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Stochastic modeling is a method for forecasting outcomes that depend on chance. A stochastic model represents uncertain inputs as random variables with probability distributions, then simulates thousands of possible futures to show the range of results and the probability of each. Banks use it to project investment returns, epidemiologists to forecast outbreaks, and insurers to estimate the losses a hurricane season could bring to every building in a portfolio.
The Havasu catalog holds the two layers a physical risk model joins: Overture building footprints as exposure, and the Colorado property risk explorer, which scores every building in the state against five perils.
A stochastic model is a mathematical model in which one or more inputs are random variables. A random variable takes different values with defined probabilities, described by a probability distribution such as the normal, lognormal, or Poisson. The NIST/SEMATECH e-Handbook of Statistical Methods catalogs the common distributions and their uses.
Because the inputs vary, each run of a stochastic model produces a different result. One run is a single possible future. Thousands of runs together form an output distribution, and that distribution is the answer.
A stochastic process is the time-ordered version: a sequence of random variables indexed by time or space. Daily rainfall at a gauge, the path of a hurricane, and the price of a stock are all modeled as stochastic processes. Analysts group them by whether time and state are discrete or continuous, which gives four classic types: Markov chains, autoregressive time series, Poisson processes, and Brownian motion.
A deterministic model returns the same output every time for the same inputs. A retirement projection that assumes a fixed 5% annual return is deterministic: $100,000 grows to about $163,000 in ten years, every time.
A stochastic version draws each year's return from a distribution with a 5% mean and a set volatility. One run ends at $120,000, another at $210,000. After 10,000 runs, the model reports the median outcome and the probability that the balance falls below a target.
The two approaches often work together. NOAA's HRRR weather model runs deterministically, one forecast per cycle. NOAA's Global Ensemble Forecast System generates 21 separate forecasts, called ensemble members, to account for uncertainty in the input data and the model, and the spread of those members measures forecast uncertainty.
Most stochastic models follow four steps.
The number of runs sets precision. Estimates of the mean settle quickly. Estimates of rare outcomes, such as a 1-in-250 year loss, need far more runs, because only a few simulated years land in that tail.
Stochastic models appear wherever outcomes depend on chance.
Physical risk is the most spatial application of stochastic modeling. A hurricane, flood, or wildfire has a location, a footprint, and an intensity at every point it touches. A stochastic model of physical risk simulates thousands of those events and measures their effect on real buildings.
Catastrophe models are built on a stochastic event set: a catalog of simulated hurricanes, floods, earthquakes, or wildfires, each with an annual rate of occurrence. Model developers generate the catalog by fitting distributions to the historical record, such as the hurricane tracks in NOAA's HURDAT2 database, and sampling tens of thousands of years of plausible events, including storms larger than any yet observed.
Each event carries a hazard footprint: peak wind speed, flood depth, ground shaking, or flame length across a grid. The model joins every footprint to the exposure, meaning the buildings and parcels in a portfolio with their construction and value. A vulnerability curve converts the intensity at each building into a damage ratio. Summing damage across buildings gives one loss per event.
Repeating that across the full catalog produces the loss distribution. Average annual loss (AAL) is the mean loss per simulated year. The exceedance probability (EP) curve gives the probability that annual loss exceeds each value, and the return period is its inverse: a loss with a 1% annual exceedance probability is the 100-year loss.
The open-source Oasis Loss Modelling Framework runs catastrophe models in this structure, and FEMA's Hazus applies the same hazard, exposure, and vulnerability chain to estimate losses from earthquakes, floods, hurricanes, and tsunamis.
Some physical risk models simulate the weather that drives the hazard. A stochastic weather generator produces thousands of years of synthetic rainfall, temperature, and wind. Those sequences feed flood models, which route water over a digital elevation model to produce depth grids for each simulated storm.
