Nothing
Simulation study
In AMISforInfectiousDiseases: Implement the AMIS Algorithm for Infectious Disease Models
\newcommand{\Exp}{\text{Exp}}
\newcommand{\N}{{\cal N}}
In this simulation study, we aim to see whether AMIS is capable of recovering the true parameter values used to simulate data.
Data generating process
\cite{anderson1991infectious} \citep{anderson1991infectious}
We assumed that the number of worms $X$ per host has negative binomial distribution NB($W$,$k$), where $W$ is the mean number of worms and $k$ the dispersion parameter describing the degree of clumping of parasites. The probability mass function is given by
\begin{equation}
\text{Pr}(X=x) = \frac{\Gamma(x+k)}{\Gamma(k)x!} \left(\frac{k}{k+W}\right)^k \left(\frac{W}{k+W}\right)^x, \quad x=0,1,2,\dots.
\end{equation}
As such, the prevalence is given by the probability of observing worms:
\begin{align}
P &= 1 - \text{Pr}\big(X=0 \ \vert \ W, k \big)\
&= 1 - \left( 1 + \frac{W}{k} \right)^{-k}.
\end{align}
We assumed that the mean number of worms is spatially-varying:
[
W_l = 3 \exp\big{-0.5 \ \mathbf{s}l'\Sigma \mathbf{s}_l \big}, \quad l=1,\dots,L.
]
where $\mathbf{s}_l = (\text{lon}_l, \text{lat}_l)'$ are the spatial coordinates of location $l$ and $\Sigma$ is a $2 \times 2$ matrix with entries $\Sigma{11}=\Sigma_{22}=1$ and $\Sigma_{12}=\Sigma_{21}=0.7$. We generated data on a regular grid of $L=50\times50=2500$ coordinate values, with $\text{lon}_l \in [-4,4]$ and $\text{lat}_l \in [-2,2]$.
Finally, we assumed the dispersion parameter is given by
[
k_l = 0.5 \exp \big{0.3 W_l\big}, \quad l=1,\dots,L,
]
so that it is also spatially-varying.
We assumed each location $l$ has $n_l$ hosts, so that the number of worms per host in location $l$ at time $t$ was simulated by
[
X_{i,l,t} \sim \text{NB}(W_l, k_l), \quad i=1,\dots,n_l,
]
so that the prevalence in location $l$ at time $t$ is given by
[
P_{l,t} = \frac{1}{n_l}\sum_{i=1}^{n_l}\text{I}{{X{i,l,t}>0}}.
]
We set $n_l=500$ and generated $M=100$ map samples for each location at each time $t \in {1,2,3}$. Then, we fit AMIS to these map samples using a maximum of $10$ iterations, with $1000$ samples per iteration, and putting independent exponential priors on $W$ and $k$.
Loading packages
library("AMISforInfectiousDiseases")
library("ggplot2")
library("patchwork")
library("viridis")
library("sf")
Generating spatially-varying mean number of worms
lon <- seq(-4, 4, length.out=50)
lat <- seq(-2, 2, length.out=50)
simData <- expand.grid(lon=lon, lat=lat, W=NA, k=NA, expectedPrev=NA)
L <- nrow(simData) # number of locations
Sigma <- diag(2)
Sigma[1,2] <- Sigma[2,1] <- 0.7
for(l in 1:L){
pos <- as.numeric(simData[l,c("lon","lat")])
W <- 5*exp(-0.5*c(t(pos)%*%Sigma%*%pos))
k <- 0.4
simData$W[l] <- W
simData$k[l] <- k
simData$expectedPrev[l] <- 1 - (1 + W/k)^(-k)
}
Below we can see how the mean number of worms and the corresponding prevalence (at the equilibrium distribution) vary over space.
