What is Predictive Modeling? - Casualty Actuarial Society

80 Pages·2005·0.21 MB·English

What is Predictive Modeling?
Casualty Actuaries of the Northeast
Spring 2005
Sturbridge, MA
March 23, 2005
Presented by Christopher Monsour, FCAS, MAAA
©©22000054 TToowweerrss PPeerrrriinn
What is it?
(cid:132) Estimation of likely outcomes based on historical data
(cid:132) The emphasis is on estimating the parameters as a means to estimating the
outcomes
(cid:132) As opposed to financial modeling, where the emphasis is on modeling the
probabilities of various outcomes, given the parameters
(cid:132) The emphasis is on different estimates for different combinations of
characteristics or for different entities
(cid:132) In financial modeling, the emphasis is on the range of possible outcomes for
a single entity
(cid:132) Thus, predictive modeling belongs to statistics and data mining
(cid:132) Whereas financial modeling largely belongs to probability theory
(cid:132) Finally, emphasis on predictions, NOT on interpreting model parameters
(cid:132) May “interpret” parameters when building model, but only as a means to
O/3-05 developing the best model
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What sort of outcomes?
Quantitative (regression models)
(cid:132) The expected length of time to repair an automobile, given
(cid:132) Its make, model, and model year
(cid:132) The nature of the repair
(cid:132) The technician assigned
(cid:132) The day of the week service began
(cid:132) The expected losses for an insured based on that insured’s
(cid:132) Driving record
(cid:132) Age, sex, marital status
(cid:132) Location
(cid:132) Credit Rating
(cid:132) Occupation
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What sort of outcomes?
Categorical (classification models)
Soft assignment
(cid:132) The probability of your home being broken into, depending on
(cid:132) Your location
(cid:132) The life-stage of your household
(cid:132) Whether you have a burglar alarm
(cid:132) Whether you have a garage
(cid:132) The probability that an insured will buy pet health insurance if asked, based on
(cid:132) Age, sex, marital status
(cid:132) Location
(cid:132) Occupation
(cid:132) Household type
O/3-05 (cid:132) Home value
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What sort of outcomes?
Qualitative (classification models)
Hard assignment
(cid:132) Often soft assignment model plus a threshold, but not always
(cid:132) Classic example…to which subspecies does a particular botanical specimen
belong, based on:
(cid:132) Dimensions
(cid:132) Coloring
(cid:132) Is a claim fraudulent?
(cid:132) Characteristics of claim
(cid:132) Of doctors and lawyers involved
(cid:132) Of claimant
(cid:132) Of agent or broker
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What tools come from predictive models?
Rating factors
(cid:132) In a linear regression model or a GLM, the model parameters may be
interpreted more-or-less directly as indicated rating factors in an additive or
multiplicative rating scheme (depending on the type of model)
(cid:132) The model parameters in a loss ratio model may be interpreted as the amount
by which the rating factors need to change
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What tools come out of it?
Scoring Farm — Illustration of Scoring
(cid:132) In a GLM or linear regression, the model
Animals
scores are added up and a different
treatment applied to various ranges of
Horses 20
scores, such as
Sheep -10
(cid:132) Tier assignment for rating / underwriting Cattle (ranch) -30
Cattle (dairy) 20
(cid:132) Adjuster assignment for claims
Size of Farm
< 50 acres -20
50-100 acres 0
100-320 acres 10
320-640 0
640+ -30
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What tools come out of it?
Rules
(cid:132) Other models produce branching rules
Are there horses?
(cid:197) No Yes (cid:198)
Are there dairy More than 320
cattle? acres?
(cid:197) No Yes (cid:198) (cid:197) No Yes (cid:198)
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Related types of modeling
“Unsupervised” learning
(cid:132) Categorical modeling where the categories are not determined in advance
(cid:132) Effectively amounts to looking for dense patches, or “clusters”, in an
appropriate feature space
(cid:132) Classic example is subspecies classification when name and number of
subspecies is unknown in advance
(cid:132) Geographic use in insurance
(cid:132) Feature space can be one dimensional, e.g., pure premium
(cid:132) Or can be multi-dimensional, e.g., crime rate, percentage of housing units
occupied by owners, etc.
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Related types of modeling
Cause-and-effect
(cid:132) About interpretation of parameters
(cid:132) Is a certain model of automobile more dangerous than another?
(cid:132) Suppose you attempted to answer this just from accident data or insurance
data
(cid:132) Think about what you might miss
(cid:132) Well-known that the sign of a coefficient for a predictor can change in a
regression model as you add more predictors
(cid:132) Is the model correctly specified?
(cid:132) Have you added all the predictors you should have out of a possibly infinite
number?
(cid:132) Much more difficult to validate than predictions
(cid:132) There are specialized methods, used especially in psychology
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