Wildfire risk works the same way. The US Forest Service's FSim simulator models thousands of fire seasons, with random ignitions and weather, and spreads each fire across fuel and terrain grids. The burn probability maps in Wildfire Risk to Communities come from those simulations. Analysts check simulated perimeters against observed burn scars from earth observation data, such as the Sentinel-2 burn severity pipeline Wherobots ran on the Spokane firestorm.
Every simulated event in a physical risk model is a spatial object. A flood footprint is a raster of depths. A hurricane footprint is a wind field. A wildfire is a perimeter polygon. Scoring an event means sampling that raster or intersecting that polygon with every building it touches.
The arithmetic grows fast. A catalog of 10,000 events against 3 million buildings is 30 billion event-building pairs before pruning. Most pairs drop out because the event never reaches the building, and finding which ones drop out is itself a spatial join. Each event also needs a raster sample per footprint, a zonal statistic over each building polygon, and a lookup against parcel attributes.
That workload is a raster-vector join at state or national scale, repeated for every event, peril, and model version.
Wherobots does not ship a stochastic catastrophe model. WherobotsDB runs the spatial joins that a stochastic model of physical risk depends on: hazard rasters and footprints joined to buildings and parcels, in SQL, at state and national scale.
In How to score every building in a state for catastrophe risk, WherobotsDB joined 2,771,126 Overture buildings in Colorado to the Regrid parcels they sit on and scored each one across five perils. The inputs included the USFS Wildfire Risk to Communities 30 m raster, 403 million NOAA radar hail observations since 2016, and the FEMA National Flood Hazard Layer. RS_ZonalStats sampled the wildfire raster under each footprint, and the run scored the full state in a few minutes on one WherobotsDB medium runtime.
The same raster-vector pattern applies to each footprint in an event set. A separate benchmark completed a statewide zonal statistics analysis across every building in Texas in 3 minutes 28 seconds. For a hazard defined by a rainfall threshold, the El Niño 2026 debris flow analysis counted 7,713 buildings inside or within 500 m of high-hazard basins above Altadena.
Simulated loss tables are also context for AI. The models people use every day were trained on text, documents, databases, and the internet, and they cannot compute which buildings sit inside a 100-year flood footprint. Through the Wherobots MCP server, geospatial AI agents run that query against the same tables an analyst uses.
Join hazard footprints to every building in a state on the Wherobots free tier at cloud.wherobots.com.
Stochastic modeling is a way to forecast an uncertain quantity by treating its inputs as random. The model draws input values from probability distributions, runs thousands of times, and reports the range of outcomes and how likely each one is. A deterministic model returns a single answer for a fixed set of inputs.
Monte Carlo simulation is the most common method for running a stochastic model. It draws random samples from each input distribution, computes the outcome for each draw, and repeats the process thousands or millions of times. The collected outcomes approximate the probability distribution of the result. Stochastic modelling is the broader idea; Monte Carlo is a technique for solving it.
A deterministic model produces the same output every time it runs with the same inputs. A stochastic model includes random variables, so each run produces a different output, and many runs together form a probability distribution. A fixed 5% interest projection is deterministic; a projection that draws each year’s return from a distribution is stochastic.
Stochastic processes are commonly grouped by whether time and the state are discrete or continuous: discrete time with discrete states (a Markov chain), discrete time with continuous states (an autoregressive time series), continuous time with discrete states (a Poisson process), and continuous time with continuous states (Brownian motion).
The terms overlap, and many authors use them interchangeably. Probabilistic modeling is the broader category: any model that represents uncertainty with probability distributions. Stochastic modeling usually refers to models of random processes that evolve over time or space, solved by simulating many sample paths.
A stochastic event set is a catalog of simulated catastrophes, such as hurricanes, floods, earthquakes, or wildfires, each with an annual rate of occurrence and a hazard footprint. Catastrophe models run the event set against buildings and policies to produce loss distributions, average annual loss, and exceedance probability curves.
Stochastic modeling is used in finance for asset returns and retirement planning, in insurance for reserving and catastrophe risk, in epidemiology for outbreak spread, in operations for queues and inventory, and in weather and climate science for ensemble forecasts and weather generators.
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