simData_sf <- sf::st_as_sf(simData, coords=c("lon","lat"))
th <- theme(axis.text=element_text(size=10),
legend.text=element_text(size=10))
plots_true_data <- vector(mode = "list", length = 2)
plots_true_data[[1]] <- ggplot(data=simData_sf) +
geom_sf(aes(colour=W),shape=15,size=5) + xlab("Lon") + ylab("Lat") + th +
scale_colour_gradientn(colours=rev(viridis::magma(6)), name="W", na.value="grey100")
plots_true_data[[2]] <- ggplot(data=simData_sf) +
geom_sf(aes(colour=expectedPrev),shape=15,size=5) +
xlab("Lon") + ylab("Lat") + th +
scale_colour_gradientn(colours=rev(viridis::magma(6)),
name="E[P]", na.value="grey100",
limits=c(0,1))
wrap_plots(plots_true_data, guides = 'keep', ncol = 2)
Generating map samples for multiple time points
set.seed(1)
n_hosts <- 500 # number of hosts per location
M <- 100 # number of statistical map samples per location
n_tims <- 3 # number of time points
prevalence_map <- vector(mode = "list", length = n_tims)
for(t in 1:n_tims){
prevs_t <- matrix(NA,L,M)
for (l in 1:L) {
for(m in 1:M){
W <- simData$W[l]
k <- simData$k[l]
num_worms_l <- rnbinom(n=n_hosts, mu=W, size=k)
prevs_t[l,m] <- sum(num_worms_l>0)/n_hosts
}
}
prevalence_map[[t]]$data <- prevs_t
}
Choosing the transmission model function
transmission_model <- function(seeds, params, n_tims){
n_samples <- nrow(params)
p <- matrix(NA, nrow=n_samples, ncol=n_tims)
for(tt in 1:n_tims){
for (i in 1:n_samples){
W <- params[i,1]
k <- params[i,2]
p[i,tt] <- 1-(1+W/k)^(-k)
}
}
return(p)
}
Choosing the prior distributions and AMIS control parameters
# Prior distribution for the model parameters
rprior <- function(n) {
params <- matrix(NA, n, 2)
colnames(params) <- c("W", "k")
params[,1] <- rexp(n=n, rate=lambda_W)
params[,2] <- rexp(n=n, rate=lambda_k)
return(params)
}
dprior <- function(x, log=FALSE) {
if (log) {
return(dexp(x=x[1], rate=lambda_W, log=TRUE) + dexp(x=x[2], rate=lambda_k, log=TRUE))
} else {
return(dexp(x=x[1], rate=lambda_W) * dexp(x=x[2], rate=lambda_k))
}
}
prior <- list(rprior=rprior,dprior=dprior)
amis_params <- AMISforInfectiousDiseases:::default_amis_params()
amis_params$n_samples <- 500
amis_params$target_ess <- 10000
amis_params$max_iters <- 10
amis_params$delta <- 0.1
Running AMIS
In the lines below, we fit AMIS to the statistical maps by using different prior specifications for $k$, namely $\Exp(\lambda_k), \ \lambda_k \in {0.1, 0.3, 1}$.
lambda_W <- 1/3
lambda_k_values <- c(0.1,0.3,1)
num_lambda_k <- length(lambda_k_values)
outList <- vector("list", num_lambda_k)
i <- 1
for(lambda_k in lambda_k_values){
outList[[i]] <- amis(prevalence_map, transmission_model, prior, amis_params, seed=1)
i <- i + 1
}
Looking at posterior distribution of parameters
We can look at the posterior distribution for $k$ at some particular location, e.g. the location with the largest mean number of worms:
loc <- which.max(simData$W)
xlimW <- c(0,10)
Wvals <- seq(xlimW[1],xlimW[2],len=100)
W_prior_dens <- dexp(Wvals, rate=lambda_W)
xlimk <- c(0,10)
kvals <- seq(xlimk[1],xlimk[2],len=100)
i <- 1
plots_k <- vector(mode = "list", length = num_lambda_k)
plots_W <- vector(mode = "list", length = num_lambda_k)
for(lambda_k in lambda_k_values){
k_prior_dens <- dexp(kvals, rate=lambda_k)
out <- outList[[i]]
# plotting W
plot(out, what = "W", type="hist", breaks=50, xlim=xlimW,
locations=loc, main=NA)
lines(Wvals, W_prior_dens, col="blue", lwd=2, lty=2)
abline(v = simData$W[loc], col="red", lwd=2, lty=2)
plots_W[[i]] <- recordPlot()
# plotting k
plot(out, what = "k", type="hist", breaks=100, xlim=xlimk,
locations=loc, main=bquote(lambda[k]*"="*.(lambda_k)))
lines(kvals, k_prior_dens, col="blue", lwd=2, lty=2)
abline(v = simData$k[loc], col="red", lwd=2, lty=2)
plots_k[[i]] <- recordPlot()
i <- i + 1
}
plots_W[[1]]
plots_k[[1]]
plots_W[[2]]
plots_k[[2]]
plots_W[[3]]
plots_k[[3]]
We can clearly see that the posterior distribution of $k$ is largely determined by the prior, and that the existence of multiple time points did not help the recovery of the true parameter values.
