The results that you can get from a MCMC analysis will look like this : With this notebook, we have simulated and carried out a MCMC analysis for a source with the following parameters: \(Index=2.0\), \(Norm=5\times10^\) (50 TeV) for 20 hours. Now let’s try to put a picture on the ideas described above. This will provide the errors and correlations between parameters. We can compute theĭistribution of each parameter by simply approximating it with the histogram of the samples projected into the parameter space. This means that, once we have obtained the chain of samples, we have everything we need. Once it has reached this stage, each successive elements of the chain are samples of the target posterior distribution. If you start far away from the truth value, the chain will take some time to converge until it reaches a stationary state. The goal is to produce a “chain”, i.e. a list of \(\theta\) values, where each \(\theta\) is a vector of parameters for your model. The idea is that we use a number of walkers that will sample the posterior distribution (i.e. sample the Likelihood profile). For most readers this sentence was probably not very helpful so here we’ll start straight with and example but you should read the more detailed mathematical approaches of the method here and The goal of Markov Chain Monte Carlo (MCMC) algorithms is to approximate the posterior distribution of your model parameters by random sampling in a probabilistic space. MCMC sampling using the emcee package Introduction Source files: mcmc_sampling.ipynb | mcmc_sampling.py This is a fixed-text formatted version of a Jupyter notebook
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