Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 278
홍차넷
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 34
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 45
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 47
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 51
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 237
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 34
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 45
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 47
Warning: Use of undefined constant r - assumed 'r' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/outlogin_toby.php on line 51
Warning: Use of undefined constant memo - assumed 'memo' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 237
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/zero_header.php on line 269
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/zero_header.php on line 300
Warning: Use of undefined constant title - assumed 'title' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 16
티타임
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 21
Warning: Use of undefined constant header - assumed 'header' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 31
- 다양한 주제에 대해 자유롭게 글을 작성하는 게시판입니다.
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 519
Warning: Use of undefined constant use_category - assumed 'use_category' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/include/print_category.php on line 9
전체기타일상/생각꿀팁/강좌방송/연예도서/문학영화의료/건강문화/예술경제생활체육과학/기술철학/종교정치요리/음식역사여행육아/가정IT/컴퓨터음악창작게임스포츠사회오프모임
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/setup.php on line 29
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/setup.php on line 41
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 398
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
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Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
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Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
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Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
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Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant subject - assumed 'subject' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 402
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
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Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 403
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 405
Warning: Use of undefined constant total_comment - assumed 'total_comment' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 406
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 2
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/memo_replace.php on line 3
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 10
Warning: Use of undefined constant use_category - assumed 'use_category' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 40
