TIA is a forecasting method that permits extrapolations of historical trends to be modified in view of expectations about future events.

TIA: Extrapolation that allows surprises

The past may not predict the future accurately.

How to do it?

(1) A curve is fitted to historical data to calculate the future trend, given no unprecedented future events;

Typical Event Impact Parameters

Modifying surprise-free extrapolations

Judgment and imagination are crucial to the second step of TIA. At this point, the program modifies the surprise-free extrapolation to take into account important unprecedented unexpected

future events.

Cross-Impact Analysis

Based on a simple question: can forecasting be based on perceptions about how future events may interact?

Method

We know from experience that most events and developments are in some way related to other events and developments.

**1) TREND IMPACT ANALYSIS (TIA)**

2) CROSS-IMPACT ANALYSIS

2) CROSS-IMPACT ANALYSIS

What is TIA?

The events can have a wide span to include technological, political,

social, economic, and value-oriented changes.

Quantitative methods based on historical data are

used to produce forecasts by extrapolating such data into the future, but such methods ignore the effects of unprecedented future events.

(2) Expert judgments are used to identify a set of future events that, if they were to occur, could cause deviations from the extrapolation of historical data.

For each such event, experts judge the probability of occurrence as a function of time and its expected impact on the future trend, should the event occur.

An event with high impact is expected to swing the trend relatively far, in a positive or negative direction, from its unimpacted course.

TIA provides a systematic means for combining surprise-free extrapolations with judgments about the probabilities and impacts of selected future events.

First, a list of such potential events is prepared.

These events should be plausible, potentially powerful in impact, and verifiable in retrospect.

The TIA computer program combines the impact and event-probability judgments with results of the surprise-free extrapolation to produce an adjusted extrapolation.

Impacts

This analysis typically includes estimates of upper and lower quartile limits or limits at some other probability levels.

The expected value of the combined impacts is computed by summing the products of the probabilities of impacting events for each year in which they were possible with the magnitude of their expected impacts, taking into account the specified impact lags.

Events Used in Trend Impact Analysis

Strengths and Weaknesses

One of the most important strengths of the TIA method is gained from requiring the analyst to

specify what events will make a difference in the future ("these are the events I've taken into account.")

The events and judgments about them constitute a scenario. In fact, TIA can be used to add quantification to a scenario. When TIA is used in a scenario, the method helps ensure internal consistency.

When a series of TIAs are carried out as part of a forecasting study, it is possible through sensitivity analysis to identify those events that "swing" important variables.

TIA provides a range rather than a single-point forecast, uncertainty can be considered explicitly in decision analyses.

First, the list of events is almost certainly

incomplete.

Second, even if the list of events was complete, what about the accuracy of the

probabilities and impact judgments? Such lists of events are simply expectations about the future that may or may not be correct.

At the very least, they express assumptions about the future that

are otherwise unstated.

The cross-impact method is an analytical approach to the probabilities of an item in a forecasted set.

Its probabilities can be adjusted in view of judgments concerning potential interactions among the forecasted items.

The interrelationship between events and developments is called "cross-impact."

Spaceships!

Saturn Rockets: used in Apollo missions

Vergeltungswaffe 2 (V2 rocket)

How to do it?

1) Define the events to be included in the study.

Any influences not included in the event set will, of course, be completely excluded from the study.

The inclusion of events that are not pertinent can complicate the analysis unnecessarily.*

An initial set of events is usually compiled by conducting a literature search and interviewing key experts in the fields being studied.

*number of event pair interactions to be considered is equal to n2 - n (where n is the number of events), the number of interactions to be considered increases rapidly as the number of events increases.

2) Estimate the initial probability of each event.

Probabilities indicate the likelihood that each event will occur by some future year.

Two approaches:

2.a. In the initial application of cross impact and in some current applications, the probability of each event is specified, assuming that the other events have not occurred.The probability of each event is judged in isolation and the cross-impact analysis is used to adjust the initial probabilities for the influences of the other events.

2.b. Initial probabilities assume that the experts making the probability judgments have in mind a view of the future that includes the set of events and their likelihoods'. Thus, in estimating the probability of each event, the possibility of the other events occurring is taken into account from the beginning. In this case, the cross-impact analysis is used to determine whether the judgments about initial and conditional probabilities are coherent.

