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I am interested in using Bayesian modele averaging as a selection creteria (BMA) vs AIC. I read that BMA is widely implemented in clustering models.

Suppose that we need to fit M models to a data and select the best among them using BMA. Suppose that BIC for each model is calculated. Then, I read that some author use BIC as weight for BMA. However, instead of using BIC directly, they substract maximum or minimum BIC from each BIC_M of each fitted model.

As here Use BIC or AIC as approximation for Bayesian Model Averaging

Suppose we have three fitted models. Suppose the BICs values as follows:

BIC_1 = -122 BIC_2 = - 130 BIC_3 = - 230

So, if we substract the lowest value which is BIC_3, then, BIC_ - BIC_3 = 0.

Is that Ok?. I mean if we substract the lowest BIC from itself we will have a zero.

Any help, please?

Richard Hardy
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Alice
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  • The weights are not the $\operatorname{BIC}_i$s but $w_i = \exp{-\operatorname{BIC}_i/2} / \sum_i \exp{-\operatorname{BIC}_i/2}$; that is, the $\operatorname{BIC}_i$s exponentiated and then normalized to sum up to 1. The $\exp$ function has the following property: $\exp(x+y)=\exp(x)\exp(y)$. You can use it to show that subtracting the same value from all $\operatorname{BIC}_i$s doesn't change the corresponding weights. The linked answer also explains why it's a good idea to calculate the weights this way. – dipetkov Sep 24 '23 at 14:11

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