APPLICATION OF PROBABILITY TO ASSESS
RISK IN MANAGEMENT DECISIONS, RISK
ANALYSIS
Jim Kennedy
CONCEPTS
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.

VARIABLE OR UNCERTAINTY

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

Uncertainties are uncontrolled but predictable.
 Prevalence
 Immune
response
 When will a shear pin break
 Who will win the final four
PREDICTION=PROBABILITY=UNCERTAINTY

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.
GRAPHICAL REPRESENTATIONS OF
UNCERTAINTIES
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.

SIMULATION MODELING

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.
STOCHASTIC MODELING

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.
MAKING THE MODEL

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.
MODELS GET COMPLICATED QUICKLY

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.
OTHER ASSUMPTIONS
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.

SOME PROBABILITY DISTRIBUTIONS OF
INTEREST
Pert Distribution
Normal Distribution
Normal(7.0000, 1.5000)
Pert(3.0000, 8.0000, 10.000)
0.35
0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
5.0%
90.0%
5.226
11.1
9.8
8.5
7.2
5.9
4.6
3.3
2.0
< 5.0%
4.533
90.0%
11
9
10
8
7
6
5
4
0.00
0.00
3
0.05
5.0% >
9.467
5.0%
9.370
Uniform Distribution
Uniform(0.0000, 50.000)
2.5
Hypergeometric Distribution
HyperGeo(20, 12, 100)
2.0
Values x 10^-2
0.35
0.30
0.25
0.20
0.15
1.5
1.0
0.5
0.10
90.0%
0.00
90.0%
2.50
47.50
60
50
40
30
20
0
5.0%
5.00
10
14
12
10
8
6
4
2
0
-2
0.0
0.00
-10
0.05
SIMULATION MODELING
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.

RANDOM SELECTION FOR SIMULATION MODELS
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.

AVAILABLE AT A PRICE
Software programs to do simulation modeling
are available, such as @Risk 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.

PREGNANCY TESTING 500# FEEDLOT HEIFERS

Question: Would it be more cost effective to
pregnancy test 5000 500# 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?