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sbfnk committed Aug 8, 2024
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2 changes: 1 addition & 1 deletion NEWS.md
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- `epinow()` now returns the "timing" output in a "time difference"" format that is easier to understand and work with. By @jamesmbaazam in #688 and reviewed by @sbfnk.
- The interface for defining delay distributions has been generalised to also cater for continuous distributions
- When defining probability distributions these can now be truncated using the `tolerance` argument
- Ornstein-Uhlenbeck and 5 / 2 matern kernels have been added. By @sbfnk in # and reviewed by @.
- Ornstein-Uhlenbeck and 5 / 2 Matérn kernels have been added. By @sbfnk in # and reviewed by @.

## Bug fixes

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6 changes: 3 additions & 3 deletions R/opts.R
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Expand Up @@ -426,13 +426,13 @@ backcalc_opts <- function(prior = c("reports", "none", "infections"),
#' 'matern_order = Inf'), 3 over 2 oder 5 over 2 Matern kernel ("matern", with
#' `matern_order = 3/2` (default) or `matern_order = 5/2`, respectively), or
#' Orstein-Uhlenbeck ("ou", or "matern" with 'matern_order = 1/2'). Defaulting
#' to the Matern 3 over 2 kernel for a balance of smoothness and
#' to the Matérn 3 over 2 kernel for a balance of smoothness and
#' discontinuities.
#'
#' @param matern_order Numeric, defaults to 3/2. Order of Matern Kernel to use.
#' @param matern_order Numeric, defaults to 3/2. Order of Matérn Kernel to use.
#' Currently the orders 1/2, 3/2, 5/2 and Inf are supported.
#'
#' @param matern_type Deprated; Numeric, defaults to 3/2. Order of Matern Kernel
#' @param matern_type Deprated; Numeric, defaults to 3/2. Order of Matérn Kernel
#' to use. Currently the orders 1/2, 3/2, 5/2 and Inf are supported.
#'
#' @param basis_prop Numeric, proportion of time points to use as basis
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8 changes: 4 additions & 4 deletions man/gp_opts.Rd

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8 changes: 4 additions & 4 deletions vignettes/gaussian_process_implementation_details.Rmd
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Expand Up @@ -41,7 +41,7 @@ k(t,t') = k(|t - t'|) = k(\Delta t)

with the following choices available for the kernel $k$

## Matern 3/2 covariance kernel (the default)
## Matérn 3/2 covariance kernel (the default)

\begin{equation}
k(\Delta t) = \alpha \left( 1 + \frac{\sqrt{3} \Delta t}{l} \right) \exp \left( - \frac{\sqrt{3} \Delta t}{l}\right)
Expand All @@ -55,13 +55,13 @@ with $l>0$ and $\alpha > 0$ the length scale and magnitude, respectively, of the
k(\Delta t) = \alpha \exp \left( - \frac{1}{2} \frac{(\Delta t^2)}{l^2} \right)
\end{equation}

## Ornstein-Uhlenbeck (Matern 1/2) kernel
## Ornstein-Uhlenbeck (Matérn 1/2) kernel

\begin{equation}
k(\Delta t) = \alpha \exp{\left( - \frac{\Delta t}{2 l^2} \right)}
\end{equation}

## Matern 5/2 covariance kernel
## Matérn 5/2 covariance kernel

\begin{equation}
k(\Delta t) = \alpha \left( 1 + \frac{\sqrt{5} \Delta t}{l} + \frac{5}{3} \left(\frac{\Delta t}{l} \right)^2 \right) \exp \left( - \frac{\sqrt{5} \Delta t}{l}\right)
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\beta_j \sim \mathcal{Normal}(0, 1)
\end{equation}

The function $S_k(x)$ is the spectral density relating to a particular covariance function $k$. In the case of the Matern 3/2 kernel (the default in `EpiNow2`) this is given by
The function $S_k(x)$ is the spectral density relating to a particular covariance function $k$. In the case of the Matérn 3/2 kernel (the default in `EpiNow2`) this is given by

\begin{equation}
S_k(x) = 4 \alpha^2 \left( \frac{\sqrt{3}}{\rho}\right)^3 \left(\left( \frac{\sqrt{3}}{\rho} \right)^2 + w^2 \right)^{-2}
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