Priors

Why priors are central in this model

The likelihood for VR counts depends on the product of the latent mortality rate and the reporting completeness:

$$\mu = E \cdot \lambda \cdot \rho.$$

Without additional information, many combinations of $\lambda$ and $\rho$ can produce the same $\mu$. This means priors are not a minor detail; they are part of what makes inference possible.

This vignette explains:

• which priors exist in the base model,
• what they mean, and
• how to change them using [vrc_priors()].

The prior interface

vrcmort uses a simple prior specification system inspired by rstanarm and epidemia.

You create a prior bundle with vrc_priors() and pass it into vrcm() or vrc_fit().

pri <- vrc_priors(
  beta_conf = normal(0.3, 0.2),
  beta_mort = normal(0, 0.5, autoscale = TRUE),
  gamma_rep = normal(0, 0.7, autoscale = TRUE),
  phi = exponential(1)
)

fit <- vrcm(
  mortality = vrc_mortality(~ facility),
  reporting = vrc_reporting(~ facility),
  data = vr_long,
  t0 = conflict_start_month,
  priors = pri,
  chains = 4,
  iter = 1000
)

You can inspect the resolved priors (after autoscaling) with:

vrc_prior_summary(fit)

Baseline completeness priors

The most influential priors are the baseline completeness terms $\kappa_{0,g}$ on the logit scale.

In the base model:

$$\text{logit}(\rho_{r,t,a,s,g}) = \kappa_{0,g} + \ldots$$

A practical way to think about this is that $\kappa_{0,g}$ sets the typical completeness before conflict starts.

If you have strong prior knowledge (for example from capture-recapture work, demographic methods, or historical audits), you should use it here.

In vrcmort the default priors are intentionally different for trauma and non-trauma (for $G=2$):

• trauma completeness is often lower (facility-based capture),
• non-trauma completeness can be higher pre-conflict.

To change these priors, provide a vector on the logit scale:

# Suppose you believe pre-conflict completeness is around:
# trauma ~ 0.6, non-trauma ~ 0.9
pri <- vrc_priors(
  kappa0 = normal(qlogis(c(0.6, 0.9)), c(0.6, 0.4))
)

Conflict effect priors

Mortality conflict effect (beta_conf)

The mortality submodel includes a conflict effect $\beta_{conf,g}$ on the log rate.

The base model constrains this parameter to be non-negative:

$$\beta_{conf,g} \ge 0.$$

This encodes a weak but important assumption: conflict should not reduce true mortality.

A typical weakly informative prior is a half-normal (implemented as normal() on a constrained parameter in Stan):

pri <- vrc_priors(
  beta_conf = normal(0.2, 0.3)
)

Reporting conflict effect (gamma_conf)

The reporting submodel includes $\gamma_{conf,g}$ on the logit completeness.

This can be either positive or negative. For non-trauma, it is often negative (conflict reduces completeness). For trauma, it can be closer to zero or even positive if conflict-related trauma is preferentially recorded.

pri <- vrc_priors(
  gamma_conf = normal(0, 0.5)
)

Random effect scale priors

Random effect standard deviations control how much regions and time periods are allowed to differ.

Examples:

• $\sigma^{(\lambda)}_{u,g}$: region variation in mortality
• $\sigma^{(\rho)}_{u,g}$: region variation in completeness
• $\sigma^{(\lambda)}_{v,g}$: smoothness of the national time random walk

The default priors are weakly regularising half-normals. You can tighten them if you find the model is over-fitting noise.

Dispersion priors

The observation model uses a negative binomial with dispersion parameter $\phi_g$ per cause.

In vrcmort we use an exponential prior on $\phi_g$:

$$\phi_g \sim \text{Exponential}(\text{rate}).$$

Smaller $\phi$ implies more over-dispersion. Larger $\phi$ approaches a Poisson model.

# More over-dispersion
pri <- vrc_priors(phi = exponential(2))

# Less over-dispersion (more Poisson-like)
pri <- vrc_priors(phi = exponential(0.5))

Age-selective reporting priors

The age-selective reporting penalty is implemented as a monotone sequence $\delta_a$ that is multiplied by post and applied to non-trauma completeness.

The priors on the increments and overall scale control how strongly the model is allowed to down-weight older ages post-conflict.

If your data clearly show older deaths disappearing from VR, loosening these priors can help the model explain the age shift through reporting rather than through implausible mortality changes.

Prior recipes

Here are three common prior bundles as starting points.

1. Conservative completeness collapse

Assume VR remains fairly complete post-conflict.

pri <- vrc_priors(
  kappa_post = normal(0, 0.3),
  delta_age_scale = normal(0, 0.5)
)

2. Strong reporting collapse for non-trauma

Assume non-trauma completeness drops sharply after conflict starts.

pri <- vrc_priors(
  kappa_post = normal(c(0, -1.5), c(0.5, 0.5)),
  gamma_conf = normal(c(0, -0.5), c(0.5, 0.5))
)

3. Strong prior that conflict increases trauma mortality

pri <- vrc_priors(
  beta_conf = normal(c(0.6, 0.1), c(0.3, 0.2))
)

These are not universally correct; the goal is to make your assumptions explicit and test sensitivity.