| Date |
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 53 15/11/02 11:16:29 Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 56 |
| Name | Beer Inside |
| Subject | 베이즈 정리, 몬티홀의 문제, 삶과 죽음의 확률 |
 잊어 먹을만 하면 한번 씩 나와서 답을 아는 사람과 모르는 사람 모두 암걸리게 하는 문제입니다. 1970년대 방송인 몬티 홀이 진행하는 퀴즈쇼에서 일어난 상황인데 1990년 칼럼니스트 마릴린 사반트가 잡지 ‘퍼레이드’에서 이 문제를 질문한 독자의 편지에 대해 답을 하면서 유명해졌습니다. 한 곳에는 스포츠카가 나머지 두 곳에는 염소가 들어있습니다. 문을 열었을 때 스포츠카가 있을 확률은 3분의 1. 퀴즈 참가자가 1번 문을 찍었다. 이때 ‘스포츠카가 어디에 있는지 알고 있는’ 홀이 3번 문을 활짝 열었고 염소가 모습을 드러냈다. 그리고 홀이 참가자에게 물었습니다. “선택을 바꾸시겠습니까?” 몬티홀 문제의 핵심은 참가자가 새로 얻게 된 정보(3번 방에는 스포츠카가 없다)를 어떻게 추론에 반영하느냐 하는 것입니다. 이 때 사용하는 것이 베이즈 정리입니다. 베이즈는 영국의 목사로 살아 생전 단 두편의 논문만 출간했는데, 한편은 종교 다른 한편은 수학이였다고 합니다. 이 베이즈가 죽고난 후 친구인 리차드 프라이스가 정리해서 발표했습니다. 베이즈(싸이코의 노먼 베이츠 아닙니다.) 정리는 이전의 경험과 현재의 증거를 토대로 어떤 사건의 확률을 추론하는 알고리즘으로, 극단적으로 단순화하면 먼저 일어나는 사건 A가 있고 시간상 다음에 일어나는 사건 B가 있을 때 사건 B가 일어난 것을 전제로 한 사건 A의 조건부 확률을 구하는 것이라고 생각할 수 있습니다.  (이해 하기 쉬우라고 수식을 쓰지만 수식만 보면 토할 것 같습니다.) 직관적으로 생각하면 각 방에 스포츠카(C)가 있을 확률은 3분의 1로 똑 같고 (P(C1)=P(C2)=P(C3)=1/3) 참가자가 일단 1번 방을 선택한 뒤 진행자가 3번 방을 열었기 때문에(따라서 3번 방은 아니다) 1번 방과 2번 방에 스포츠카가 있을 확률이 1/2로 똑 같을 것 같습니다. 따라서 굳이 선택을 바꿀 필요는 없을 것 같습니다. 바꿔도 기대 확률은 마찬가지이기 때문입니다. 하지만, 마음 속 깊은 곳이나 뒷골 어디인가에서 바꾸고 싶다. 바꾼다고 특별히 달라지는 것은 없을 것 같지만 격렬하게 바꾸고 싶다는 생각이 들지 않습니까? 베이즈 정리에 따르면 선택을 2번으로 바꾸는 것이 답입니다. 이 경우 맞출 확률이 3분의 2로 2배나 높아지기 때문입니다. 이 칼럼이 나가고 설명을 이해할 수 없다는 독자 편지가 쇄도했고 전문가들 사이에서도 논란이 일었습니다. 심지어 폴 에르되시 같은 일급 수학자조차 “왜 선택을 바꿔야하는지 이해하지 못 하겠다”는 반응을 보였습니다. (그러니 유머란에 이 문제가 다시 나와도 암걸릴 것 같은 사람은 또 생길겁니다.) 몬티홀 문제의 핵심은 참가자가 새로 얻게 된 정보(3번 방에는 스포츠카가 없다)를 어떻게 추론에 반영하느냐 하는 것입니다. 이때 베이즈 정리를 쓰면 선택을 바꿔야 하는 깔끔하게 이유가 설명됩니다. 새로운 정보, 즉 진행자가 3번 방을 열었을 때(O3) 1번 방에 스포츠카(C1)가 있을 확률은 다음의 베이즈 정리로 나타낼 수 있다. P(C1|O3)=P(O3|C1)P(C1)/P(O3)=(1/2)×(1/3)/(1/2)=1/3 차가 1번에 있다면 진행자는 2번이나 3번 문을 열 수 있습니다. 따라서 P(O3|C1)는 2분의 1입니다. 한편 참가자의 관점에서 자기가 1번 방을 선택했기 때문에 진행자는 2번이나 3번 문을 열 수 밖에 없으므로 P(O3) 역시 2분의 1입니다. 이제 진행자가 3번 방을 열었을 때(O3) 2번 방에 스포츠카가 있을 확률을 베이즈 정리로 구해봅시다. 차가 2번에 있다면 진행자는 3번 문을 열 수 밖에 없습니다. 따라서 P(O3|C2)는 1입니다. P(C2|O3)=P(O3|C2)P(C2)/P(O3)=1×(1/3)/(1/2)=2/3 결국 홀이 3번 문을 열고 난 뒤, 즉 새로운 정보가 알려진 뒤 2번 방에 스포츠카가 있을 확률은 3분의 2로 2배 높아집니다. 따라서 참가자가 자신의 감을 믿지 않고 순전히 확률이 높은 쪽을 택하기로 했다면 무조건 2번으로 선택을 바꿔야 합니다. 그깟 몬티홀 문제 풀지 않으면 그만 아니냐구요. 그럼 이 문제는 어떤가요? 45세 골드미스 A씨는 자신의 가슴을 만져보다가 이상한 느낌이 들어서 병원에 갔습니다. (몬티홀 문제를 너무 오래 쳐다 보았나 봅니다.) 유방암 검사를 했고 검사 결과는 양성이였습니다. 그리고 이 검사의 검사 정확도는 90%입니다. A씨는 결혼도 못하고 아이도 없는데 유방암이라는 진단이 나와서 기가 막혀서 진료실에서 눈물을 흘렸습니다. 하지만 이 놈의 의사 자식은 웃으면서 이 상태에서는 유방암일 확률이 10%도 되지 않으니 추가 검사를 해 보자고 합니다. 자꾸 돈들게 말입니다. 이 싸이코패스 같은 의사는 유방암에 걸린 여성은 성인 여성의 1% 수준이고 (실제는 10만명당 321명이 발생합니다. 대략 0.3%) 검사 정확도가 90%이므로 정상인데도 검사에서 유방암에 걸린 것으로 나올 확률은 10%다. 따라서 설사 검사에서 양성으로 나왔더라도 진짜 유방암에 걸렸을 확률은 8%에 불과하다는 겁니다. (암이라는데 확률강의를 하는 싸이코패스 의사야!)  A씨의 사례는 ‘양성반응일 때 유방암일 확률’을 구하는 것 입니다. 즉 양성반응이라는 조건에서 유방암일 확률을 ‘P(암|양성)’으로 나타내면, P(암|양성)=P(양성|암)P(암)/P(양성) P(양성|암) = 0.9 P(암) = 0.01 P(양성) = 암일 때 양성일 확률 + 암이 아닐 때 양성일 확률 = 0.9*0.01+0.1*0.99= 0.108 따라서 P(암|양성) = 0.9* 0.01/0.108 = 0.083 즉 검사에서 양성일 경우 유방암일 확률은 8.3%가 됩니다. 만약 이 검사에서 음성으로 나오면 음성예측치는 90%이므로 추가 검사할 필요가 없다고 보아야겠지요. 