By: Ron Smith (CEH) and Anders L. Madsen (HUGIN)
13 September 2016
Cryptosporidium parasites are a major cause of enteric disease in neonatal livestock and are also major contaminants of the environment and water supplies in particular. The parasites can survive for 18 months to 2 years in water and are a source of infection for people. Normal water treatments such as chlorination are not effective against Cryptosporidium and the parasite is a major issue for water companies.
The main aim of this research, undertaken in collaboration with The Crown Estate (owners of the Glenlivet Estate), the Moredun Research Institute and Scottish Water, is to examine whether nature-based interventions within the catchment areas could improve the quality and safety of water supplies by minimizing this contamination.
There are a set of directions, available from the website of the Drinking Water Quality Regulator for Scotland, which includes a framework for assessing the risk of Cryptosporidium in public water supplies in Scotland, and shows how to assign a score to an individual water supply depending on the assessed risk.
The work illustrated here translates the framework for a surface water risk assessment within the Cryptosporidium (Scottish Water) Directions 2003 into a BBN. This is a deterministic scoring system where every question has a single answer. The second part adds in a degree of uncertainty in both the answers and the interpretation of the scores. This is an academic exercise to explore how the recognition of uncertainty in some of the answers could alter the outcome.
Below are some HUGIN widgets for interacting with the model. Under the Scores tab you will find the deterministic scores model and under the Uncertainty tab you will find a model extended with a degree of uncertainty.
In the Scores tab you replace the --select-- by one entry from the drop-down menu which is your assessment of the single state applicable to the whole catchment, so for cattle you choose one of none, less than 1 per hectare, more than one per hectare, and unknown. This is the assessment of the number of cattle within the catchment over the entire year. If you do not enter any value, each state is assumed to be equally likely (i.e., the variable has a uniform prior probability distribution), so the score system only works once there is an entry for every input variable. Once this is done, the model will produce a single value for each score (animals, agricultural practice, discharges and catchment management).
In the equivalent entry under the Uncertainty tab, you can either select a single state as before, or you can change the weighting of the states of a variable using the number entry fields. The easiest way of thinking about this is that you are assessing how much of that catchment is in each of the allowed states, so you can enter percentages such as 10 in none, 40 in less than 1 per hectare, 30 in more than one per hectare, and 20 in unknown. The numbers you enter will always be translated into proportions, so if your percentages did not add up to 100 then they will be adjusted inside the computer code. These choices have only been implemented in the Animals column of the Uncertainty model. Technically, the numbers entered are interpreted as likelihoods on the variable with uniform prior probability distribution. The consequence is that the prior distribution used in the model is equal to the (normalized) distribution specified by the user. This version also allows for uncertainty in the appropriate score value assigned to the state of a variable in the Animals column. For example, Cattle at more than one per hectare normally score 12, but in some circumstances maybe another score value such as 11 or 13 would be better. This is achieved by moving away from a one-to-one match of score to state and allowing the model to use a probability distribution over the possible score values for each state of the variable.
Once the scores from all the raw water categories have been added together, the Cryptosporidium (Scottish Water) Directions 2003 prescribe a raw water monitoring frequency related to the surface water score and the throughput of the water plant. This monitoring frequency is a (non-monetary) measure of the risk perceived by the particular configuration of activities within the water catchment. In the Scores model, this will be a single risk category as specified by the monitoring frequency. However, in the Uncertainty model there can be a (posterior) distribution of risk measures indicating the uncertainty around the risk evaluation given the model chosen and the data that have been input.
Useful references for those interested in BBN include:
Kjærulff, U. B. and Madsen, A. L. (2013) Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Springer, Second Edition.
For further details on the paper: Ron Smith
For further details on the use of Bayesian networks and web deployment of models contact: Anders L Madsen (alm(at)hugin(dot)com)