## Sites with warnings

Showing sites that are predicted to have accidents next year with probability or higher.

There are sites with warnings.

(Demonstration Mode)

Use historical data from local sites to find trends that predict which sites will become collision blackspots in the future, all while accounting for the characteristics at each site and statistical phenomena like regression to the mean. We provide advanced statistical modelling to assist your decision-making processes allowing you to implement safety measures at dangerous locations before it's too late.

Combining the expertise of leading transport software producers at PTV Group and academic knowledge from Newcastle University. The features demonstrated here are a prototype for a future add-in for PTV VISUM Safety

The partnership would also like to acknowledge the generous contribution from the Northumbria Safer Roads Initiative (NSRI) who have provided financial and in-kind support to the development of the software tools.

If you are a bit unsure about a part of the application, look out for our help tags.

You can *hover* over small help icons such as these:

Or you can *click or hover* on the larger help buttons like these:

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A full version will be released as an add-in to PTV Visum Safety. Sign up to our mailing list and we'll let you know when it's ready and how you can obtain a copy.

Register your interest734 sites from Halle, Germany.

435 sites from Suffolk, England.

Accident counts involving cyclists at 10 London sites.

Ensure your variable selection settings are correctly configured before testing your model.

The correlation between variables in the uploaded dataset:

Note that this correlation matrix only shows the correlation between numeric data in your dataset. Missing values are ignored when computing the correlations.

When validation mode is active, you can hide 1 or more years from the end of your dataset when fitting the model. The results section then shows what was forecasted to happen, and compares that with what was actually observed in the year that was hidden. Having predictions close to what was actually observed provides a good indication that the model is able to forecast well.

Select which of the available models you wish to use for the analysis:

This model is described as: $$ y_{year} \sim \mathrm{NegBin}\left( \frac{1}{e^{\tau(now-year)}}, \frac{\lambda_{year}}{e^{\tau(now-year)}-1} \right) $$ where $$ \lambda_{year} = a \mu_{year} \exp(-b(now-year)) $$

This model is described as: $$ y_{year} \sim \mathrm{NegBin}\left( \frac{1}{e^{\tau(now-year)}}, \frac{\lambda_{year}}{e^{\tau(now-year)}-1} \right) $$ where $$ \lambda_{year} \sim \mathrm{Gamma}(\mu_{year} \gamma \exp(-b(now-year)), \gamma) $$

Set the maximum number of IWLS iterations that can be peformed when fitting the Negative Binomial generalised linear model. This setting should be increased if an error message is returned stating that "glm.nb failed to converge within maxiter iterations", but it can lead to longer fitting times.

Prior distributions can be edited here and previewed at the bottom of the page. Vague prior distributions are used by default.

**Proceed with caution:**
Setting bad prior distributions can have a highly detrimental effect on the accuracy of your results! We recommend that you do not alter these settings unless you understand how they will affect the model.

The paramater controlling the variance inflation component of our model. Larger values indicate we are less trusting of past values

The parameter describing the site specific trend in accident counts.

The zero inflation component of the trend where the overall site specific trend is given by \(b=b_n \times b_z\). Smaller values indicate it is more likely for there to be no true site specific trend present.

These settings determine how long the simulation will take to complete and how accurate the results will be. For the purposes of this demo, we have reduced the default number of iterations that are performed. This allows results to be produced quickly for the purposes of a demonstration but they may not be as accurate as a longer analysis.

No dataset provided!

No sites selected!

Variable Selection has not been performed yet

You need to perform a simulation on the dataset by clicking on the "Run simulation" button above. Once the simulation has finished, the results will automatically appear here.

Click on a row in the results table above to open a plot of the results for that site. Plots appear in the "Site prediction plots" section below.

Click on a site in the results table above to view a plot of our predictions.

Showing sites that are predicted to have accidents next year with probability or higher.

There are sites with warnings.

The forecast probability table lists the probabiility of having X collisions in the next (forecasted) year, for each possible number of collisions, X.

For example, the first column, "0", lists the probabilities that each site has zero collisions next year; the next column, "1", lists the probabilities of each site having 1 collision; and so on. These probabilities correspond to the bar plots in each Site Prediction Plot.

Symbols will appear for each variable used to fit the
APM based on which significance levels the corresponsing
*p*-value falls between on this probability scale:

0 ★★★ 0.001 ★★ 0.01 ★ 0.05 ⚪ 0.01 1

This can be interpreted as:

- ★★★ =
*p*less than 0.001 - ★★ =
*p*between 0.001 and 0.01 - ★ =
*p*between 0.01 and 0.05 - ⚪ =
*p*between 0.05 and 0.1 - And
*p*greater than 0.1 in all other cases.

In the Global APM model, the \(\alpha\) parameter in the model accounts for discrepancies between the APM and the observed accident counts due to factors which were not, or could not, be monitored during the data collection phase. Click on a row in the results table to open a density histogram of \(\alpha\) values for the corresponding site.

Validation mode measurements are not available in forecasting mode

The scatter plot compares the expected number of accidents against what was actually observed at each of the sites. A strong correlation along the 1-to-1 line is a good indication that the model would have produced an accurate forecast.

Number of sites

Average forecast error

Overestimated

Underestimated

In 50% range

In 90% range

In 95% range

In 99% range

Mean square error

*R*^{2}

A histogram of exceedance probabilities for all the sites is provided. The exceedance probability is defined as the probability, according to the forecast distribution, of observing the actual number of accidents
*or more*
for the time period analysed by the validation mode.

The (mean) average exceedance probability from this dataset is .

The proportion of sites (solid red line, as a percentage) that lie within any given probability interval size. Ideally, this should be as close as possible to the 1:1 ratio (dotted line) across the range to indicate that probability interval sizes are accurate. We expect there to be some deviation at low probability interval sizes.

A full version will be released as an add-in to PTV Visum Safety. Sign up to our mailing list and we'll let you know when it's ready and how you can obtain a copy.

Register your interest