Analysis Note

This model utilizes a weighted adjustment methodology. It begins with the historical baseline for the selected claim type and shifts the probability based on the strength of your case-specific evidence and legal arguments.

📚 Mathematical Foundation: General Linear Model

This tool implements a multiple regression model, a special case of the General Linear Model (GLM). Following Olsson (2002), the observed outcome $y_i$ is modelled as a linear function of independent variables:

Our application: We adapt this framework for case success prediction, where the response variable is probability of success ($P_{\text{success}}$) and the predictors are normalised factor scores:

📚 Mathematical Foundation: Bayesian Networks

This tool utilizes Bayesian Networks (BNs), a powerful probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG).

Inference in Bayesian Networks, the process of computing the posterior probability of a variable given evidence, is performed using algorithms like Variable Elimination or Message Passing.

📚 Mathematical Foundation: Bayes-Laplace Theorem

This tool implements Bayesian inference, updating prior beliefs in light of new evidence using the Bayes-Laplace formula (Bayes, 1763; Laplace, 1774):

This tool's implementation: We model uncertainty using Beta distributions for probabilities and Normal distributions for monetary values. The posterior is computed via conjugate updating, which has closed-form solutions for these distribution families.

📚 Mathematical Foundation: Monte Carlo & PERT

This tool models litigation uncertainty using Monte Carlo simulation. It performs thousands of trials, sampling from probability distributions for each head of loss to generate a range of potential outcomes.

By aggregating these distributions (e.g., Unfair Dismissal + Vento + Pension), the model reveals the probability density of the total award, helping to identify the most likely settlement range.