In section 3.2, the paper builds constraints on lost cities under "short detour" and "pit stop" assumptions. Though the assumptions seem reasonable to me, the choice of parameters (lambda and mu) are relatively loose. The explanation for this is to prevent from getting empty sets for the admissible regions for the cities of Purushaddum and Kuburnat. However, for a peripheral city, the reliability of the embedded estimation method under gravity model is challenged. Hence, the estimated location of the city of Purushaddum is quite far from what was speculated from historians and not believed to be near the true site. Moreover, for the case of Kuburnat, there is no inference provided for the deviation from the estimated location and the conjectures from historians. Are these facts suggesting that trade-relevant data are not sufficient for determining the location for the two lost cities? If so, can we ignore the constraints caused by the two cities and choose "tighter" parameters since they might improve the precision of the estimation of the admissible regions for other lost cities?
Thanks for presenting this interesting paper!
In section 3.2, the paper builds constraints on lost cities under "short detour" and "pit stop" assumptions. Though the assumptions seem reasonable to me, the choice of parameters (lambda and mu) are relatively loose. The explanation for this is to prevent from getting empty sets for the admissible regions for the cities of Purushaddum and Kuburnat. However, for a peripheral city, the reliability of the embedded estimation method under gravity model is challenged. Hence, the estimated location of the city of Purushaddum is quite far from what was speculated from historians and not believed to be near the true site. Moreover, for the case of Kuburnat, there is no inference provided for the deviation from the estimated location and the conjectures from historians. Are these facts suggesting that trade-relevant data are not sufficient for determining the location for the two lost cities? If so, can we ignore the constraints caused by the two cities and choose "tighter" parameters since they might improve the precision of the estimation of the admissible regions for other lost cities?