Inference

A risk model earns its keep the moment evidence arrives. Inference is how you turn “the ground survey came back poor” into a revised number for “we overrun”.

Chapter 1 built a model of what drives project uncertainty. But a static model is a museum piece. The value comes when something happens — a leading indicator trips, a milestone slips, a test fails — and you need to know what that means for the outcomes you care about. Inference is the computation that answers it: given the evidence you’ve observed, what is the probability of the query you’re worried about?

1The question inference answers

Formally you want a conditional probability like P(cost overrun | poor ground, subcontractor late). The model already contains everything needed to compute it — the answer is implied by the network — but reading it off requires summing over all the factors you haven’t observed and don’t directly care about. Those unobserved variables have to be “summed out”, and how you do that efficiently is the whole game.

Figure 1. Inference in action. Heavy rain is now observed (dashed border — this is evidence); we query the probability of the highlighted cost overrun. Inference propagates the evidence through the intervening “schedule slip” to update the downstream belief.

2Exact inference — and its ceiling

The exact approach, variable elimination, is disciplined bookkeeping: eliminate the unwanted variables one at a time, in a sensible order, multiplying and summing the relevant tables and reusing partial results instead of recomputing them. Done well it is exact and often fast. A related technique, belief propagation, passes “messages” between neighbouring nodes until the whole network agrees.

There is a hard limit, though. The cost of exact inference is governed by how tangled the network is — how much everything connects to everything. For loosely connected models it’s cheap; for densely interlinked ones the work explodes, and in the general case exact inference is provably intractable. Real project models, with feedback and shared drivers, often live on the wrong side of that line.

3When exact fails: estimate by simulation

When you can’t compute the answer, you can sample it. Monte Carlo methods run the model forward thousands of times — each run a plausible synthetic project consistent with the model — and simply count how often the thing you’re asking about occurs. The fraction is your estimate; more runs, tighter estimate.

Direct sampling draws whole scenarios from the model. Simple, but wasteful when your evidence is rare, since most scenarios won’t match it.
Likelihood weighting fixes the observed values in place and weights each sample by how consistent it is, so every run counts.
Gibbs sampling (a Markov-chain method) walks from one configuration to a neighbouring one, gradually producing samples that converge to the correct distribution even for awkward, highly-coupled models.

If you have ever run a quantitative schedule or cost risk simulation and read off “P80 = 14 weeks”, you have already done inference by sampling. The tool ran the network forward across thousands of iterations and counted.

Key idea

Exact inference reads the answer straight from the model when the model is simple enough; simulation estimates the same answer by brute force when it isn’t. Both compute the identical quantity — a probability, updated for what you now know.

Choosing an inference approach
Situation	Approach	Why
Small, loosely-connected model	Exact (variable elimination)	Fast and precise; no sampling error
Dense model, rare evidence	Likelihood weighting	Every sample respects the evidence
Highly coupled, feedback-heavy	Gibbs / MCMC	Converges where direct methods stall
Continuous, roughly linear	Gaussian (closed form)	Exact update via linear algebra

What it means in practice

Treat every leading indicator as evidence to feed back into the model, not just a line item to note. When a driver fires, inference tells you how much your downstream exposure actually moved — the difference between reacting to noise and reacting to a genuine shift. And when your model is too interconnected for a clean answer, don’t abandon it: simulate it. A number with a stated confidence beats an adjective every time.

Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review Inference. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to convert the subject into a governed decision, owned work, usable evidence and a reviewable outcome. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Use Inference as a decision instrument rather than an administrative form. The subject terms—inference, exact, posterior, risk, elimination—need an explicit connection to the project objective, business value and stakeholder commitments. Before completing the artefact, write one sentence stating who will use it, what decision it supports and when that decision is required.

Apply a disciplined information model. Separate facts supported by evidence, forecasts derived from a method, assumptions awaiting validation, constraints that limit choice, risks that may occur, issues that already exist and actions assigned to people. Each material entry should have an owner, date, status and next review point. Where probability or impact scores are used, define the scale so different reviewers interpret it consistently.

A baseline is useful only when changes are visible. Give the artefact an identifier, version, approval state and effective date. Define which changes require reapproval, how superseded versions are retained and where supporting evidence is stored. During reviews, focus on exceptions, decisions and trends rather than reading every field aloud. Record the decision and rationale, not merely that a meeting occurred.

Close the loop beyond delivery. Confirm acceptance criteria, unresolved items, transferred responsibilities and operational ownership. Where benefits are expected, identify the outcome measure, baseline, target, observation period and owner who remains accountable after the project team disbands. Lessons should describe the condition, consequence and reusable action; a generic statement such as “communicate better” cannot improve the next project.

Step-by-step operating method

Clarify the decision. Name the outcome, sponsor, affected stakeholders and decision that this work must enable.
Set boundaries. Record scope, assumptions, constraints, dependencies, tolerances and escalation conditions.
Plan the evidence. Define deliverables, measures, owners, due dates and acceptance criteria before execution.
Control delivery. Compare actual performance with the baseline, assess changes and manage risks and issues explicitly.
Close the loop. Confirm acceptance, transfer ownership, capture lessons and track benefits beyond handover.

Completion and governance protocol

Start with a short drafting workshop involving the accountable owner and the people who hold the evidence. Complete high-consequence fields first: objective, scope, owner, baseline, acceptance, dependencies and escalation. Mark unknowns as assumptions or actions rather than hiding them behind vague prose. Circulate a review draft, resolve conflicting interpretations, baseline the approved version and place the next review date in an owned schedule.

Information type	Minimum useful content	Review test
Outcome	Observable change and intended recipient	Not merely a deliverable or activity
Measure	Definition, baseline, target, frequency and source	Two reviewers would calculate it the same way
Ownership	One accountable role plus contributors and approver	Authority matches responsibility
Uncertainty	Assumption, risk or issue with response and trigger	Status reflects current reality
Control	Version, approval, review date and change rule	Current baseline is identifiable

Common failure modes and recovery actions

1. Watch for

Producing a document with no named decision or accountable owner.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Mixing risks, current issues, assumptions and actions in one unstructured list.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Measuring activity or output while leaving the intended outcome undefined.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Accepting changes without evaluating effects on value, scope, schedule, cost and risk.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Closing the project at delivery even though benefit ownership has not transferred.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.