For observational data, the derivation of confidence intervals must use subjective models, as emphasized by Ronald Fisher and his followers.
fɔːɹ ɑːbzɚvˈeɪʃənəl dˈeɪɾə, ðə dˌɛɹɪvˈeɪʃən ʌv kˈɑːnfɪdəns ˈɪntɚvəlz mˈʌst jˈuːz sʌbdʒˈɛktɪv mˈɑːdəlz, æz ˈɛmfɐsˌaɪzd baɪ ɹˈɑːnəld fˈɪʃɚ ænd hɪz fˈɑːloʊɚz.