Thank you so much for your detailed reply. I do want to use censoring. I modified the y_err for case of upper and lower limit by myself so that I can flag the censored and uncensored data. For high-y I only know the lower limit on ys and for low-y I only know the upper limit so I modified their errors so as to flag them. Still with your modification and as also can be seen from your plot, the fit is not very well taking into account the last four lower limits on y’s know? Do you think it should be like this only, if the data points beyond some x values are having lower y values then I would expect fit to be steeper know? And this is indeed what I am getting when my datapoints in simulation are less scattered.