Introducing intervention
Now, we assume that an intervention (reduction of the mean number of worms by $70\%$) occurs at time $t=2$ and still has effect at $t=3$.
for(t in 2:3){
prevs_t <- matrix(NA,L,M)
for (l in 1:L) {
for(m in 1:M){
W <- simData$W[l] * 0.3
k <- simData$k[l]
num_worms_l <- rnbinom(n=n_hosts, mu=W, size=k)
prevs_t[l,m] <- sum(num_worms_l>0)/n_hosts
}
}
prevalence_map[[t]]$data <- prevs_t
}
The intervention is known and is also taken into account in the transmission model:
transmission_model <- function(seeds, params, n_tims){
n_samples <- nrow(params)
p <- matrix(NA, nrow=n_samples, ncol=n_tims)
for(t in 1:n_tims){
for (i in 1:n_samples){
if(t==1){
W <- params[i,1]
}else{
W <- params[i,1] * 0.3
}
k <- params[i,2]
p[i,t] <- 1-(1+W/k)^(-k)
}
}
return(p)
}
We then fit AMIS using different priors for $k$ as before.
outList <- vector("list", num_lambda_k)
i <- 1
for(lambda_k in lambda_k_values){
outList[[i]] <- amis(prevalence_map, transmission_model, prior, amis_params, seed=1)
i <- i + 1
}
Now, after introducing intervention, the posterior distribution for $k$ is no longer determined by the prior:
xlimk <- c(0,3)
kvals <- seq(xlimk[1],xlimk[2],len=100)
i <- 1
for(lambda_k in lambda_k_values){
k_prior_dens <- dexp(kvals, rate=lambda_k)
out <- outList[[i]]
# plotting W
plot(out, what = "W", type="hist", breaks=50, xlim=xlimW,
locations=loc, main=NA)
lines(Wvals, W_prior_dens, col="blue", lwd=2, lty=2)
abline(v = simData$W[loc], col="red", lwd=2, lty=2)
plots_W[[i]] <- recordPlot()
# plotting k
plot(out, what = "k", type="hist", breaks=100/lambda_k, xlim=xlimk,
locations=loc, main=bquote(lambda[k]*"="*.(lambda_k)))
lines(kvals, k_prior_dens, col="blue", lwd=2, lty=2)
abline(v = simData$k[loc], col="red", lwd=2, lty=2)
plots_k[[i]] <- recordPlot()
i <- i + 1
}
plots_W[[1]]
plots_k[[1]]
plots_W[[2]]
plots_k[[2]]
plots_W[[3]]
plots_k[[3]]
In what follows, using the model with $\Exp(0.1)$ prior on $k$, we look at the posterior median for $W$ over space at time $t=1$.
out <- outList[[3]]
th <- theme(plot.title = element_text(size = 16, hjust = 0.5))
limits <- c(0,5)
W_post_medians <- sapply(1:L, function(l) calculate_summaries(out, what="W", locations=l)$median)
simData_sf$W_post_medians <- W_post_medians
plot_W_post_median <- ggplot(data=simData_sf) +
geom_sf(aes(colour=W_post_medians),shape=15,size=5) +
scale_colour_gradientn(colours=viridis::turbo(10),
name="Value",
na.value = "grey100",
limits = limits) +
xlab("Lon") + ylab("Lat") + th +
ggtitle("Posterior median of W")
pWtrue <- ggplot(data=simData_sf) +
geom_sf(aes(colour=W),shape=15,size=5) +
scale_colour_gradientn(colours=viridis::turbo(10),
name="Value",
na.value = "grey100",
limits = limits) + xlab("Lon") + ylab("Lat") + th +
ggtitle("True W")
wrap_plots(list(pWtrue, plot_W_post_median), guides = 'collect', ncol = 2)
Note that we assumed a constant true parameter value $k=0.4$ for all locations, but obtained posterior samples for each location. To see how much the estimates for $k$ varied over space, we can look at the posterior median of each location:
k_post_medians <- sapply(1:L, function(l) calculate_summaries(out, what="k", locations=l)$median)
summary(k_post_medians)
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 0.340 0.348 0.419 0.413 0.462 0.573
Try the AMISforInfectiousDiseases package in your browser
Any scripts or data that you put into this service are public.