How to do it? Part 2

How to do it? Part 3

3) Estimate the conditional probabilities.

Typically, impacts are estimated in response to the question, "If event m occurs, what is the new probability of event n?"

The entire cross-impact matrix is

completed by asking this question for each combination of occurring event and impacted event.

Some math

(skip if necessary)

The calculation for a range of conditional probabilities that will satisfy this consistency

requirement is easy. The initial probability of an event can be expressed as follows:

P(l) = P(2) × P(1/2) + P(2c) × P(l/2c)

where:

P(l) = probability that event 1 will occur;

P(2) = probability that event 2 will occur;

P(1/2) = probability of event 1 given the occurrence of event 2;

P(2c) = probability that event 2 will not occur; and

P(1/2c) = probability of event 1 given the nonoccurrence of event 2.

This expression can be rearranged to solve for P(1/2):

P(1/2) = {P(l) - P(2c) × P(l/2c)}/ P(2) (2)

Since P(l) and P(2) are already known (the initial probability estimates) and P(2c) is simply 1 -

P(2), only P(1/2) and P(1/2c), the conditional probabilities, are unknown. By substituting zero

for P(1/2c) (the smallest value it could possibly have), the maximum value for P(1/2) can be

calculated. Thus:

P(1/2) <= P(1)/P(2) (3)

Similarly, by substituting 1.0 for P(1/2c) (the largest possible value for P(1/2c), the minimum

value for P(1/2) can be calculated:

P(1/2) >= {P(1) – P(2c)}/P(2) (4)

Thus, the limits of the new probability of event 1 given the occurrence of event 2 are:

{P(1) – P(2c)}/P(2) =< P(1/2) <= P(1)/P(2) (5)

Cross-Impact Probability Matrix

Cross-Impact Odds Matrix

Ocurrence Odds Ratios

Two results for two scenarios

2.a. If the initial event probabilities were estimated in isolation, that is, assuming that cross impacts were not part of the picture, the event probabilities obtained after the cross-impact procedure produce new estimates of event probabilities that take into account the interrelationships among the events.

The matrix produced in this way can then be used to test the sensitivity of the event

probabilities to the introduction of a new event, to the changes in initial probability (simulating an R&D investment, for example), or to changes in event interactions (simulating, for example, a policy that changes the consequence of an event).

2.b. If the initial event probabilities were estimated assuming that all other events are possible, the calibration probabilities obtained after the cross-impact procedure may be quite similar to the initial probabilities.

In this case, differences between the initial and the final probabilities can be viewed as resulting from inconsistencies in judgments and the omission of higher order combinations. The cross-impact exercise produces new estimates of event probabilities that simply account for the higher order interrelationships among the events, as before.

Policy testing

Sensitivity testing consists of selecting a particular judgment (an initial or a conditional probability estimate) about which uncertainty exists. This judgment is changed, and the matrix is run again. If significant differences occur between this run and the original run, the judgment that was changed is apparently an important one.

Sensitivity testing

Accomplished by first defining an anticipated policy or action that would affect the events in the matrix. The matrix is then changed to reflect the immediate effects of the policy, either by changing the initial probabilities of one or more events or by adding a new event to the matrix. A new run of the matrix is then performed and compared with the calibration run. The differences are the effects of the policy.

Strengths and Weaknesses

The cross-impact method forces attention to chains of causality: x affects y; y affects z.

If the input to a cross-impact matrix falls outside of acceptable probabilistic bounds, or if the result of a cross-impact run is surprising, then the researcher is forced to reexamine his or her view of expected reality. The method shares this attribute with other approaches to simulation modeling.

The disaggregation required by the method is usually illuminating.

Inserting a cross-impact matrix into another model often adds power to that model by bringing into its scope future external events that may, in the limit, change the structure of the model (see Stover, for example). This integration also provides a means of testing sensitivity to changes in probabilities of future events and contemplated policies, an important consideration in planning studies.

However, the collection of data can be fatiguing and tedious.

A ten-by-ten matrix requires that 90 conditional probability judgments be made. A 40-by-40 matrix requires that 1,560 judgments be made. The chances for falling asleep before completion are high.

Furthermore, this method assumes that, somehow and in some applications, conditional probabilities are more accurate than estimates of a priori probabilities; this is unproved.