EpiBayes_s(H, k, n, seasons, reps, MCMCreps, poi = "tau", y = NULL, mumodes = matrix(c(0.5, 0.7, 0.5, 0.7, 0.02, 0.5, 0.02, 0.5), 4, 2, byrow = TRUE), pi.thresh = 0.02, tau.thresh = 0.05, gam.thresh = 0.1, tau.T = 0, poi.lb = 0, poi.ub = 1, p1 = 0.95, psi = 4, omegaparm = c(100, 1), gamparm = c(100, 1), tauparm = c(1, 1), etaparm = c(100, 6), thetaparm = c(100, 6), burnin = 1000)H x 1).sum(k) x 1).sum(k) x 1).gam) or the cluster-level prevalence (tau), indicating which variable
with which to compute the simulation output p2.tilde, p4.tilde, and
p6.tilde. Character scalar.NULL). Integer matrix (reps x sum(k)).poi prevalences
to show ability to capture poi with certain probability. Real scalars.poi prevalence is below / above the thresholds
pi.thresh or tau.thresh or within specified bounds. Real scalar.omega, which
is the probability that the disease is in the region. Real vector (2 x 1).gam, which
is the subzone-level prevalence (or the prevalence among subzones). Real
vector (2 x 1).tau, which is the
cluster-level prevalence (or the prevalence among clusters). Real vector (2 x 1).eta, which is the
sensitivity of the diagnostic test. Real vector (2 x 1).theta, which is
the specificity of the diagnostic test. Real vector (2 x 1).EpiBayes_s, and diagnose issues before continuing with
the 'no storage' model, EpiBayes_ns, for faster results, especially if
it is being used as a simulation-type model and not a poserior inference-type model.
Nevertheless, below are the outputs of this model.| Output | Attributes |
| Description |
p2.tilde |
| Real scalar | Proportion of simulated data sets that result in the probability of poi prevalence below poi.thresh with probability p1 |
p4.tilde |
Real scalar |
Proportion of simulated data sets that result in the probability of poi prevalence above poi.thresh with probability p1 |
p6.tilde |
| Real scalar | Proportion of simulated data sets that result in the probability of poi prevalence between poi.lb and poi.ub with probability p1 |
taumat |
Real array (reps x H x MCMCreps) |
Posterior distributions of the cluster-level prevalence for all simulated data sets (i.e., reps) |
gammat |
Real matrix (reps x MCMCreps) |
Posterior distribution of the subzone-level prevalence |
omegamat |
Real matrix (reps x MCMCreps) |
| Posterior distribution of the probability of the disease being in the region |
z.gammat |
Real matrix (reps x MCMCreps) |
Posterior distribution for the latent indicator denoting whether the disease is present among the subzones |
z.taumat |
Real array (reps x H x MCMCreps) |
| Posterior distribution for the latent indicator denoting whether the disease is present among the clusters |
pimat |
Real array (reps x sum(k) x MCMCreps) |
Posterior distribution for the subject-level (or within-cluster) prevalence |
z.pimat |
Real array (reps x sum(k) x MCMCreps) |
| Posterior distribution for the latent indicators denoting whether the disease is present within any given cluster |
mumat |
Real matrix (reps x 4 x MCMCreps) |
Posterior distribution for the mean prevalence within diseased clusters |
psi |
Real scalar |
User-input psi value |
etamat |
Real matrix (reps x MCMCreps) |
Posterior distribution for the sensitivity of the diagnostic test |
thetamat |
Real matrix (reps x MCMCreps) |
| Posterior distribution for the specificity of the diagnostic test |
c1mat |
Real array (reps x sum(k) x MCMCreps) |
Posterior disribution for the latent indicators denoting true positive results from the diagnostic test |
c2mat |
Real array (reps x sum(k) x MCMCreps) |
| Posterior disribution for the latent indicators denoting true negative results from the diagnostic test |
mumh.tracker |
Real matrix (reps x 4) |
Vector of proportions of accepted Metropolis-Hastings proposals for the simulation from the posterior of input mu |
y |
Integer matrix (reps x sum(k)) |
| Matrix of observed counts of diseased subjects per cluster per simulated data set (or the actual observed counts input by the user) |
ForOthers |
Various other data not intended to be used by the user, but used to pass information on to the plot, summary, and print methods |
taumat, can be manipulated after it is
returned with the coda package after it is converted to an mcmc object.
