The central quantity in Bayesian inference, the posterior, can usually not be calculated analytically, but needs to be estimated by numerical integration, which is typically done with a Monte-Carlo algorithm. The three main algorithm classes for doing so are Rejection sampling Markov-Chain Monte Carlo (MCMC) sampling Sequential Monte Carlo (SMC) sampling I have previously given…
As announced a while ago, we had moved our now already traditional summer school in Bayesian Statistics to Bergen, Norway this year. Maybe fitting for such a course, the weather turned out to be very different from the long-term frequency, in what must be the upper 1% quantile of sun intensity for the region at…
Approximate Bayesian Computing and similar techniques, which are based on calculating approximate likelihood values based on samples from a stochastic simulation model, have attracted a lot of attention in the last years, owing to their promise to provide a general statistical technique for stochastic processes of any complexity, without the limitations that apply to “traditional”…
Our new review on statistical inference for stochastic simulation models is now available at Ecology Letters. The paper discusses how approximate likelihood functions can be generated from stochastic simulations. Such simulation-based likelihood approximations are a very general and powerful tool because they allow us to apply statistical methods to a large class of models such…
While there are certainly good software packages out there to do the job for you, notably BUGS or JAGS, but also our own BayesianTools package with general-purpose MCMC samplers, it is instructive to program a simple MCMC yourself. In this post, I give an educational example of the Bayesian equivalent of a linear regression, sampled…
theoretical ecology 