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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="author" content="Fabienne Krauer" />
<meta name="date" content="2022-09-03" />
<title>Bayesian workflow for fitting SEIR models using the BayesianTools package</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8).
document.addEventListener('DOMContentLoaded', function(e) {
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a = h.attributes;
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});
</script>
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) 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<h1 class="title toc-ignore">Bayesian workflow for fitting SEIR models
using the BayesianTools package</h1>
<h4 class="author">Fabienne Krauer</h4>
<h4 class="date">2022-09-03</h4>
</div>
<div id="intro" class="section level2">
<h2>Intro</h2>
<div id="the-bayesian-workflow" class="section level3">
<h3>The Bayesian workflow</h3>
<p>The <a href="https://arxiv.org/abs/2011.01808">Bayesian workflow</a>
was proposed by Andrew Gelman, Aki Vehtari and others, and describes the
process of model building, inference and model checking/improvement. The
Bayesian workflow is not a straight line but an iterative process of
checking and refining or discarding components of the model.</p>
<p>Why should I follow the workflow? Bayesian inference for IDD models
is hard, and most models are too complex to be fitted without any
problems. The workflow helps to narrow down where the problem is and may
help to improve inference.</p>
<p>The process can be summarised as follows (for a graphical
representation, see Gelman’s publication):</p>
<ol style="list-style-type: decimal">
<li>Define a model</li>
<li>Define the prior and perform a prior predictive check, modify the
prior if necessary</li>
<li>Fit the model</li>
<li>Validate the computation (diagnostics)</li>
<li>Address potential issues with computation (MCMC)</li>
<li>Evaluate the model fit: posterior predictive intervals</li>
<li>Modify the model and/or the prior if necessary, or add/change the
data</li>
<li>Compare models</li>
</ol>
<p>We will go through some of these steps with an easy example
below.</p>
</div>
<div id="the-bayesiantools-package" class="section level3">
<h3>The BayesianTools package</h3>
<p><a href="https://cran.r-project.org/web/packages/BayesianTools/BayesianTools.pdf">BayesianTools</a>
is a general purpose R package, which offers various MCMC and SMC
samplers, as well as plot and diagnostic functions for Bayesian
statistics, with a particular focus on calibrating complex system
models. BT is a modular package, where the user defines the likelihood
function and the priors separately. It does not require the use of
domain-specific language (such as Stan).</p>
<p>Samplers: 1) standard Metropolis-Hastings (MH) 2) adaptive
Metropolis-Hastings 3) standard or adaptive Metropolis-Hastings with
delayed rejection 4) standard Metropolis-Hastings with Gibbs updating 5)
standard Metropolis-Hastings with Gibbs updating and tempering 6)
Differential Evolution (DE), optional with snooker update (DEzs) 7)
Differential Evolution Adaptive Metropolis (DREAM) 8) t-walk MCMC 9)
Sequential Monte Carlo (SMC)</p>
<p>Delayed rejection sampling means that a second (or third, etc.)
proposal is made before rejection. This second proposal is drawn from a
different distribution, allowing for a greater flexibility of the
sampler.</p>
<p>Gibbs sampling means that in each iteration, only a subset of the
parameters is updated.</p>
<p>Tempering is similar to simulated annealing, and means that the
acceptance rate is increased during the burnin phase. This should help
to speed up convergence.</p>
<p>Differential Evolution algorithms are genetic algorithms with
multiple chains, which inform each other during the burnin phase. If in
doubt which one to choose, prefer “DEzs”. The DE sampler uses the
current position of two other chains to generate the proposal for each
chain. DEzs also uses past states of the two other chains in the
creation of the proposal. This allows for fewer chains (i.e. 2x3 chains
are usually enough for up to 200 parameters).</p>
</div>
</div>
<div id="workflow" class="section level2">
<h2>WORKFLOW</h2>
<p>First we load the required libraries and set a seed:</p>
<pre class="r"><code>library(deSolve)
library(tidyverse)</code></pre>
<pre><code>## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──</code></pre>
<pre><code>## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.7 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1</code></pre>
