## Presence

The presence indicator estimates the number of people who are present (i.e. have a network event recorded) in a given area at some point during the time period of interest.

The usual resolution for this indicator is:

• Temporal: daily

This indicator can be used to monitor the variation in the number of people present in an area over time.

Calculation

We calculate the presence indicator using the presence aggregate, the number of unique subscribers recorded in a given area in a given period of time.

We can adjust the estimated number of subscribers present in an area with respect to the changes in the number of active subscribers in the area of interest.

We can also convert the indicator from the number of subscribers to the number of people present in an area using a static population figure, such as that produced by a census. We may also adjust the indicator for representation biases based on mobility errors estimated from survey data.

## Presence per square kilometre

The presence per square km estimates the density of people who are present in a given area at some point during the time period of interest, expressed as a number of people per square km.

The usual resolution for this indicator is:

• Temporal: daily

This indicator can be used to monitor the variation in the density of people in an area over time.

Calculation

We estimate the number of people in a given area using the presence aggregate as described above.

We then divide this by the size of the given area, in square kilometres, to derive the number of people per square kilometre.

We can adjust the estimated number of subscribers present in an area with respect to the changes in the number of active subscribers in the area of interest.

We can also convert the indicator from the number of subscribers to the number of people present in an area using a static population figure, such as that produced by a census. We may also adjust the indicator for representation biases based on mobility errors estimated from survey data.

## Presence difference

The presence difference indicator estimates the difference in the number of people who are present in an area during a given time period compared to the number present during a reference period. If the number of people present in the area has increased, the indicator will have a positive value; if the number has decreased, the value will be negative.

The usual resolution for this indicator is:

• Temporal: daily

This indicator can be used to determine the change in the number of people in a given area over time.

Calculation

We calculate the presence difference indicator from the presence aggregate and the baseline number of people during a reference period. The baseline can be calculated using the presence aggregate, for example by calculating the median number of unique subscribers present in a given area during the reference period.

We estimate the change in the number of unique subscribers by deriving the presence indicator from the presence aggregate as described above. We then subtract the baseline presence from the presence during the period of time of interest.

We can adjust the estimated number of subscribers present in an area with respect to the changes in the number of active subscribers in the area of interest.

We can also convert the indicator from the number of subscribers to the number of people present in an area using a static population figure, such as that produced by a census. We may also adjust the indicator for representation biases based on mobility errors estimated from survey data.

## Percent change in presence difference

The percentage change in presence indicator estimates the change in number of people present in an area during a time period relative to the number of residents in the reference period. The difference is expressed as a percentage of a baseline value calculated for the reference period. If the number of people present in the area has increased, the indicator will have a positive value; if the number has decreased, the value will be negative.

The usual resolution for this indicator is:

• Temporal: daily

This indicator can be used to monitor the variation in the number of people in an area over time.

Calculation

We calculate the percentage change in presence indicator using the presence aggregate and the baseline presence in the area during a reference period. The baseline can be calculated using the presence aggregate, for example by calculating the median number of unique subscribers during the reference period.

We estimate the difference in the number of unique subscribers relative to the baseline as described above for the presence difference indicator. We divide this difference by the baseline number of residents in the reference period and multiply by 100 to derive the percentage change.

We can adjust the estimated number of subscribers present in an area with respect to the changes in the number of active subscribers in the area of interest.

We can also convert the indicator from the number of subscribers to the number of people present in an area using a static population figure, such as that produced by a census. We may also adjust the indicator for representation biases based on mobility errors estimated from survey data.

## Abnormality

The presence abnormality indicator measures the deviation of the number of people present in a given area during a period of time relative to a reference period, expressed as a z-score. A positive value for this indicator greater than 3 indicates a statistically significant increase in the number of people present in a given area; a value less than -3 indicates a statistically significant decrease in presence.

The usual resolution for this indicator is:

• Temporal: daily

This indicator describes how unusual the number of people present in an area during a given time period is, given the amount of variation observed during the reference period. Higher absolute values indicate greater deviation from the normal variation in presence, and therefore greater probability that the change is meaningful. Such changes may be associated with specific events or may be caused by technical issues. Very large abnormalities (absolute values greater than 6), however, may also be indicative of a technical issue.

Calculation

We calculate the presence abnormality indicator using the presence aggregate and the baseline presence in the area during a reference period. The baseline can be calculated using the presence aggregate, for example by calculating the median number of unique subscribers during the reference period.

The presence abnormality is the z-score, or the number of standard deviations the number of unique subscribers present in an area in a given period is above or below the median number of subscribers in the reference period.

To calculate the z-score, we calculate the difference in presence relative to the baseline as described above for the presence difference indicator. We then divide this difference by the median absolute deviation (MAD) in the number of unique subscribers during the reference period.

We can adjust the estimated number of subscribers present in an area with respect to the changes in the number of active subscribers in the area of interest.

As this indicator is expressed as a z-score (i.e. a number of standard deviations) this indicator does not need to be scaled to the size of the population.

## Trips in

The trips in indicator estimates the number of trips into an area from any other areas during the same time period. This indicator could include multiple trips into an area by the same subscriber, unlike the travellers in indicator which only counts each unique subscriber once.

The usual resolution for this indicator is:

• Temporal: daily

This indicator can be used to monitor the variation in the number of trips into an area (inflows) from any other locations over time.

Calculation

We calculate the trips in indicator from the count of travellers aggregate as the sum of the counts of subscribers who were present in an area after being present in any other area during a given period of time.

We can adjust the estimated number of trips into an area with respect to the changes in the number of active subscribers in the area of interest.

We can also convert the indicator from the number of trips by subscribers to the number of trips by people between areas. We may also adjust the indicator for representation biases based on mobility errors estimated from survey data.

## Trips out

The trips out indicator estimates the number of trips from an area to any other area during the same time period. This indicator could include multiple trips out of an area by the same subscriber, unlike the travellers out indicator which only counts each unique subscriber once.

The usual resolution for this indicator is:

• Temporal: daily