Data Analysis: Probabilistic vs Statistical Models

Athena Intelligence
6 min readMay 8, 2024

In the realm of the insurance industry, actuaries play a pivotal role in maintaining financial stability. The architects behind setting premiums, managing reserves, assessing risks, and crafting underwriting rules use an array of tools. Two distinct pillars of data analysis are probabilistic and statistical models.

Within the realm of wildfire analysis, the insurance sector has predominantly leaned towards statistical models, renowned for their simplicity, transparency, and interpretability. These models offer a straightforward approach to gaining approval from regulatory bodies and and to say “No” in the face of changing risks.

On the other hand, probabilistic models, also known as stochastic models, explicitly model uncertainty using probability distributions. They offer flexibility, scalability, and principled reasoning in the face of a changing world. Forward thinking actuaries can use AI and machine learning to leverage the power of probabilistic modeling to extract valuable insights in the face of uncertainty and make informed decisions.

Athena Intelligence’s Voice of the Acre®, while falling under the umbrella of probabilistic modeling, distinguishes itself with its integration of geospatial analysis which reflects changing conditions. With conditional profiles, Athena’s prefire model generates a probabilistic projections of the risk a catastrophic wildfire in the next 12 months.

More than a dozen factors related to the conditions of the land, which impacts wildfire behavior, for miles around each 30 sq meter is incorporated into the profile. are taken into account. In Athena’s probabilistic model, these factors are converted into nearly 100 indexes and derivatives are weighted and correlated with historic fires in the bioregion.

Statistical models analyze historical data and create large numbers of hypothetical events. Sometimes referred to as experience studies, statistical models seek to identify patterns and trends in historical data. Observed data is used to estimate parameters, but statistical models are not location specific and remain static simulations. They use the power of computers to evaluate many possible future events occurring, without regard to current conditions.

The concept of a 100-year event hinges on the capacity of statistical models to assign probabilities to hypothetical scenarios. However, with shifting global conditions, there’s an increasing realization that what were once considered rare events are now occurring more frequently. This suggests that the traditional understanding of a 100-year event occurring once in a century is no longer true. As humans grapple with the evolving dynamics of our planet, it’s becoming increasingly evident that we must recalibrate our strategies to adapt to this new reality.

While both probabilistic models and pure statistical models share the common goals of interpreting data, but there is a key distinction in their treatment of uncertainty. Probabilistic models explicitly model uncertainty using probability distributions, allowing for principled reasoning about uncertainty and decision-making. In contrast, pure statistical models treat uncertainty as a feature of the data and rely on sampling variability to quantify uncertainty in estimates.

Probabilistic models offer several advantages over pure statistical models, including the ability to model complex dependencies among variables, incorporate prior knowledge into the modeling process, and propagate uncertainty through the model structure. These probabilistic or stochastic models are well-suited for tasks that require principled reasoning about uncertainty, such as decision-making under uncertainty, probabilistic reasoning, and Bayesian inference. However, probabilistic models are computationally intensive and require large amounts of data to accurately estimate model parameters.

Athena looks at the conditions of the land just before actual wildfires, using historic information and a probabilistic risk model to create conditional profiles. Using Bayesian networks rooted in the principles of probability theory, Athena’s probabilistic model has the advantage of capturing complex dependencies among variables. This provides a mathematical framework for representing uncertainty and making predictions based on probabilistic reasoning.

Athena’s stochastic wildfire algorithm uses no hypotheticals, but rather incorporates all the information that relates to wildfires and their propensity to spread, for miles around a pixel (a 30 sq meter location). Then this profile is compared to profiles in and around historic wildfires in a bioregion, to create a conditional, probabilistic assessment of risk.

Thus, using Athena for wildfire risk, an insurance actuary can say, “In past fires, this set of conditions on the land occurs in 50% of all Texas wildfires. Therefore, ANY Texas property with these conditions, can only be insured with a high premium.” (A different set of conditions would exist for Northern California, Colorado, or other bioregions.) In a location where these conditions exist, but has no history of wildfires, statistical models may find the property to be low risk.

Ultimately, Athena’s stochastic model shows a direct correlation between actual fires and current conditions at a specific location, even if no fire has occurred in that location.

Conventional Wisdom, “There is no big wildfire risk in Northern Texas”

Athena’s strength is tying the model into geospatial analysis. In this cohesive framework, variables are represented as nodes in a graphical model, with connections between them depicted as edges. This graphical model structure effectively encodes conditional dependencies between variables, facilitating efficient inference and prediction processes.

Athena can precisely estimate future wildfire perimeters and generate probabilistic predictions. This holistic approach not only enhances the accuracy of predictions but also enables customers to make informed decisions based on insights into future risks gleaned from the model’s outputs.

Athena may be alone in wildfire risk assessment, but probabilistic models are widely used in various fields, including natural language processing, bioinformatics, and healthcare. Probabilistic models excel at handling uncertainty and incorporating prior knowledge into the modeling process. For example, in medical diagnosis, probabilistic models can combine patient symptoms with prior probabilities of disease to make accurate predictions about patient outcomes.

In the face of climate change, stochastic models may be better tools for assessing, pricing and managing risks faced by property insurance companies. Probabilistic risk models are also ideal for stress tests to evaluate the risk of catastrophic events, optimizing risk portfolios and price reinsurance and risk transfer programs.

While probabilistic models and pure statistical models share common goals of understanding and interpreting data, they differ significantly in their underlying principles and methodologies. One of the key distinctions between the two approaches lies in their treatment of uncertainty. Probabilistic models explicitly model uncertainty using probability distributions, allowing for principled reasoning about uncertainty propagation and decision-making. In contrast, pure statistical models treat uncertainty as a feature of the data and rely on sampling variability to quantify uncertainty in estimates.

Another important distinction between probabilistic models and pure statistical models is their treatment of parameters. In probabilistic models, parameters are typically treated as random variables with prior distributions, which are updated based on observed data using Bayesian inference. This allows for flexible modeling of complex data dependencies and incorporation of prior knowledge into the modeling process. In contrast, pure statistical models treat parameters as fixed but unknown values, which are estimated from the data using frequentist estimation techniques. While this approach provides unbiased estimates of parameters under certain conditions, it may lead to overfitting and lack of robustness in complex modeling scenarios.

In conclusion, probabilistic models and pure statistical models represent two distinct approaches to data analysis. While probabilistic models offer flexibility, scalability, and principled reasoning about uncertainty, pure statistical models provide simplicity, transparency, and less nuanced interpretability. In light of the many variables in play in wildfire behavior, Athena has found stochastic modeling to produce superior prefire risk assessment.

Athena Intelligence is a data vendor with a geospatial, conditional, profiling tool that pulls together vast amounts of disaggregated wildfire and environmental data to generate spatial intelligence, resulting in a digital fingerprint of wildfire risk. (athenaintel.io)

Clients include communities, power companies, insurance and financial services — with Athena’s geospatial intelligence incorporated into CWPPs, wildfire mitigation plans (WMP) and public safety power shutoffs. Data is available to catastrophe modelers for property underwriting and portfolio risk optimization.

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Athena Intelligence

Athena Intelligence weaves vast amounts of disaggregated environmental data. Drop us a line (Info@Project-Athena.com), or visit www.athenaintel.io