# Bayesian updating normal distribution sample

It can range from minus infinite to plus infinite. To get a feel what is behind the math the following reasoning may suffice. Now, let's start thinking about this as a Bayesian estimation problem. Process distribution, the distribution resulting from a data generating process.

The distribution of this parameter is updated. Predictive distribution, the distribution of future observations. For prospect appraisal this is usually a worldwide sampling as used in the Gaeapas appraisal program. Params is an object that encapsulates these values.

Starting at different points yields different flows over time. This is especially so, as an appraiser may not have such a wide experience himself. In general, for nearly all conjugate prior distributions, the hyperparameters can be interpreted in terms of pseudo-observations. First, mesh is the Cartesian product of the parameter arrays.

If several new observations are made, the mean value of these is used and compared to the prior distribution. The following data and calculation shows what happens in this example. This greatly simplifies the analysis, as it otherwise considers an infinite-dimensional space space of all functions, space of all distributions. It combines in the simulation model the world-wide variation of a variable and the relevant local data to give the most realistic value and its uncertainty. It could be that the new information samples are not all from m depth, but from betwen and meter, say.

The predictive variance must then still be calculated, invoving the sample size of the process, if available. Since we don't need a lot of precision, I'll draw a sample. When a prior dataset can be roughly represented by a normal distribution, bayesian statistics show that sample information from the same process can be used to obtain a posterior normal distribution. The latter is a weighted combination of the prior and the sample. Note that this distribution is that of the mean.

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