AMISforInfectiousDiseases documentation built on April 4, 2025, 1:45 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
\newcommand{\Exp}{\text{Exp}} \newcommand{\N}{{\cal N}}
In this simulation study, we aim to see whether AMIS is capable of recovering the true parameter values used to simulate data.
Data generating process
\cite{anderson1991infectious} \citep{anderson1991infectious} We assumed that the number of worms $X$ per host has negative binomial distribution NB($W$,$k$), where $W$ is the mean number of worms and $k$ the dispersion parameter describing the degree of clumping of parasites. The probability mass function is given by \begin{equation} \text{Pr}(X=x) = \frac{\Gamma(x+k)}{\Gamma(k)x!} \left(\frac{k}{k+W}\right)^k \left(\frac{W}{k+W}\right)^x, \quad x=0,1,2,\dots. \end{equation}
As such, the prevalence is given by the probability of observing worms:
\begin{align} P &= 1 - \text{Pr}\big(X=0 \ \vert \ W, k \big)\ &= 1 - \left( 1 + \frac{W}{k} \right)^{-k}. \end{align}
We assumed that the mean number of worms is spatially-varying: [ W_l = 3 \exp\big{-0.5 \ \mathbf{s}l'\Sigma \mathbf{s}_l \big}, \quad l=1,\dots,L. ] where $\mathbf{s}_l = (\text{lon}_l, \text{lat}_l)'$ are the spatial coordinates of location $l$ and $\Sigma$ is a $2 \times 2$ matrix with entries $\Sigma{11}=\Sigma_{22}=1$ and $\Sigma_{12}=\Sigma_{21}=0.7$. We generated data on a regular grid of $L=50\times50=2500$ coordinate values, with $\text{lon}_l \in [-4,4]$ and $\text{lat}_l \in [-2,2]$.
Finally, we assumed the dispersion parameter is given by [ k_l = 0.5 \exp \big{0.3 W_l\big}, \quad l=1,\dots,L, ] so that it is also spatially-varying.
We assumed each location $l$ has $n_l$ hosts, so that the number of worms per host in location $l$ at time $t$ was simulated by [ X_{i,l,t} \sim \text{NB}(W_l, k_l), \quad i=1,\dots,n_l, ] so that the prevalence in location $l$ at time $t$ is given by [ P_{l,t} = \frac{1}{n_l}\sum_{i=1}^{n_l}\text{I}{{X{i,l,t}>0}}. ]
We set $n_l=500$ and generated $M=100$ map samples for each location at each time $t \in {1,2,3}$. Then, we fit AMIS to these map samples using a maximum of $10$ iterations, with $1000$ samples per iteration, and putting independent exponential priors on $W$ and $k$.
Loading packages
library("AMISforInfectiousDiseases") library("ggplot2") library("patchwork") library("viridis") library("sf")
Generating spatially-varying mean number of worms
lon <- seq(-4, 4, length.out=50) lat <- seq(-2, 2, length.out=50) simData <- expand.grid(lon=lon, lat=lat, W=NA, k=NA, expectedPrev=NA) L <- nrow(simData) # number of locations Sigma <- diag(2) Sigma[1,2] <- Sigma[2,1] <- 0.7 for(l in 1:L){ pos <- as.numeric(simData[l,c("lon","lat")]) W <- 5*exp(-0.5*c(t(pos)%*%Sigma%*%pos)) k <- 0.4 simData$W[l] <- W simData$k[l] <- k simData$expectedPrev[l] <- 1 - (1 + W/k)^(-k) }
Below we can see how the mean number of worms and the corresponding prevalence (at the equilibrium distribution) vary over space.
