Alternative Assessment Module

The main part of the framework body is this module, which attempts to address the uncertainty of decision-making process. A Bayesian belief network, also called a causal network or belief network, is a powerful tool for knowledge representation and reasoning under conditions of uncertainty and visually presents the probabilistic relationships among a set of variables. It is frequently applied in real-world problems such as medical diagnosis, forecasting, automated vision, sensor fusion, and manufacturing control It has been extended to other applications including transportation, ecosystem and environmental management, and project risk management (Bayraktar and Hastak 2009; Lee et al. 2009; Trucco et al. 2008).

The Bayesian belief network approach has been selected as the tool for modeling MTP front-end phase process over the course of this research because it was found well- suited for the condition this research problem. A Bayesian belief network has many advantages such as suitability for small and incomplete data sets, structural learning possibility, combination of different sources of knowledge, explicit treatment of uncertainty and support for decision analysis, and fast responses. It is therefore applied to decision support systems with uncertainty (Lee et al. 2009). For instance, that belief networks try to model the real world, i.e., not the expert. A belief network model includes an explicit representation of the relationships among the variables, factors, processes, and events in the proposed framework for the problem. Also, construction risks are not always independent or additive. The impact of two events in a construction management environment is not always the sum of their individual impacts (Nasir et al. 2003). Moreover, it is indicated in the literature that the graphical nature of belief networks

allows variables to be added or removed from the network without impacting the rest of the network. This feature becomes possible if the modifications to the network are isolated. Additionally, rule-based expert systems allow information or evidence to be fed only at specific entry points, and the output information is generally not changing (Bayraktar and Hastak 2009).

The Bayesian Belief Network (BBN) model is proposed as an evaluation method to address the uncertainties and interrelationship between the factors. The identified critical factors and Decision Indicators in previous research steps formed the body of BBN. The BBN is able to simulate the impact of interrelated factors (cause-effect relation) under uncertain situation using the conditional probability theorem. The methodology and steps to create this module is summarized in Figure 4-2.

Start Extensive literature review Decision indicators Factors and relationsh ip Questionnaire survey of DOTs & MPOs Interview of select MTP Refined decision indicators Refined factors and relationshi p Getting experts’ opinions Bayesian Belief networks End Generic influence pattern Cause and effect matrix

Getting data for specific project and

customization

Input prior and conditional probabilities

Decision indicators’ state probability

As mentioned in chapter 2, a Bayesian network can be described in terms of a qualitative component, consisting of a directed acyclic graph (DAG), and a quantitative component, consisting of a joint probability distribution that factorizes into a set of conditional probability distributions governed by the structure of the DAG. The first component of the network is shown in Figure 4-3 schematically.

The construction of a Bayesian network thus runs in two phases. First, given the MTP alternatives at hand, the relevant factors and decision indicators and the (causal) relations among them are identified (results in the generic BBN shown in Figure 4-3). This generic BBN is unique for each project based on its specification and should be customized for it. The resulting DAG specifies a set of dependence and independence assumptions that will be enforced on the joint probability distribution, which is next to be specified in terms of a set of conditional probability distributions. As explained in chapter 2, if there is an arrow (edge) from one node to another node, then the node in the starting point of arrow is a parent of the node in the tail. If the value of a node is known, it is referred to as an evidence node. A node that has no incoming arrows is said to have no

A 1 Costs A 2 A 3 Benefits B 1 B2 B3 Technical F 1 F F3 Financial G G G Economi c C 1 C2 C3 Social D 1 D2 D3 D4 Environmen tal E 1 E2 E 3 E

parents, and can be described probabilistically by a prior (or unconditional) probability distribution. A node can represent any kind of variable such as an observed measurement, a parameter, a latent variable, or a hypothesis. Relationships between variables are described probabilistically in a conditional probability table (CPT). This approach facilitates a change in the likelihood of a state of a variable to be propagated through the network. In this way, the state of the entire system can be calculated given changes in any part of it (Bayraktar and Hastak 2009; Trucco et al. 2008; Kjaerulff and Madsen 2008).

