diff --git a/paper.md b/paper.md index fa7b574..0f777fb 100644 --- a/paper.md +++ b/paper.md @@ -66,25 +66,28 @@ The main idea of `xspline` is to provide a python class that allows user to interact with basis splines, their derivatives and integrals and extrapolation options more easily. -The computation of splines is based on B-spline or basis spline from -[@de1978practical]. Upon this, we derived the derivatives and definite integrals -from the recursive relationship between the splines. - -To support the spline basis computation, we also created modules that provide -convenient interface with indicator and polynomial function and their arbitrary -order of derivatives and definite integrals. We boundle all those useful -functions into a main interface class called `XFunction` which allow user call -the function with specified order, where positive order represent derivatives -and negative order represent definite integrals. - -At end very end, we allow user to specify the way they want to extrapolate by +The computation of splines is based on basis splines (B-splines), see +[@de1978practical] for a canonical reference. Using this reference, we derived recursive relationships to +compute both derivatives and definite integrals from recursive splie relationships. + +To support the spline basis computation, we also created modules that provide a +convenient interface with indicator and polynomial functions, and their +derivatives and definite integrals of any order. All of these useful functions are +bundled into a main interface class called `XFunction`, which allows the user to call +the function with a specified order, where positive order represents derivatives +and negative order represents definite integrals. + +We also allow user to specify the way they want to extrapolate by matching the smoothness at the end knots. -With all of the above features, we created a easy to use and very useful spline -package for statistical model building. For more examples please check [here](https://ihmeuw-msca.github.io/xspline/quickstart.html). +With all of the above features, we created a easy to use spline +package for statistical model building, which has been widely used in +global health statistical analysis, see references below. +For more examples please check [here](https://ihmeuw-msca.github.io/xspline/quickstart.html). More information about the structure of the library can be found in [documentation](https://ihmeuw-msca.github.io/xspline/api_reference/), -while the mathematical use cases are extensively discussed in [@zheng2021trimmed] and [@zheng2022burden] in the context of fitting risks. +while the mathematical use cases are extensively discussed in [@zheng2021trimmed] and [@zheng2022burden] in the context of fitting nonlinear dose-response +relationships. # Ongoing Research and Dissemination