial
• Cubic Spline
5. Least Squares Fitting
• Straight Line
• Transform to Straight Line
• Numerical recipes: fit and fitexy
• Robust estimation (removing outliers)
• Fitting a Polynomial (routine lfit)
6. Non-Linear Functions
• An artform!
• Consider choice of starting parematers, method of solution, step size
• Be aware of multiple solutions
• Convergence conditions
• Grid Search techniques