# Probabilistic modeling

Probabilistic modeling

## What is the underlying standard Normal space?

The uncertain model parameters are transformed into independent standard Normal random variables. For the performance and stability of numerical algorithms, performing such a transformation step is sometimes preferable.

ONLINE TOOL
Probabilistic modeling

## Poisson process: post-processing

Use our web app to quantify the uncertainty about the rate of a Poisson process based on observing a specific number of event occurrences within a given time.
try it ...

ONLINE TOOL
Probabilistic modeling

## Poisson process: estimate required experiment duration

Use our web app to decide how long an experiment needs to run in order to demonstrate that your system is reliable.
try it ...

Probabilistic modeling

## For how long do you need to observe a Poisson process to ensure that its rate is smaller than a specified threshold?

With assumptions on how many events will occur, one can determine the time required to demonstrate that the rate is below a target value with a specified credible level.

Probabilistic modeling

## What conclusions can we draw if we did not observe any occurrences of a Poisson process within a given time interval?

Using a Bayesian post-processing strategy, the uncertainty about the rate of a Poisson process can be fully quantified even if no occurrences were observed.

Probabilistic modeling

## Does it make a difference whether or not a discretized Poisson process is used in Bayesian post-processing?

Even though the underlying posterior distributions are of different type, the results will be the same if the rate of the Poisson process is sufficiently small and weakly informative and consistent priors are used.

Probabilistic modeling

## What prior to use when learning the rate of a Poisson process?

A weakly informative prior that follows a Gamma distribution with shape parameter 1 and rate parameter 2 is a suitable choice for many problems. Working with informative prior distributions requires careful handling and a close look at the quantiles.

Probabilistic modeling

## How to quantify the uncertainty about the rate of a Poisson process?

We explain a Bayesian post-processing step for learning the rate of a Poisson process. It is ideally suited to quantify the uncertainty and to evaluate credible intervals.

Probabilistic modeling

## What is a Poisson process?

A Poisson process is used to model the occurrence of independent random events along a continuous axis. It is a very important stochastic process in probabilistic modeling.