| Parameter | (3-level) Description |
| (2-level) Description |
omega |
| Probability of disease being in the region. | Not used. |
gam |
Subzone-level (between-subzone) prevalence. |
| Probability of disease being in the region. |
z.gam |
| Subzone-level (between-subzone) prevalence latent indicator variable. | Not used. |
tau |
Cluster-level (between-cluster) prevalence. |
| Same as (3-level). |
z.tau |
| Cluster-level (between-cluster) prevalence latent indicator variable. | Same as (3-level). |
pi |
Subject-level (within-cluster) prevalence. |
| Same as (3-level). |
z.pi |
| Subject-level (within-cluster) prevalence latent indicator variable. | Same as (3-level). |
mu |
Mean prevalence among infected clusters. |
| Same as (3-level). |
psi |
(Related to) variability of prevalence among infected clusters (inversely related so higher psi -> lower variance of prevalences among diseased clusters). |
Same as (3-level). |
eta |
Diagnostic test sensitivity. |
| Same as (3-level). |
theta |
| Diagnostic test specificity. | Same as (3-level). |
c1 |
Latent count of true positive diagnostic test results. |
| Same as (3-level). |
c2 |
| Latent count of true negative diagnostic test results. | Same as (3-level). |
taumat instead of plain tau to denote that that variable is a
matrix (or, more generally an array) of values.EpiBayes_ns except
it stores the posterior distributions of all of the parameters in the model and
hence takes a bit longer to run.
This model is a Bayesian hierarchical model that serves two main purposes:
The posterior distributions are avaialable for a particular parameter, say
tau, by typing name_of_your_model$taumat.
Note: be careful about the size of the taumat matrix you are calling. The
last index of any of the variables from above is the MCMC replications and so we
would typically always omit the last index when looking at any particular variable.
tau) for the first replication, we will note that taumat is
a matrix with rows indexed by replication and columns by MCMC replications. Then,
we will type something like name_of_your_model$taumat[1, ] to visually
inspect the posterior distribution in the form of a vector. For the second
replication, we can type name_of_your_model$taumat[2, ], and so forth.
Then, we can make histograms of these distributions if we so desire by the
following code:
hist(name_of_your_model$taumat[1, ], col = "cyan");box("plot").
To observe a trace plot, we can type:
plot(name_of_your_model$taumat[1, ], type = "l")
for all of the MCMC replications and we can look
at the trace plot after a burnin of 1000 iterations by typing:
plot(name_of_your_model$taumat[1, -c(1:1000)], type ="l").
pi) for the tenth replication in the third cluster, we would
type name_of_your_model$pimat[10, 1, ] since the matrix containing the
posterior distributions for the subject-level prevalences are indexed by
replications in the first dimension, clusters in the second, and MCMC
replications in the third. We can make histograms and trace plots using the same
code as from above.
EpiBayes_ns stores less output so the user may run the model
more quickly, while losing the ability to diagnose any model fit or convergence
issues.
testrun_storage = EpiBayes_s(
H = 2,
k = rep(30, 2),
n = rep(rep(150, 30), 2),
seasons = rep(c(1, 2, 3, 4), each = 15),
reps = 10,
MCMCreps = 10,
poi = "tau",
y = NULL,
mumodes = matrix(c(
0.50, 0.70,
0.50, 0.70,
0.02, 0.50,
0.02, 0.50
), 4, 2, byrow = TRUE
),
pi.thresh = 0.05,
tau.thresh = 0.02,
gam.thresh = 0.10,
tau.T = 0,
poi.lb = 0,
poi.ub = 1,
p1 = 0.95,
psi = 4,
omegaparm = c(100, 1),
gamparm = c(100, 1),
tauparm = c(1, 1),
etaparm = c(100, 6),
thetaparm = c(100, 6),
burnin = 1
)
testrun_storage
print(testrun_storage)
testrun_storagesummary = summary(testrun_storage, prob = 0.90, n.output = 5)
testrun_storagesummary
plot(testrun_storage$taumat[1, 1, ], type = "l")
plot(testrun_storage$gammat[1, ], type = "l")
## Can look at all posterior distributions
plot(testrun_storage$pimat[1, 1, ], type = "l")
plot(testrun_storage$omegamat[1, ], type = "l")
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