<pre><code>## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()</code></pre>
<pre class="r"><code>library(BayesianTools)
library(coda)
set.seed(42)</code></pre>
<div id="model" class="section level3">
<h3>Model</h3>
<p>We start by defining the model. This is a simple SEIR model without
demographic changes and permanent immunity:</p>
<pre class="r"><code>model_SEIR <- function(times, inits, theta) {
SEIR <- function(times, inits, theta) {
S = inits[["S"]]
E = inits[["E"]]
I = inits[["I"]]
R = inits[["R"]]
N = S + E + I + R
beta <- theta[["beta"]]
sigma <- theta[["sigma"]]
gamma <- theta[["gamma"]]
dS <- -beta*S*I/N
dE <- beta*S*I/N - sigma*E
dI <- sigma*E - gamma*I
dR <- gamma*I
dC <- beta*S*I/N
list(c(dS, dE, dI, dR, dC))
}
traj <- data.frame(lsoda(inits, times, SEIR, theta))
# Calculate the incidence per time step from the cumulative state:
traj$inc <- c(inits["I"], diff(traj$C))
return(traj)
}</code></pre>
<p>Next, we define the parameters and the initial conditions for the
model. The initial conditions assume that everyone is susceptible,
except one person, which is the first infectious individual:</p>
<pre class="r"><code>beta <- 0.55 # transmission rate
sigma <- 1/5 # =1/duration of latency
gamma <- 1/5 # = 1/duration of infectiousness
theta <- c(beta=beta, sigma=sigma, gamma=gamma) # combine in one vector "theta"
inits <- c("S"=10000-1, "E"=0, "I"=1, "R"=0, "C"=1) </code></pre>
<p>We the define the time points at which the ODE solution is saved.
Note, the unit of the time steps MUST BE the same as the unit of your
parameters, i.e. if <span class="math inline">\(\gamma\)</span> = 1/5
days, then one time step (e.g. 1 to 2) is 1 day. Also remember that
integration is computationally costly, so save only the time steps you
need.</p>
<pre class="r"><code>times <- seq(1:100)</code></pre>
<p>Run model once and plot the trajectory:</p>
<pre class="r"><code>traj <- model_SEIR(times, inits, theta)</code></pre>
<p>This is a closed population model. It is always a good idea to do a
“sanity check”: the sum of all states must be constant and equivalent to
the total number of individuals. If it increases or decreases, there is
probably a mistake in your model code.</p>
<pre class="r"><code>summary(rowSums(traj[,c(2:5)]))</code></pre>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10000 10000 10000 10000 10000 10000</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="data" class="section level3">
<h3>Data</h3>
<p>We now generate some data from the model (“synthetic data”) for the
fitting process. The advantage of simulated data is that you know the
“true” parameter values that generated the data, which makes learning
about inference easier.</p>
<p>Since case data are commonly count data, we here assume that the
observation process is a Poisson process:</p>
<pre class="r"><code>data <- data.frame(obs=sapply(traj$inc, function(x) rpois(1, x)),
time = times)</code></pre>
<p>and plot the generated data and the modelled trajectory:</p>
<pre class="r"><code>ggplot() +
geom_line(data=traj, aes(x=time, y=inc)) +
geom_point(data=data, aes(x=time, y=obs))</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="priors" class="section level3">
<h3>Priors</h3>
<p>We now define the prior distributions. For convencience, we define
the lower and upper limits for ALL parameter, even if we don’t fit them
all initially. You should carefully think about the bounds of each
parameter, and whether they make sense from a mechanistic/biological
point of view.</p>
<pre class="r"><code># Estimated params
estpars <- c("beta", "sigma") # parameters to estimate, can be modified
index <- which(names(theta) %in% estpars) # index of estimated params
# Priors
lower = c("beta"=0, "sigma"=0)
upper = c("beta"=0.5, "sigma"=0.1)</code></pre>
<p>We then create a prior object. BT has a function to
<code>createUniformPrior()</code> to generate uniform priors for all
parameters. It is a good starting point, but you often need to define
other distributions for some priors.</p>
<pre class="r"><code># Create uniform prior
prior_unif <- createUniformPrior(lower=lower,
upper=upper)</code></pre>
</div>
<div id="prior-predictive-check" class="section level3">
<h3>Prior predictive check</h3>
<p>Before we do any fitting, it is often useful to check whether the
prior distributions you have chosen actually generate a model trajectory
that overlaps with the data. If your prior is poorly specified, getting
a posterior is not possible. We can do this by sampling from the prior
and forward simulating the model trajectory with the sampled values.
