scan_bayes_negbin_cpp: Calculate the "Bayesian Spatial Scan Statistic" by Neill et...
In scanstatistics: Space-Time Anomaly Detection using Scan Statistics

scan_bayes_negbin_cpp

R Documentation

Calculate the "Bayesian Spatial Scan Statistic" by Neill et al. (2006).

Description

Calculate the "Bayesian Spatial Scan Statistic" by Neill et al. (2006), adapted to a spatio-temporal setting. The scan statistic assumes that, given the relative risk, the data follows a Poisson distribution. The relative risk is in turn assigned a Gamma distribution prior, yielding a negative binomial marginal distribution for the counts.

Usage

scan_bayes_negbin_cpp(
  counts,
  baselines,
  zones,
  zone_lengths,
  outbreak_prob,
  alpha_null,
  beta_null,
  alpha_alt,
  beta_alt,
  inc_values,
  inc_probs
)

Arguments

`counts`	An integer matrix (most recent timepoint in first row).
`baselines`	A matrix with positive entries (most recent timepoint in first row).
`zones`	An integer vector (all zones concatenated; locations indexed from 0 and up).
`zone_lengths`	An integer vector.
`outbreak_prob`	A scalar; the probability of an outbreak (at any time, any place).
`alpha_null`	A scalar; the shape parameter for the gamma distribution under the null hypothesis of no anomaly.
`beta_null`	A scalar; the scale parameter for the gamma distribution under the null hypothesis of no anomaly.
`alpha_alt`	A scalar; the shape parameter for the gamma distribution under the alternative hypothesis of an anomaly.
`beta_alt`	A scalar; the scale parameter for the gamma distribution under the alternative hypothesis of an anomaly.
`inc_values`	A vector of possible values for the increase in the mean (and variance) of an anomalous count.
`inc_probs`	A vector of the prior probabilities of each value in `inc_values`.

Value

A list with elements priors (list), posteriors (list), and marginal_data_prob (scalar). The list priors has elements

null_prior: The prior probability of no anomaly.
alt_prior: The prior probability of an anomaly.
inc_prior: A vector (matrix with 1 row) of prior probabilities of each value in the argument m_values.
window_prior: The prior probability of an outbreak in any of the space-time windows.

The list posteriors has elements

null_posterior: The posterior probability of no anomaly.
alt_posterior: The posterior probability of an anomaly.
inc_posterior: A data frame with columns inc_values and inc_posterior.
window_posteriors: A data frame with columns zone, duration, log_posterior and log_bayes_factor, each row corresponding to a space-time window.
space_time_posteriors: A matrix with the posterior anomaly probability of each location-time combination.
location_posteriors: A vector (matrix with 1 row) with the posterior probability of an anomaly at each location.