# calculus

1. ### Restricted Maximum Likelihood (REML) Estimate of Variance Component.

Let, \mathbf y_i = \mathbf X_i\mathbf\beta + \mathbf Z_i\mathbf b_i+ \mathbf\epsilon_i, where \mathbf y_i\sim N(\mathbf X_i\mathbf\beta, \Sigma_i=\sigma^2\mathbf I_{n_i}+\mathbf Z_i \mathbf G\mathbf Z_i'), \mathbf b_i\sim N(\mathbf 0, \mathbf G), \mathbf\epsilon_i\sim N(\mathbf 0...
2. ### Differentiation Involving Determinant.

I have to compute the following differentiation : \frac{\partial}{\partial\sigma^2}\det[\mathbf X_{p\times n}'(\sigma^2 \mathbf I_{n}+\mathbf Z_{n\times q}\mathbf G_{q\times q}\mathbf Z_{q\times n}')^{-1}\mathbf X_{n\times p}], where \sigma^2 is a scalar, \det denotes determinant, \mathbf...
3. ### Statistics without calculus?

I have been battling this question for quite some time now, and it seems this question has been debated countless times. I am drawn to many subjects in statistics, mostly applied in nature. I especially enjoy statistical computing, graphing, machine learning, and exploratory analysis. I have...
4. ### Physics Teacher with a question of appropriate use of regression equaitons

Is it ever acceptable to replace discrete measured values with a continuous function if you are certain you have the right model? For the last week my students have been working on using experimental results and statistical tests as evidence to either accept or refute someone else s or their...