이 환자는 8.3%의 확률을 확인하기 위해서 조직 검사를 했고 조직검사상 양성이 나왔습니다. (조직검서의 민감도는 100%라고 합시다. Borderline pathologisit가 아니라면...) 이후 A씨는 잘 지내다가 5년 후인 50세에 다시 가슴에 무엇인가 느껴집니다. 이번에는 별것 아니라는 생각에 병원에 방문해서 저번에 그 의사가 미친놈 같았지만 결과가 좋았으므로 다시 그 의사에게 유방암 검사를 합니다. 이번에도 양성이 나왔는데, 의사의 표정이 좋지 않습니다. A씨는 이 넘이 오늘 기분이 좋지 않나 생각을 하는데, 이 싸이코패스가 또 통계 강의를 합니다. 5년 동안 유방암 진단기술이 발전해서 민감도가 99%로 증가했다는 것 입니다.  P(양성|암) = 0.99 P(암) = 0.01 P(양성) = 암일 때 양성일 확률 + 암이 아닐 때 양성일 확률 = 0.99*0.01+0.01*0.99= 0.0198 P(암|양성) = 0.99*0.01/0.0198 = 0.5 따라서 암일 확률은 50%라고 합니다. 그러니 의사를 잘 만나야 합니다. 이런 설명을 자세하게 해 주는 의사는 높은 확률로 싸이코패스일겁니다. 하지만 스텐포드의 에프론 교수는 무시무시한 Impact Factor를 가진 Science에서 오늘날 응용통계를 이용한 논문의 25%는 베이즈 정리를 이용하고 있다고 합니다. 베이즈 정리가 나온지 250년이 넘었고, 최근들어 여러 문제를 해결하는데 자주 쓰이고 있지만 이에 대한 비판도 있습니다. 베이즈 정리는 사전 정보(prior)가 확실한 것일 때만 성립하는 것인데 실제 상황에서는 이 정보가 100% 확실한 경우가 별로 없기 때문입니다. 결국 불확실한 사전 정보를 토대로 사후 확률(posterior)을 추측하는 것이 타당한가에 대한 입장이 엇갈리고 있습니다. 이글은 아래 글을 참고해서 작성했습니다. Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 133 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 146 Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 161 7 이 게시판에 등록된 Beer Inside님의 최근 게시물
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Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 542
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Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 429
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 605
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Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 609
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Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 644
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 646
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Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/cmt_replace.php on line 3
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 6
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 28
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 65
20839 class="iamcmt" style="display:none;"> Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 66
20839 class='vcm '>
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 70
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 71
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 76
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 117
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 118
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 119
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 120
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 121
20839'> 세인트
Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 133
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
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15/11/02 11:25
20839>삭제 주소복사
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 150
이과 흥했으면... 크크 재밌네요 근데 전 수알못이라 몬티홀 이야기 나올때마다 골이 아파요 흐흐
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
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