SLIDE 6 11/15/2019 6
Uncertain information
Classical methods assume certainty. In real life, certain information hardly exists. However, the degree of uncertainty varies. In general, we use distributions for representation
- f knowledge with uncertainty.
For binary information, we may just supply the probability. For continuous information, we supply for instance a normal distribution with a mean and a variance. A small variance implies that we are rather certain about the value. For consistent processing of data, a model is needed.
Department of Veterinary and Animal Sciences Slide 16
Uncertainty: Pregnancy status of a cow
For the replacement decision we want to know the pregnancy status of a cow, but it is (most often) unobservable, so we have only indirect observations:
- If a cow has not been inseminated, the probability of
pregnancy is zero.
- If it has been inseminated, the probability is 0.4,
because the conception rate of the herd is 0.4.
- If, after 5 weeks, the cow has not shown heat, the
probability increases. Assuming a heat detection rate of 0.5, the probability increases to 0.7.
- A positive pregnancy diagnosis will further increase the
probability, but only a calving will increase it to 1.
We need a method for consistently combining the indirect observations into an updated probability of pregnancy. We may use a Bayesian Network model for that!
Department of Veterinary and Animal Sciences Slide 17
Models for monitoring under uncertainty
Assessing the distribution of a key figure from the distribution of data (later this lecture):
Statistical quality control models based on time series analysis:
- More or less “black box” approach
Dynamic Linear Models based on Bayesian updated time series with Kalman filtering:
- Structured model
- Data of same kind
Bayesian networks
- Highly structured models
- Data from different sources
Department of Veterinary and Animal Sciences Slide 18