To illustrate the Bayesian belief network and interrelationships between the identified factors, a simple example of is provided here. Figure 4-4 depicted a belief network for project cost. “Project Costs” decision indicator would be influenced by “investment cost” and “operating and maintenance cost”. “Investment costs” is associated with “planning cost”, “cost of design”, “land and property cost” and “cost of construction”. “The cost of land and property” can be analyzed as “land acquisition costs” and “legal costs”.

By focusing on “land and property cost” part of this example (highlighted nodes and arrows in Figure 4-4), that has four variables, we can show the network elements on it. “Legal cost” and “Land acquisition cost” are parent nodes and “land and property cost” acts as child node here. The important point that becomes obvious in the network is that once the value of “Land and property cost” is available, “Legal cost” and “Land acquisition cost” values are not necessary to predict “Project cost” values. This conditional independence is presented by the absence of a directly connecting arrow between “Legal cost” or “Land acquisition cost” and “Project cost”. This feature simplifies the modeling process by facilitating the development of separate sub-models

for each conditional relationship indicated by the presence of an arrow. These sub-models may be acquired from either (i) mathematical representation of dominant processes, (ii) statistical associations derived from historical data, or (iii) probabilistic quantities elicited from scientific experts. Any model representation or level of mechanistic detail is appropriate as long as the uncertainty associated with each relationship can be calculated using a conditional probability distribution.

Figure 4-4: Simple project cost belief network

Once all significant system variables are linked in a single network using conditional probabilistic relationships, predictive distributions of model endpoints can be generated for any set of values for up-arrow variables. These predicted endpoint probabilities, and the relative change in probabilities between alternative scenarios (corresponding to changed values of other variables) convey the expected system response to management while accounting for predictive uncertainties (Kjaerulff and Madsen 2008).

Project cost

Planning cost Design cost Land and property

cost Construction _cost

Legal cost Land acquisition cost

There are various types of software to build and calculate the probabilities of BBN available in the market. For this research, AgenaRisk is utilized to run the second module.

To provide flexibility in modeling the complexity of the problem and also to simplify the computational efforts, some assumptions have been considered. Generally, three assumptions were applied in developing the Bayesian belief network. Firstly, the nodes with at least one parent node in the influence pattern, are only conditionally dependent on their parent nodes. This kind of nodes can only be influenced by its parent(s). The second assumption indicated that starting nodes which have no parent nodes, represent prior probabilities which may be provided by the user. The other factors which are not shown in the influence pattern but may impact the project indicators and are called external factors, can only impact the starting nodes directly. Such impacts are integrated in the probabilities of the starting nodes and are further reflected in the children nodes of the starting nodes through conditional probabilities. Lastly, it was assumed that the factors provided in the influence pattern provide a mutually exclusive and collectively exhaustive list of variables required for the analysis as necessary for the use of certain probability distributions throughout the analysis.

The definition of the influence pattern as a “closed” system imposed the first and second assumptions, which is regarding the influence of the external factors only through the starting nodes. These assumptions were essentially needed to form an organized environment in order to compute the influence of the nodes on each other, and prevent getting lost in the complex nature of possible relationships between the external factors and the factors included in the influence pattern.

A conditional probability is a probability or likelihood of a variable that is dependent on the state of another variable. Belief networks use Bayes’ theorem defined as:

𝑃(𝐵|𝐴) = 𝑃(𝐴|𝐵) ∗ 𝑃(𝐵)

𝑃(𝐴)

Bayes’ theorem may also be used to analyze multiple influences as:

𝑃(𝐵_𝑖|𝐴) = _∑ 𝑃(𝐴|𝐵𝑖) ∗ 𝑃(𝐵𝑖)

𝑃(𝐴|𝐵_𝑘)

𝑛

𝑘=1 ∗ 𝑃(𝐵𝑘)