Jim Kennedy

 Quantitative Risk Analysis is a tool used to aid in management decisions when uncertainty has to be considered.  A mathematical equation is a model composed of one to an infinite number of variables, and uncertainties.

 Variables are controllable  Weight/volume of a chemical used in a reaction  Amount of antibiotic administered  Cost of a diagnostic test  Sensitivity and specificity of a diagnostic test  ?

 Uncertainties are uncontrolled but predictable.  Prevalence  Immune response  When will a shear pin break  Who will win the final four

 Uncertainty is the level of ignorance.  Uncertainty is lessened by knowledge  Literature reviews  Expert opinions  Further data gathering and analysis  Until an uncertain event becomes 100% controlled it is a function of probability.  Uncertainties, like variables, may be discrete or continuous.  Whether an unborn calf is male, female, or a hermaphrodite would be a discrete uncertainty.  The weight of a calf at birth is a continuous uncertainty, it could weigh 75.0 lbs 75.1, 75.15…etc. an infinite number of possibilities.

 Discrete uncertainties and their probabilities are more easily understood if represented visually by a bar graph.  Continuous uncertainties and their probabilities are more correctly represented by a line.  A graphical representation of an uncertainty and its probability may be cumulative or may be a single point.

 Using probability to make a management decision.  Putting together a series of variables and uncertainties into a mathematical formula produces a model.  Values to each variable and uncertainty can be given and the outcome of the mathematical formula be determined, a deterministic model.  An alternate method is to assign probabilities to all or some of the uncertainties and allow the probability distribution to determine a mean value, upper and lower limits, and a standard deviation for the uncertainty.

 Accounts for an uncertainty occurring dependent on the probability of that uncertainty.  We are uncertain of the prevalence of a disease within a herd, but we can make a guess and assign a probability to that guess.  Your best guess is that 10 of 100 animals are infected, but you know that it is possible that none are infected or that all are infected, you are uncertain.  If the decision to be made is metaphylaxis or not, a stochastic model might allow the best decision be made.

 Assuming your decision rests on whether metaphylaxis would be more cost effective than to pull and treat you would consider factors such as:  the cost of metaphylaxis  the cost to treat  the ability of the pen rider to pull sick animals  the number of head requiring treatment  how many animals will require treatment despite metaphylaxis  how many animals die although treated  etc.

 Most of the factors for consideration from the previous slide are uncertainties  A model with too many uncertainties may produce invalid results, you may end with odds of making the correct decision based on the model of 50:50, you didn’t need a model just a coin.  To avoid the dilemma you make assumptions such as the pen riders are the best or the treatment never fails, but assumptions decrease the validity of the model.

 Besides the assumptions of the model you also make assumptions about the probability distribution of the uncertainties.  The more precisely the probability distribution of an uncertainty can be defined the more precisely the model will depict reality.

Pert Distribution Normal Distribution Hypergeometric Distribution Uniform Distribution

 Simply stated a random set of values are placed into a mathematical formula and the results recorded.  A list of values could be placed in a spreadsheet and selected at random this might not reflect the probability of the value actually occurring.  Different methods of random selection of the values such as Monte Carlo or Latin Hypercube sampling exist.

 Monte Carlo and Latin Hypercube simulation interpose the probability distribution of the event on the selection of the random value.  The resulting difference between the two methods in most cases is minor, Latin Hypercube is faster (requires less cpu time) than the Monte Carlo method.

 Software programs to do simulation modeling are available, such and Crystal Ball.  These programs are pricey and offer some challenge in applying.  Programs/software of this type are used by industries and governmental agencies in decision making. I would suspect that one of these programs may have been used to reach a decision on the Wall Street bailout, or if not it should have been.

 Question: Would it be more cost effective to pregnancy test # heifers or do nothing?  Cost to pregnancy test  Lost revenue for pregnant heifer  Prevalence of pregnant heifers in group  Which are variables and which are uncertainties?