This is called the prior predictive check. The following function does
this (cave: it’s slow and not optimised) and summarises the min and max
trajectory values for each time step in the model. (You can also choose
to sample <code>prob = c(0.025, 0.975)</code>, which will result in a
95% interval). The observation process (here a Poisson) is also included
to account for the observation uncertainty:</p>
<pre class="r"><code>sample_prior_Pois <- function(prior, model, times, inits,
theta, index, estpars, nsims) {
traj <- vector("list", nsims)
for (i in 1:nsims) {
theta_est <- prior$sampler() # sample from the prior
names(theta_est) <- estpars
theta_updated <- c(theta[-index], theta_est)
inc <- match.fun(model)(times, inits, theta_updated)[,c("inc")]
inc_obs <- sapply(inc, function(x) rpois(1, x))
traj[[i]] <- inc_obs
}
trajdf <- t(plyr::ldply(traj, rbind))
quantiles <- data.frame(t(apply(trajdf, 1, quantile, prob = c(0.0, 1.0))))
quantiles$time <- times
colnames(quantiles)[1:2] <- c("min", "max")
return(quantiles)
}</code></pre>
<p>Let’s sample and plot:</p>
<pre class="r"><code>priorpred <- sample_prior_Pois(prior_unif, model_SEIR, times, inits,
theta, index, estpars, nsims=500)
ggplot() +
geom_point(data=data, aes(x=time, y=obs)) +
geom_ribbon(data=priorpred, aes(x=time, ymin=min, ymax=max), alpha=0.5, fill="red")</code></pre>
<p><img 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width="672" /></p>
<p>The prior predictive does not include all the data points, which is
no surprise given that the “true” parameter values are outside the prior
range.</p>
<p>Let’s update the prior ranges and redo the prior predictive:</p>
<pre class="r"><code># Priors
lower = c("beta"=0, "sigma"=0)
upper = c("beta"=5.0, "sigma"=1.0)
prior_unif <- createUniformPrior(lower=lower,
upper=upper)
priorpred <- sample_prior_Pois(prior_unif, model_SEIR, times, inits,
theta, index, estpars, nsims=500)
ggplot() +
geom_point(data=data, aes(x=time, y=obs)) +
geom_ribbon(data=priorpred, aes(x=time, ymin=min, ymax=max), alpha=0.5, fill="red")</code></pre>
<p><img 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" width="672" /></p>
<p>This time the data range is covered in the prior predictive, meaning
that the prior boundaries are well chosen. The prior predictive also
reveals that a lot of parameter samples will lead to trajectories far
away from the data. This can potentially make the inference process more
challenging if you have a large number of parameters to estimate. You
may have to adjust the prior in the process of the fitting, to
facilitate the sampling.</p>
</div>
<div id="likelihood-function" class="section level3">
<h3>Likelihood function</h3>
<p>The log-likelihood function is the core of Bayesian inference. Again,
we are assuming the observations arise from a Poisson process (count
data). In BT, you need to define a function that takes the parameters
and returns a single log-likelihood value:</p>
<pre class="r"><code>ll_Pois <- function(model, theta, inits, times, data) {
traj <- match.fun(model)(times, inits, theta)
datapoint <- data$obs
modelpoint <- traj$inc
if (any(is.na(modelpoint))) {
ll <- -Inf
}
else { # Minimize the log likelihood
ll <- sum(dpois(x=datapoint,
lambda=modelpoint,
log=TRUE), na.rm=TRUE)
}
return(ll)
}</code></pre>
<p>You should always test the LL function:</p>
<pre class="r"><code># test
ll_Pois(model_SEIR, theta, inits, times, data)</code></pre>
<pre><code>## [1] -306.7037</code></pre>
<p>We also have to define a wrapper function for the log-likelihood
function, because BT requires that the LL-function takes only one
argument, which are the estimated parameters. Remember to adjust this
function when you change the names of the arguments of the likelihood
function:</p>
<pre class="r"><code>ll_Pois_wrapper <- function(par) {
parX = theta
parX[index] = par
return(ll_Pois(model=model_SEIR,
theta=parX,
inits=inits,
times=times,
data=data))
}
# Test (should return the same as ll_pois())
ll_Pois_wrapper(theta[index])</code></pre>
<pre><code>## [1] -306.7037</code></pre>
</div>
<div id="set-up-and-run-the-mcmc" class="section level3">
<h3>Set up and run the MCMC</h3>
<p>Finally, we define the setup for the sampler and run the MCMC. We
here choose the simplest sampler (standard Metropolis Hastings), and run
3 chains with 20_000 iterations each. It is not always easy to determine
the number of iterations to run, the best thing to do is to start with
