"RegressionCoefficientDistribution": The join distribution over a and b."UnderlyingValueDistribution": Similar to "PredictiveDistribution", but this distribution give the possible values of a + b x without the randomness error term.This distribution accounts for all relevant uncertainties in the model: model variance caused by the term randomness uncertainty in the values of a and b and uncertainty in sigma. By filling in a value for x, you get a distribution that tells you where you could expect to find future y values. "PredictiveDistribution": A distribution that depends on the independent variables ( x in the example above)."Posterior", "Prior": These two keys each hold an association with 4 distributions:."Basis", "IndependentVariables": Simply the basis functions and independent variable specified by the user.The evidence has the virtue that it naturally penalizes models for their complexity and therefore does not suffer from over-fitting in the way that measures like the sum-of-squares or likelihood do. "LogEvidence": In a Bayesian setting, the evidence (also called marginal likelihood) measures how well the model fits the data (with a higher evidence indicating a better fit).Fitting polynomialsįirst generate some test data: data = RandomVariate[ The code is in this file, in case you're interested in taking a look under the hood. Please refer to the GitHub README.md file (which is displayed on the homepage of the repository) for instructions about installing the BayesianInference package. The example notebook in the repository provides several examples of how the function can be used, some of which I will reproduce below. I also submitted the code for this function to the Wolfram function repository to make it easier to access, so the function can also be used with ResourceFunction. Recently I updated my Bayesian inference reporitory with a new function called BayesianLinearRegression to provide a Bayesian alternative to Mathematica's LinearModelFit. Finance, Statistics & Business Analysis.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha.
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