simData_sf <- sf::st_as_sf(simData, coords=c("lon","lat")) th <- theme(axis.text=element_text(size=10), legend.text=element_text(size=10)) plots_true_data <- vector(mode = "list", length = 2) plots_true_data[[1]] <- ggplot(data=simData_sf) + geom_sf(aes(colour=W),shape=15,size=5) + xlab("Lon") + ylab("Lat") + th + scale_colour_gradientn(colours=rev(viridis::magma(6)), name="W", na.value="grey100") plots_true_data[[2]] <- ggplot(data=simData_sf) + geom_sf(aes(colour=expectedPrev),shape=15,size=5) + xlab("Lon") + ylab("Lat") + th + scale_colour_gradientn(colours=rev(viridis::magma(6)), name="E[P]", na.value="grey100", limits=c(0,1)) wrap_plots(plots_true_data, guides = 'keep', ncol = 2)
Generating map samples for multiple time points
set.seed(1) n_hosts <- 500 # number of hosts per location M <- 100 # number of statistical map samples per location n_tims <- 3 # number of time points prevalence_map <- vector(mode = "list", length = n_tims) for(t in 1:n_tims){ prevs_t <- matrix(NA,L,M) for (l in 1:L) { for(m in 1:M){ W <- simData$W[l] k <- simData$k[l] num_worms_l <- rnbinom(n=n_hosts, mu=W, size=k) prevs_t[l,m] <- sum(num_worms_l>0)/n_hosts } } prevalence_map[[t]]$data <- prevs_t }
Choosing the transmission model function
transmission_model <- function(seeds, params, n_tims){ n_samples <- nrow(params) p <- matrix(NA, nrow=n_samples, ncol=n_tims) for(tt in 1:n_tims){ for (i in 1:n_samples){ W <- params[i,1] k <- params[i,2] p[i,tt] <- 1-(1+W/k)^(-k) } } return(p) }
Choosing the prior distributions and AMIS control parameters
# Prior distribution for the model parameters rprior <- function(n) { params <- matrix(NA, n, 2) colnames(params) <- c("W", "k") params[,1] <- rexp(n=n, rate=lambda_W) params[,2] <- rexp(n=n, rate=lambda_k) return(params) } dprior <- function(x, log=FALSE) { if (log) { return(dexp(x=x[1], rate=lambda_W, log=TRUE) + dexp(x=x[2], rate=lambda_k, log=TRUE)) } else { return(dexp(x=x[1], rate=lambda_W) * dexp(x=x[2], rate=lambda_k)) } } prior <- list(rprior=rprior,dprior=dprior) amis_params <- AMISforInfectiousDiseases:::default_amis_params() amis_params$n_samples <- 500 amis_params$target_ess <- 10000 amis_params$max_iters <- 10 amis_params$delta <- 0.1
Running AMIS
In the lines below, we fit AMIS to the statistical maps by using different prior specifications for $k$, namely $\Exp(\lambda_k), \ \lambda_k \in {0.1, 0.3, 1}$.
lambda_W <- 1/3 lambda_k_values <- c(0.1,0.3,1) num_lambda_k <- length(lambda_k_values) outList <- vector("list", num_lambda_k) i <- 1 for(lambda_k in lambda_k_values){ outList[[i]] <- amis(prevalence_map, transmission_model, prior, amis_params, seed=1) i <- i + 1 }
Looking at posterior distribution of parameters
We can look at the posterior distribution for $k$ at some particular location, e.g. the location with the largest mean number of worms:
loc <- which.max(simData$W) xlimW <- c(0,10) Wvals <- seq(xlimW[1],xlimW[2],len=100) W_prior_dens <- dexp(Wvals, rate=lambda_W) xlimk <- c(0,10) kvals <- seq(xlimk[1],xlimk[2],len=100) i <- 1 plots_k <- vector(mode = "list", length = num_lambda_k) plots_W <- vector(mode = "list", length = num_lambda_k) for(lambda_k in lambda_k_values){ k_prior_dens <- dexp(kvals, rate=lambda_k) out <- outList[[i]] # plotting W plot(out, what = "W", type="hist", breaks=50, xlim=xlimW, locations=loc, main=NA) lines(Wvals, W_prior_dens, col="blue", lwd=2, lty=2) abline(v = simData$W[loc], col="red", lwd=2, lty=2) plots_W[[i]] <- recordPlot() # plotting k plot(out, what = "k", type="hist", breaks=100, xlim=xlimk, locations=loc, main=bquote(lambda[k]*"="*.(lambda_k))) lines(kvals, k_prior_dens, col="blue", lwd=2, lty=2) abline(v = simData$k[loc], col="red", lwd=2, lty=2) plots_k[[i]] <- recordPlot() i <- i + 1 }
plots_W[[1]] plots_k[[1]]
plots_W[[2]] plots_k[[2]]
plots_W[[3]] plots_k[[3]]
We can clearly see that the posterior distribution of $k$ is largely determined by the prior, and that the existence of multiple time points did not help the recovery of the true parameter values.