something like 20_000 iterations (for random walk samplers only. For
gradient-based samplers like HMC/NUTS you can start with 1000). We also
want to run more than one chain to determine convergence.</p>
<p>Note that I have suppressed the messages to the console for this
tutorial with <code>message = FALSE</code>, but you should have message
enabled (the default) to monitor the progress of the fitting.</p>
<pre class="r"><code>mcmc_settings1 <- list(iterations = 20000,
nrChains = 3,
message = FALSE,
optimize=FALSE,
adapt=FALSE)
bayesianSetup_unif <- createBayesianSetup(prior = prior_unif,
likelihood = ll_Pois_wrapper,
names = names(theta[index]),
parallel = FALSE)
system.time({chain_unif1 <- runMCMC(bayesianSetup = bayesianSetup_unif,
sampler = "Metropolis",
settings = mcmc_settings1)})</code></pre>
<pre><code>## user system elapsed
## 144.91 0.37 145.73</code></pre>
</div>
<div id="diagnostics" class="section level3">
<h3>Diagnostics</h3>
<p>The first thing you do is to visually inspect the trace plots:</p>
<pre class="r"><code>plot(chain_unif1)</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>The chains seem to have converged, but the mixing is very poor (no
caterpillar), the chains stick too long in one place suggesting that the
proposal is poorly chosen.</p>
<p>The summary also shows that the rejection rate is very high:</p>
<pre class="r"><code>summary(chain_unif1)</code></pre>
<pre><code>## # # # # # # # # # # # # # # # # # # # # # # # # #
## ## MCMC chain summary ##
## # # # # # # # # # # # # # # # # # # # # # # # # #
##
## # MCMC sampler: Metropolis
## # Nr. Chains: 3
## # Iterations per chain: 20000
## # Rejection rate: 0.997
## # Effective sample size: 15
## # Runtime: 145.65 sec.
##
## # Parameters
## psf MAP 2.5% median 97.5%
## beta 172.340 0.565 0.492 0.600 4.766
## sigma 28.311 0.187 0.009 0.197 0.720
##
## ## DIC: Inf
## ## Convergence
## Gelman Rubin multivariate psrf: 969.21
##
## ## Correlations
## beta sigma
## beta 1.000 0.791
## sigma 0.791 1.000</code></pre>
<p>We will thus try a adaptive MCMC, which alters the proposal
distribution during the fit, and also extend the iterations:</p>
<pre class="r"><code>mcmc_settings2 <- list(iterations = 50000,
nrChains = 3,
message = FALSE,
optimize=FALSE,
adapt=TRUE)
system.time({chain_unif2 <- runMCMC(bayesianSetup = bayesianSetup_unif,
sampler = "Metropolis",
settings = mcmc_settings2)})</code></pre>
<pre><code>## user system elapsed
## 344.28 0.82 345.76</code></pre>
<pre class="r"><code>plot(chain_unif2)</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>Including the adaptation of the proposal has improved the mixing
substantially. We remove the first 10_000 iterations (burn-in
phase):</p>
<pre class="r"><code>nburn <- 15000
plot(chain_unif2, parametersOnly = TRUE, start =nburn)</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<pre class="r"><code>summary(chain_unif2)</code></pre>
<pre><code>## # # # # # # # # # # # # # # # # # # # # # # # # #
## ## MCMC chain summary ##
## # # # # # # # # # # # # # # # # # # # # # # # # #
##
## # MCMC sampler: Metropolis
## # Nr. Chains: 3
## # Iterations per chain: 50000
## # Rejection rate: 0.868
## # Effective sample size: 400
## # Runtime: 345.7 sec.
##
## # Parameters
## psf MAP 2.5% median 97.5%
## beta 1.001 0.562 0.412 0.561 0.612
## sigma 1.001 0.189 0.154 0.190 0.546
##
## ## DIC: 457.843
## ## Convergence
## Gelman Rubin multivariate psrf: 1.002
##
## ## Correlations
## beta sigma
## beta 1.000 -0.878
## sigma -0.878 1.000</code></pre>
<p>The rejection rate is much better and the effective sample size (ESS)
has also increased. The ESS is an estimate for the number of independent
samples (taking into account autocorrelation of the individual samples)
generated by the MCMC run. There is no universal threshold for how large
the ESS should be, but you should aim for at least 100 independent
samples.</p>
<p>We then check convergence mathematically with the PSRF. The PSRF
gives the scale reduction factor for each parameter. A PSRF of 1 means
that variance between and within the chains are equal, which is the
goal. As a rule of thumb, a if PSRF < 1.05, convergence is very
likely. But you should always also check the traceplots</p>
<pre class="r"><code>gelmanDiagnostics(chain_unif2, plot=FALSE, start=nburn)</code></pre>
<pre><code>## Potential scale reduction factors:
