Hi UQWorld!

I’m using the Bayesian Linear regression example proposed by UQLab, in order to calibrate a macroseismic model for the seismic vulnerability assessment of existing buildings on urban scale.

**CONTEXT**

The model that I use defines the seismic vulnerability index (Iv) of a existing building, as the sum of scores (C_i) assigned to 14 structural features, multiplied with appropriate weights (p_i), in function of the importance of the parameter in the dynamic behaviour of the construction, during a seismic event.

Seismic vulnerability index:

Iv=∑pi∙ci ,where{c_i=score of the parameter "“i”; p_i=weight of the parameter “i”)

The model is calibrated, combining the expected damage scenario, evaluated through a specific formulation that contains the seismic vulnerability index (Iv), with the real damage scenario of a case study hit by the recent 2016 Italian earthquake.

Real damage = Expected damage scenario = 2.5+3· tanh ((I+6.25 ∙ Iv -12.7)/Q)

**PURPOSE OF THE CALIBRATION:**

The purpose of the calibration is to change the 14 weights used for the evaluation of the seismic vulnerability of each building in an historical center composed by 67 buildings, in order to elaborate a theoretical damage scenario, similar to the one detected.

I tried to calibrate my model with different systems like the genetic algorithm, a pure monte carlo approach and optimization tools, but the Bayesian linear regression is the one that works best.

**QUESTION:**

Can I force the Metropolis algorithm to search only positive values that fit the problem and that are around a range of specific values?

Example: Point estimate in the posterior distribution: x1 = [1 ÷ 2] , x2 = [0,5 ÷ 1], …, x14 = [1 ÷ 2,5].

Sorry for the long explanation but I wanted to be precise. I am also available to send the model, that I have prepared if someone is interested. Any kind of anwer or suggestion is welcome

I will be highly grateful to you and thank you UQLab for you work.

Best Regards

Federico Romis