Sites with warnings
Showing sites that are predicted to have accidents next year with probability or higher.
There are sites with warnings.
Hotspot Identification
(Demonstration Mode)
Identify hotspots before they happen
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.
A collaboration between PTV Group and Newcastle University
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.
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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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Let's keep in touch
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.
Preview of uploaded data
Variable Selection
Select the variables to use
Show helpTest-fit the accident prediction model
Ensure your variable selection settings are correctly configured before testing your model.
Options
Collision counts over time
Correlation Matrix
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.
Validation mode
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.
Current selection: Forecasting Mode
Model Selection
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 $$ \lambda_{year} \sim \mathrm{Gamma}(\mu_{year} \gamma \exp(-b(now-year)), \gamma) $$
GLM convergence
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 Distribution Settings
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.
\(\tau\)
The paramater controlling the variance inflation component of our model. Larger values indicate we are less trusting of past values
\(b_n\)
The parameter describing the site specific trend in accident counts.
\(b_z\)
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.
Prior distribution previews
Simulation settings
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.
Final Checks
No dataset provided!
No sites selected!
Variable Selection has not been performed yet
Perform simulation
Results
Where are my results?
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.
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.
Predicted number of accidents at each site
Tip:
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 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.
Plotting options
Site prediction plots
Click on a site in the results table above to view a plot of our predictions.
Plot interpretation guide
Clicking on a row in the results table opens more detailed plots for the corresponding site. You are provided with two plots:
- A time-series plot of accident counts
- A probability distribution of accidents in the next time period
Plots for an example site are shown below which we will use as an example. The data for this site contained accident counts each year from 2004 to 2012 (inclusive). The forecast is made for the next time period, which is the year 2013 in this example. The prediction interval size is set to 95% for these plots.
Time-series plot
The time-series plot shows the following features:
- Black points representing the observed number of accidents at this site in previous years.
- An orange line representing what the model calculated the expected (mean average) number of accidents was in each of the previous years once trend and regression to the mean has been taken into account. The shaded area around this line shows the uncertainty around this estimate— in this case, the 95% probability interval around the estimate of the mean.
- The red dot shows the expected (mean average) number of accidents for the time period being forecast (year 2013). The line extending above/below this point is a 95% probability interval to show the uncertainty around this estimate.
- A smaller cyan dot showing the modal number of accidents for the time period being forecast (year 2013). The modal number of accidents is always a whole number of accidents with the highest probability of occuring.
- A dashed green line showing what a standard accident prediction model (APM) believed would be the correct number of accidents in each of the observed years.
FAQ: Is there a trend to accident counts over time at my site?
Looking at the orange line can indicate whether accident counts are changing over time at a particular site. This was the average number of accidents expected at the site once regression to the mean has been filtered out. If the value of the orange line increases over time, this may indicate that accident counts are increasing over time. Conversely, a decreasing orange line may indicate accident counts are falling.
It must be noted that the model gives more weight (influence) to more recent observations, therefore the orange line will be more heavily influenced by the recent observations.
The expected number of accidents (orange line) is likely to increase or decrease by some amount over time—it rarely stays at the same level over time. The fact that this line is not level is not a guarantee that the accident count is changing significantly over time. Wide probability intervals and shallow orange lines will often suggest there is no significant change in the accident rate over time.
FAQ: Why is the expected number of accidents outside of its 50% probability range? Or, why do I have no probability interval around my forecast?
This can happen when you use a small probability interval and the probability distribution for next year's accident count is highly skewed to low values. The probability interval for next year's forecast is constructed as a "highest probability interval" to give the narrowest and most useful range. This means starting from the most likely accident count (the mode) and widening the range until at least 50% of the greatest probabilities are covered by this range. For a site that often has zero accidents, there could be, for example, a 60% chance of zero accidents occuring next year. In which case, the 50% probability interval will already be covered in the range [0, 0], while the mean of this probability distribution will be above zero. The mode will always be inside the probability interval.
FAQ: How can a site expect to have 3.47 accidents next year?
The expected number of accidents (red dot on the plot) is a statistical mean of a probability distribution and will almost never be a whole number. The probability distribution considers every possible number of accidents that could occur in the next year, from zero accidents to the terrifying prospect of an infinite number of accidents, and how likely each of these outcomes is likely to occur. The mean accounts for all possible outcomes and their likelihoods to give the best way of representing an average number of accidents for this site in the next year, even though you'll never see 0.47 of an accident next year.
Probability distribution of accidents
The probability distribution shows the probability of observing that number of accidents in the forecasted time period.
The modal bar is the longest—this is the most likely number of accidents that will happen next year. It corresponds with the small cyan point on the time-series plot.
The key things to look at in this probability distribution is where the bars are longest—to indicate what quantity of accidents are most likely in the next time period—and how spread out the bars are—if the distribution is spread out over a wide range, this indicates large uncertainty around the modal number of accidents.
The time series plot and probability distribution of accidents are designed to have the same scale used for accidents on the y-axis for each site. This is to allow you to directly compare the probability distribution of accidents against the accidents in the time series plot.
Site Warnings
Forecast probability table
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.
Results From Accident Prediction Model
Significance codes
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.
Summary of site discrepancy factors
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.
Feature not available
Validation mode measurements are not available in forecasting mode
Expectation vs. Reality
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.
Validation measures
Number of sites
Average forecast error
Overestimated
Underestimated
In 50% range
In 90% range
In 95% range
In 99% range
Mean square error
R2
Exceedance probability
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 .
Probability interval accuracy
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.
Let's keep in touch
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