##
## Point est. Upper C.I.
## beta 1 1
## sigma 1 1
##
## Multivariate psrf
##
## 1</code></pre>
<p>It is also advised to check parameter correlations. Sometimes these
correlations can make inference more challenging, i.e. the posterior is
too complex with several local modes. In that case, you may need to
re-formulate (reparametrize) the model or run the chains for longer.
However, ODE models are difficult to reparametrize.</p>
<p>Depending on what the purpose of the model inference is, parameter
correlation is a larger or smaller problem. If we are not too concerned
about the mechanistic meaning of the parameters, we may accept some
degree of parameter correlation. If we are intersted in learning about
the mechanisms underlying the disease data, we may need to add
additional data for the fitting and/or change the priors to narrow down
the parameter space and reduce correlation.</p>
<pre class="r"><code>correlationPlot(chain_unif2, start=nburn)</code></pre>
<pre><code>## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter</code></pre>
<p><img 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" width="672" /></p>
<p>In this example, the parameters are strongly correlated, but 1) We
still have convergence of the chains 2) We know the posteriors are
correct 3) We cannot reparametrize this model.</p>
<p>Thus, we will leave the model as it is and accept the parameter
correlation. However, in a real life study, we would want to reduce this
correlation.</p>
<p>We can also check the summary statistics of the marginal posteriors.
For this, we need to convert the chain to a coda object and summarize.
For a description of the marginal posteriors, we commonly use the median
and the equal tailed 95% CrI (credible interval), which is the 2.5% and
97.5% percentile:</p>
<pre class="r"><code>coda2 <- getSample(chain_unif2, parametersOnly = TRUE, coda=TRUE, start=nburn)
summary(coda2)</code></pre>
<pre><code>##
## Iterations = 15000:50000
## Thinning interval = 1
## Number of chains = 3
## Sample size per chain = 35001
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## beta 0.5649 0.02225 6.865e-05 0.0003852
## sigma 0.1882 0.01798 5.548e-05 0.0003050
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## beta 0.5264 0.5493 0.5631 0.5788 0.6138
## sigma 0.1534 0.1759 0.1880 0.2003 0.2244</code></pre>
<p>Alternatively, you can choose the highest posterior density interval.
We have to combine the chains to get an overall estimate:</p>
<pre class="r"><code>HPDinterval(mcmc(do.call(rbind, coda2)))</code></pre>
<pre><code>## lower upper
## beta 0.5235397 0.6100183
## sigma 0.1512821 0.2217040
## attr(,"Probability")
## [1] 0.9500014</code></pre>
</div>
</div>
<div id="evaluating-the-model-fit" class="section level2">
<h2>Evaluating the model fit</h2>
<p>If the chains are healthy and converged, and the marginal posterior
distributions are reasonable, we can check the fit to the data by
evaluating the posterior predictive. The posterior predictive
distribution is generated by taking random draws from the posterior and
forward simulating the model trajectory. The simulated trajectories are
then summarised over each time step in the model by calculating the
percentiles, e.g. 2.5th and 97.5th percentile. The resulting uncertainty
is called the (95%) posterior predictive interval.</p>
<p>The following function calculates the quantiles from a given model
and posterior:</p>
<pre class="r"><code>sample_posterior_Pois <- function(chain, theta, inits, times, model, ndraw, nburn, progress) {
#Draw n fitted parameter vectors theta from the MCMC object
sample <- getSample(chain, parametersOnly = TRUE, thin=1, numSamples=ndraw, start=nburn)
fit <- plyr::adply(.data=sample, .margins=1, .progress=progress, .parallel=F, .fun=function(x) {
#Define the theta as the estimated parameters from the current draw and the fixed parameters
theta_sample <- c(x, theta[!is.na(theta)])
#Simulate trajectory for selected theta
foo <- match.fun(model)(times, inits, theta_sample)
foo$simobs <- sapply(foo$inc, function(y) rpois(n=1, lambda=y))
return(foo)
})
colnames(fit)[1] <- "replicate"
quantiles <- plyr::ddply(.data=fit,
.variables="time",
function(x) quantile(x[, which(colnames(fit)=="simobs")], prob = c(0.025, 0.5, 0.975), na.rm=T))
