In AgueroZZ/OSplines: Constructing O Spline for univariate smoothing

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OSplines

The goal of the OSplines package is to efficiently implement model-based smoothing with the integrated Wiener's process, within a variety of Bayesian hierarchical models.

Installation

You can install the development version of OSplines from GitHub with:

# install.packages("devtools")
devtools::install_github("https://github.com/Smoothing-IWP/OSplines/tree/development")

Example

This is a basic example which shows you how to use OSplines to fit and analyze some models, we consider the following data set of COVID-19 mortality in Canada, which is available in the package:

library(OSplines)
## basic example code
head(covid_canada)

We can fit a model with $\text{IWP}_3(\sigma)$ prior using the function model_fit:

fit_result <- model_fit(new_deaths ~ weekdays1 + weekdays2 + weekdays3 + weekdays4 + weekdays5 + weekdays6 +
                          f(smoothing_var = t, model = "IWP", order = 3, k = 30), 
                        data = covid_canada, method = "aghq", family = "Poisson")

We can take a look at the posterior summary of this model:

summary(fit_result)

We can also see the inferred function $f$:

plot(fit_result)

We can use the predict function to obtain the posterior summary of $f$ or its derivative at new_data.

For the function $f$:

predict_f <- predict(fit_result, variable = "t", newdata = data.frame(t = seq(from = 605, to = 617, by = 0.1)))
predict_f %>% ggplot(aes(x = x)) + geom_line(aes(y = mean), lty = "solid") +
  geom_line(aes(y = plower), lty = "dashed") +
  geom_line(aes(y = pupper), lty = "dashed") +
  theme_classic()

For the first derivative:

predict_f1st <- predict(fit_result, variable = "t", newdata = data.frame(t = seq(from = 605, to = 617, by = 0.1)), degree = 1)
predict_f1st %>% ggplot(aes(x = x)) + geom_line(aes(y = mean), lty = "solid") +
  geom_line(aes(y = plower), lty = "dashed") +
  geom_line(aes(y = pupper), lty = "dashed") +
  theme_classic()

For the second derivative:

predict_f2nd <- predict(fit_result, variable = "t", newdata = data.frame(t = seq(from = 605, to = 617, by = 0.1)), degree = 2)
predict_f2nd %>% ggplot(aes(x = x)) + geom_line(aes(y = mean), lty = "solid") +
  geom_line(aes(y = plower), lty = "dashed") +
  geom_line(aes(y = pupper), lty = "dashed") +
  theme_classic()