Bayesian analysis

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Probabilistic modeling

Structural design: characteristic value of concrete

This web app quantifies the uncertainty about the strength of concrete probabilistically and evaluates the characteristic value.

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Reliability analysis

Post-processing of Monte Carlo simulation

Use our web app to quantify the uncertainty about the probability of failure based on a conducted Monte Carlo simulation.

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Probabilistic modeling

Normal-gamma distribution

The Normal-gamma distribution serves as conjugate prior for a Normal distribution with unknown mean and standard deviation. As parameters for the prior, the prior mean and variance can be used, along with the number of associated (pseudo-)observations.

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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.

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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.

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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.

Reliability analysis

Why should you avoid Normal confidence intervals for Monte Carlo simulation?

The underlying distribution can be highly skewed, even if the total number of samples in the Monte Carlo simultion is very large. This is why the Normal approximation often performs poorly in practice.

Reliability analysis

Why to avoid the coefficient of variation in the context of a Monte Carlo simulation?

The distribution quantifying the uncertainty about the probability of failure can be highly skewed, even for a large number of samples. The coefficient of variation is easier to interprete for symmetric distributions.