Of the three we considered, we find that the squared exponential function is generally the best choice of covariance function when estimating time derivatives, because it typically results in the ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

Other second-order expansions (Hartigan 1965; Johnson 1970; Lindley 1961, 1980; Mosteller and Wallace 1964) require computation of more derivatives of the log-likelihood function. In this article we ...

Posterior means of positive functions can be expressed as the ratio of integrals which is called fully exponential form. When approximating the posterior means analytically, we usually use Laplace's ...