# The Bayes System

`algo.bayes.Rd`

Evaluation of timepoints with the Bayes subsystem 1, 2, 3 or a self defined Bayes subsystem.

## Usage

```
algo.bayesLatestTimepoint(disProgObj, timePoint = NULL,
control = list(b = 0, w = 6, actY = TRUE,alpha=0.05))
algo.bayes(disProgObj, control = list(range = range,
b = 0, w = 6, actY = TRUE,alpha=0.05))
algo.bayes1(disProgObj, control = list(range = range))
algo.bayes2(disProgObj, control = list(range = range))
algo.bayes3(disProgObj, control = list(range = range))
```

## Arguments

- disProgObj
object of class disProg (including the observed and the state chain)

- timePoint
time point which should be evaluated in

`algo.bayes LatestTimepoint`

. The default is to use the latest timepoint- control
control object:

`range`

determines the desired timepoints which should be evaluated,`b`

describes the number of years to go back for the reference values,`w`

is the half window width for the reference values around the appropriate timepoint and`actY`

is a boolean to decide if the year of`timePoint`

also contributes`w`

reference values. The parameter`alpha`

is the \((1-\alpha)\)-quantile to use in order to calculate the upper threshold. As default`b`

,`w`

,`actY`

are set for the Bayes 1 system with`alpha`

=0.05.

## Value

- survRes
`algo.bayesLatestTimepoint`

returns a list of class`survRes`

(surveillance result), which includes the alarm value for recognizing an outbreak (1 for alarm, 0 for no alarm), the threshold value for recognizing the alarm and the input object of class disProg.`algo.bayes`

gives a list of class`survRes`

which includes the vector of alarm values for every timepoint in`range`

and the vector of threshold values for every timepoint in`range`

for the system specified by`b`

,`w`

and`actY`

, the range and the input object of class disProg.`algo.bayes1`

returns the same for the Bayes 1 system,`algo.bayes2`

for the Bayes 2 system and`algo.bayes3`

for the Bayes 3 system.

## Details

Using the reference values the \((1-\alpha)\cdot
100\%\) quantile of the
predictive posterior distribution is calculated as a threshold.
An alarm is given if the actual value is bigger or equal than this threshold.
It is possible to show using analytical computations that the predictive
posterior in this case is the negative
binomial distribution. Note: `algo.rki`

or `algo.farrington`

use two-sided prediction intervals -- if one wants to compare with
these procedures it is necessary to use an alpha, which is half the
one used for these procedures.

Note also that `algo.bayes`

calls
`algo.bayesLatestTimepoint`

for the values specified in
`range`

and for the system specified in `control`

.
`algo.bayes1`

, `algo.bayes2`

, `algo.bayes3`

call
`algo.bayesLatestTimepoint`

for the values specified in
`range`

for the Bayes 1 system, Bayes 2 system or Bayes 3 system.

`"Bayes 1"`

reference values from 6 weeks. Alpha is fixed a t 0.05.`"Bayes 2"`

reference values from 6 weeks ago and 13 weeks of the previous year (symmetrical around the same week as the current one in the previous year). Alpha is fixed at 0.05.`"Bayes 3"`

18 reference values. 9 from the year ago and 9 from two years ago (also symmetrical around the comparable week). Alpha is fixed at 0.05.

The procedure is now able to handle `NA`

's in the reference
values. In the summation and when counting the number of observed
reference values these are simply not counted.

## See also

`algo.call`

, `algo.rkiLatestTimepoint`

and `algo.rki`

for
the RKI system.

## Source

Riebler, A. (2004), Empirischer Vergleich von statistischen Methoden zur Ausbruchserkennung bei Surveillance Daten, Bachelor's thesis.

## Examples

```
disProg <- sim.pointSource(p = 0.99, r = 0.5, length = 208, A = 1,
alpha = 1, beta = 0, phi = 0,
frequency = 1, state = NULL, K = 1.7)
# Test for bayes 1 the latest timepoint
algo.bayesLatestTimepoint(disProg)
# Test week 200 to 208 for outbreaks with a selfdefined bayes
algo.bayes(disProg, control = list(range = 200:208, b = 1,
w = 5, actY = TRUE,alpha=0.05))
# The same for bayes 1 to bayes 3
algo.bayes1(disProg, control = list(range = 200:208,alpha=0.05))
algo.bayes2(disProg, control = list(range = 200:208,alpha=0.05))
algo.bayes3(disProg, control = list(range = 200:208,alpha=0.05))
```