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.
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.
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.
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.
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.
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.
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.
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.
Credible intervals express our belief that the true underlying value is contained within the interval conditional on the conducted simulation run. Contrary to that, confidence intervals are only meaningful for a large number of repeated simulation runs.