Introducing intervention
Now, we assume that an intervention (reduction of the mean number of worms by $70\%$) occurs at time $t=2$ and still has effect at $t=3$.
for(t in 2:3){ prevs_t <- matrix(NA,L,M) for (l in 1:L) { for(m in 1:M){ W <- simData$W[l] * 0.3 k <- simData$k[l] num_worms_l <- rnbinom(n=n_hosts, mu=W, size=k) prevs_t[l,m] <- sum(num_worms_l>0)/n_hosts } } prevalence_map[[t]]$data <- prevs_t }
The intervention is known and is also taken into account in the transmission model:
transmission_model <- function(seeds, params, n_tims){ n_samples <- nrow(params) p <- matrix(NA, nrow=n_samples, ncol=n_tims) for(t in 1:n_tims){ for (i in 1:n_samples){ if(t==1){ W <- params[i,1] }else{ W <- params[i,1] * 0.3 } k <- params[i,2] p[i,t] <- 1-(1+W/k)^(-k) } } return(p) }
We then fit AMIS using different priors for $k$ as before.
outList <- vector("list", num_lambda_k) i <- 1 for(lambda_k in lambda_k_values){ outList[[i]] <- amis(prevalence_map, transmission_model, prior, amis_params, seed=1) i <- i + 1 }
Now, after introducing intervention, the posterior distribution for $k$ is no longer determined by the prior:
xlimk <- c(0,3) kvals <- seq(xlimk[1],xlimk[2],len=100) i <- 1 for(lambda_k in lambda_k_values){ k_prior_dens <- dexp(kvals, rate=lambda_k) out <- outList[[i]] # plotting W plot(out, what = "W", type="hist", breaks=50, xlim=xlimW, locations=loc, main=NA) lines(Wvals, W_prior_dens, col="blue", lwd=2, lty=2) abline(v = simData$W[loc], col="red", lwd=2, lty=2) plots_W[[i]] <- recordPlot() # plotting k plot(out, what = "k", type="hist", breaks=100/lambda_k, xlim=xlimk, locations=loc, main=bquote(lambda[k]*"="*.(lambda_k))) lines(kvals, k_prior_dens, col="blue", lwd=2, lty=2) abline(v = simData$k[loc], col="red", lwd=2, lty=2) plots_k[[i]] <- recordPlot() i <- i + 1 }
plots_W[[1]] plots_k[[1]]
plots_W[[2]] plots_k[[2]]
plots_W[[3]] plots_k[[3]]
In what follows, using the model with $\Exp(0.1)$ prior on $k$, we look at the posterior median for $W$ over space at time $t=1$.
out <- outList[[3]] th <- theme(plot.title = element_text(size = 16, hjust = 0.5)) limits <- c(0,5) W_post_medians <- sapply(1:L, function(l) calculate_summaries(out, what="W", locations=l)$median) simData_sf$W_post_medians <- W_post_medians plot_W_post_median <- ggplot(data=simData_sf) + geom_sf(aes(colour=W_post_medians),shape=15,size=5) + scale_colour_gradientn(colours=viridis::turbo(10), name="Value", na.value = "grey100", limits = limits) + xlab("Lon") + ylab("Lat") + th + ggtitle("Posterior median of W") pWtrue <- ggplot(data=simData_sf) + geom_sf(aes(colour=W),shape=15,size=5) + scale_colour_gradientn(colours=viridis::turbo(10), name="Value", na.value = "grey100", limits = limits) + xlab("Lon") + ylab("Lat") + th + ggtitle("True W") wrap_plots(list(pWtrue, plot_W_post_median), guides = 'collect', ncol = 2)
Note that we assumed a constant true parameter value $k=0.4$ for all locations, but obtained posterior samples for each location. To see how much the estimates for $k$ varied over space, we can look at the posterior median of each location:
k_post_medians <- sapply(1:L, function(l) calculate_summaries(out, what="k", locations=l)$median) summary(k_post_medians) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.340 0.348 0.419 0.413 0.462 0.573
Try the AMISforInfectiousDiseases package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.