colnames(quantiles) <- c("time", "low95PPI", "median", "up95PPI")
return(quantiles)
}</code></pre>
<p>Check the fit. Note that I use <code>progress="none"</code> to
suppress the messages in the markdown file, but you should always
monitor the progress with <code>progress="text"</code></p>
<pre class="r"><code>fit_quantiles <- sample_posterior_Pois(chain_unif2, theta, inits, times, model_SEIR, ndraw=500, nburn=nburn, progress="none")
# Plot fit
ggplot() +
geom_point(data=data, aes(x=time, y=obs)) +
geom_line(data=fit_quantiles, aes(x=time, y=median), color="red") +
geom_ribbon(data=fit_quantiles, aes(x=time, ymin=low95PPI, ymax=up95PPI), alpha=0.2, fill="red")</code></pre>
<p><img 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" width="672" /></p>
<div id="final-assessment" class="section level3">
<h3>Final assessment</h3>
<ol style="list-style-type: decimal">
<li>Does the trajectory fit look good?</li>
<li>Is the chain mixing healthy?</li>
<li>Have the chains converged?</li>
<li>Are the marginal posteriors are biologically meaningful, unimodal
and informative (not too wide)?</li>
</ol>
<p>In this example, we would conclude that the requirements are met and
that we would keep the final model and chains. If the fit were poor, we
would need to reformulate the model and/or the prior distributions,
and/or add more data for fitting, or choose a different MCMC algorithm.
More complex models are often difficult to fit with a Metropolis
algorithm. Genetic algorithms, parallel tempering or gradient-based
methods such as HMC/NUTS are more appropriate in these cases.</p>
<p>If the chains do not converge, it is often a problem of a complex
posterior geometry due to a complex log likelihood surface. Tightening
the priors can remove some of these issues, but it is useful to first
investigate the log likelihood surface of the parameters of interest to
understand how the priors should be adjusted. Strictly speaking, the
prior should be independent of the data (i.e. the log likelihood), but
in reality you sometimes need to adjust the prior to get convergence at
all for ODE models.</p>
</div>
</div>
<div id="advanced-usage" class="section level2">
<h2>Advanced usage</h2>
<div id="custom-priors" class="section level3">
<h3>Custom priors</h3>
<p>Let’s assume we would have to modify the priors to make them more
informative. In BT, if you want a custom prior, you have to write out a
designated density and sampler function. We will choose a truncated
normal NT(0.5, 0.1) distribution for <span class="math inline">\(\beta\)</span>, and a Beta(2,5) distribution for
<span class="math inline">\(\sigma\)</span>. Check <a href="https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html">here</a>
and <a href="https://homepage.divms.uiowa.edu/~mbognar/applets/beta.html%20and">here</a>
to understand what these priors look like.</p>
<p>First we define the density function, which returns the joint
(summed) values of the density functions of the sampled parameters:</p>
<pre class="r"><code>density <- function(par) {
return(
msm::dtnorm(par[1], # Beta
mean = 0.5,
sd = 0.1,
lower = lower[["beta"]],
upper = upper[["beta"]],
log = TRUE) +
dbeta(par[2], # Sigma
shape1 = 2,
shape2 = 5,
log = TRUE)
)
}</code></pre>
<p>The sampler function draws one sample from the defined prior
distributions. Cave: ensure that the order of the parameters in the
density function corresponds to the order in
<code>theta[index]</code>:</p>
<pre class="r"><code>sampler <- function(n=1){
return(cbind(
msm::rtnorm(n, # Beta
mean = 0.5,
sd = 0.1,
lower = lower[["beta"]],
upper = upper[["beta"]]),
rbeta(n, # Sigma
shape1 = 2,
shape2 = 5)
))
}</code></pre>
<p>We then define a new prior object:</p>
<pre class="r"><code>prior_custom <- createPrior(density=density,
sampler=sampler,
lower=lower,
upper=upper)</code></pre>
<p>Now update the Bayesian setup and fit again:</p>
<pre class="r"><code>bayesianSetup_custom <- createBayesianSetup(prior = prior_custom,
likelihood = ll_Pois_wrapper,
names = names(theta[index]),
parallel = FALSE)
system.time({chain_custom <- runMCMC(bayesianSetup = bayesianSetup_custom,
sampler = "Metropolis",
settings = mcmc_settings2)})</code></pre>