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I would like to determine if there is a statistically significant difference between the predictions of two Bayesian models.

  • Model1 predicts the distance travelled on foot during daylight based on population density, traffic stress levels, and crime rate.

  • Model2 predicts the distance travelled on foot in the dark using the same predictors.

My goal is to determine if the effect of these factors (population density, traffic stress levels, and crime rate) changes significantly based on light conditions (daylight and dark). I have posterior means and 95% credible intervals for each model. My understanding is that I can compare these credible intervals to determine if the difference between the models is significant. If the intervals do not overlap, it indicates that the difference between the models is significant. However, if the intervals overlap, it does not necessarily mean that their difference is not statistically significant. Am I right? Therefore, I want to conduct this test to be certain that factors with overlapping credible intervals are not statistically significant.

Eugeni
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    If the only difference between the models is daytime/nighttime, why not nest them and do a Bayesian version of a t-test? – Durden Feb 03 '24 at 18:39
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    Have you considered fitting one model for distance traveled? In R Distance ~ (X1 + X2 + X3) * time_of_day where time_of_day is an indicator variable / a factor which indicates daylight or nighttime. Then look at the posterior distributions of the interaction terms between time_of_day and each of the predictors Xi. (You also mix concepts from Bayesian and classical statistics.) – dipetkov Feb 03 '24 at 21:40

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