Class 6

Building the Machine: Constructing Your First Bayesian Network

Transforming causal intuition and probability language into a working computational model of psychosocial risk

What Is a Bayesian Network?

A Bayesian network (BN) is a compact, visual, and mathematically precise way of representing how a set of uncertain variables relate to one another. Formally, it consists of two components: a qualitative structure and a quantitative parameterisation (Koller & Friedman, 2009). The qualitative structure is a directed acyclic graph (DAG) - the kind of arrow diagram you built in Chapter 4 - where nodes represent variables and directed edges (arrows) represent causal or influential relationships. The "acyclic" constraint simply means no chain of arrows can loop back on itself; causes flow forward. The quantitative component is a set of conditional probability tables (CPTs), one for every node, specifying how strongly each node's state depends on the states of its parents.

Pearl (1988) introduced this framework as a way to make probabilistic reasoning tractable. The key insight is factorisation: instead of trying to specify the probability of every possible combination of every variable simultaneously - a table that grows exponentially - a BN decomposes the joint probability distribution into a product of smaller, local conditional distributions. Each node only needs to "know about" its direct parents, not the entire network. This is what makes the approach computationally feasible and, crucially, what makes it buildable by human experts working with limited data (Fenton & Neil, 2018).

In the context of psychosocial hazards, each node might represent a workplace condition (high workload, poor rostering), a mediating state (fatigue, emotional exhaustion), or an outcome (burnout, medication errors, turnover intention). Each arrow encodes the kind of causal reasoning you practised in Chapter 4. And each CPT encodes the kind of conditional probability you learned in Chapter 5. The Bayesian network is the point where those two skill sets converge.

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The Three Components, Defined

Following the construction framework proposed by Schenekenberg et al. (2017), we can distil BN construction into three essential components that you will assemble in sequence.

1. Nodes: The Variables

Every Bayesian network begins with a decision about what to include. Nodes represent the variables relevant to your problem. For our nursing-ward scenario, drawing on the predictor categories identified in Dall'Ora et al.'s (2020) review of nursing burnout, we select six nodes: Patient Load (High / Normal), Staffing Level (Adequate / Inadequate), Rostering Quality (Good / Poor), Managerial Support (Present / Absent), Burnout (High / Low), and Adverse Outcomes (a composite of medication errors and turnover, High / Low). Each node has a finite set of mutually exclusive states - for simplicity we use binary states, though richer models can include ordered categories.

2. Edges: The Causal Structure

Edges are the arrows connecting parent nodes to child nodes. Drawing on Chapter 4's causal reasoning and the empirical patterns in the literature, we specify: Patient Load → Burnout, Staffing Level → Burnout, Rostering Quality → Burnout, Managerial Support → Burnout, and Burnout → Adverse Outcomes. Additionally, Staffing Level → Adverse Outcomes captures the direct pathway by which understaffing leads to errors independent of burnout. Notice that Patient Load, Staffing Level, Rostering Quality, and Managerial Support have no parents - they are root nodes whose probabilities are specified unconditionally.

3. Conditional Probability Tables: The Numbers

Each node requires a CPT. For root nodes, this is simply a prior probability - for example, P(Patient Load = High) = 0.60, reflecting that the ward is overloaded more often than not. For child nodes, the CPT specifies the probability of each state given every combination of parent states. Burnout, with four binary parents, requires a table with 2⁴ = 16 rows. Each row answers a question like: "If patient load is high, staffing is inadequate, rostering is poor, and managerial support is absent, what is the probability of high burnout?" Research such as García-Herrero et al. (2013) provides empirical estimates for exactly these kinds of conditional relationships.

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Step-by-Step Construction: The Nursing Ward Model

Step 1 - Define the Structure

We begin by drawing the DAG. The four root nodes sit at the top. Arrows converge on the Burnout node in the middle. From Burnout and Staffing Level, arrows proceed to Adverse Outcomes at the bottom. This structure encodes our causal theory: workplace conditions influence burnout, and burnout (alongside staffing) drives patient-safety and retention outcomes. He et al. (2023) followed a nearly identical approach in constructing their BN for psychosocial hazards among construction workers - identifying root-level workplace conditions, mediating psychological states, and downstream health outcomes.

Step 2 - Populate the CPTs

Where do the numbers come from? Three sources are available, and in practice most models blend all three (Fenton & Neil, 2018):

• Published research. Dall'Ora et al. (2020) report that nurses working shifts longer than 12 hours have burnout rates approximately 40% higher than those on standard shifts. García-Herrero et al. (2013) provide conditional probability estimates linking demand–support combinations to stress outcomes.
• Organisational data. Your hospital's HR system records turnover rates, incident reports, and roster patterns. These can be used to estimate frequencies directly.
• Expert elicitation. When data are sparse - common in psychosocial risk - structured interviews with experienced clinicians and managers can produce credible probability estimates. Podofillini et al. (2016) evaluate five formal methods for eliciting CPTs from limited expert judgement, finding that even simple interpolation techniques produce usable tables when guided by clear protocols.

The critical insight is that you do not need a massive dataset to build a useful model. Expert knowledge, anchored to whatever data exist, is a legitimate and often necessary source of quantification.

Step 3 - Validate the Model

A model is only useful if its outputs match reality. Validation involves checking whether the network's predictions - for instance, the overall probability of high burnout given current ward conditions - align with observed rates. Schenekenberg et al. (2017) recommend sensitivity analysis (systematically varying inputs to see which nodes most influence outcomes) and face validity checks (presenting results to domain experts and asking whether the patterns are credible). If the model predicts that burnout should be rare when all four risk factors are present, something is wrong with the CPTs, and they need revision.

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Putting Numbers to Causes: The CPT Workshop

The conditional probability table is where qualitative reasoning becomes quantitative power. To build intuition for how CPTs work - and why they capture effects that risk matrices miss - try the interactive exercise below. You will populate a small CPT for a three-node network and compare your estimates to expert-derived values.

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Why This Overcomes the Risk Matrix

Recall from Chapter 3 the three limitations of traditional risk matrices: they assume hazards are independent, they cannot model propagation through a system, and they ignore directionality - the asymmetry between cause and effect. A Bayesian network addresses all three.

• Interdependence. CPTs explicitly encode how combinations of parent states jointly determine a child's probability. As the widget above illustrates, the interaction between high demands and low control produces a disproportionately elevated burnout risk - not the simple sum that an independence assumption would predict (García-Herrero et al., 2013).
• Propagation. Because nodes are connected by directed edges, evidence entered at any point in the network flows through the entire structure. Observing that staffing is inadequate updates not only the Burnout node but, through Burnout, the Adverse Outcomes node as well. Pearl (1988) formalised this cascade as belief propagation.
• Directionality. Arrows point from cause to effect, preserving the asymmetry of causal influence. High workload raises burnout probability, but learning that someone is burned out does not, in the model, change the actual workload - it changes our belief about what the workload might have been, a distinction the BN handles through Bayes' theorem.

In short, the Bayesian network replaces the flat, isolated cells of the risk matrix with a living, interconnected web of probabilistic reasoning - exactly the kind of model that psychosocial hazard mapping demands.

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