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信号検出理論の解説 (Signal detection theory, a primer)

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駒場集中講義用資料。1/10 第2回講義分です。英語です。古いバージョンは消さずにこちらに誘導。

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信号検出理論の解説 (Signal detection theory, a primer)

  1. 1. SDT primerYou have a sensor (1D continuous value).You have to decide which is a signal and which is a noise, based on the sensor value.When you classify the data as signal, you are aware of the signal.
  2. 2. SDT primerYou have a sensor (1D continuous value).You have to decide which is a signal and which is a noise, based on the sensor value.When you classify the data as signal, you are aware of the signal.1) You collect samples.2) You set the criteria for optimal discrimination.3) You classify new data by comparing the sensor value and the criteria.
  3. 3. 1) You collect samples.
  4. 4. 1) You collect samples.2) You set the criteria for optimal discrimination.
  5. 5. 1) You collect samples (training data).2) You set the criteria for optimal discrimination.3) You classify new data by comparing the sensor value and the criteria.
  6. 6. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  7. 7. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  8. 8. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  9. 9. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  10. 10. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  11. 11. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  12. 12. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  13. 13. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  14. 14. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  15. 15. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  16. 16. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  17. 17. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  18. 18. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  19. 19. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  20. 20. SDT primer1) You collect samples (training data).2) You set the criteria for optimal discrimination.3) You classify test data by comparing the sensor value and the criteria.When you classify the data as signal, you are aware of the signal.Let’s do it again, with different data set.
  21. 21. 1) You collect samples (training data).
  22. 22. 1) You collect samples (training data).2) You set the criteria for optimal discrimination.
  23. 23. 1) You collect samples.2) You set the criteria for optimal discrimination.3) You classify new data by comparing the sensor value and the criteria.
  24. 24. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  25. 25. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  26. 26. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  27. 27. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  28. 28. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  29. 29. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  30. 30. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  31. 31. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  32. 32. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  33. 33. 3) You classify new data by comparing the sensor value and the criteria. Criteria
  34. 34. Recognition model (=> model-free) Unknown processes classifygenerate with criteria (c=2) awareness as decision Data (signal or noise)
  35. 35. Generative model (=> model-based) Processes with unknown parameters Noise: N(0,1); Signal: N(d’,1) Estimate parametergenerate (d’ = 4) and classify with criteria Data (signal or noise)
  36. 36. SDT primerProcesses with unknown parametersNoise: N(0,1); Signal: N(d’,1)
  37. 37. SDT primer Processes with unknown parameters Noise: N(0,1); Signal: N(d’,1)The sensitivity of the sensor is characterized as d’.d’ is independent of criteria (c).(The correct ratio depends on c.)
  38. 38. SDT primer Processes with unknown parameters Noise: N(0,1); Signal: N(d’,1)The sensitivity of the sensor is characterized as d’.d’ is independent of criteria (c).(The correct ratio depends on c.)OK, but we have no such sensor.How to estimate d’ in psychophysics?
  39. 39. By changing criteria
  40. 40. By changing criteria1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).3) You obtain data set 1 (with hit, miss, FA, CR).4) Repeat 1)-3) with different criteria.5) You reconstruct the distribution of samples.6) You estimate d’.
  41. 41. 1) You set a criterion and classify samples.
  42. 42. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  43. 43. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  44. 44. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  45. 45. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  46. 46. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  47. 47. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  48. 48. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  49. 49. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  50. 50. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  51. 51. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  52. 52. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  53. 53. signal noise yes hit ● ○ FA no miss ○ CR ●1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).
  54. 54. 1) You set a criterion and classify samples.2) You get the feedback (correct or incorrect).3) You obtain data set 1 (with hit, miss, FA, CR).
  55. 55. 4) Repeat 1)-3) with different criteria.
  56. 56. 4) Repeat 1)-3) with different criteria.
  57. 57. 4) Repeat 1)-3) with different criteria.
  58. 58. 4) Repeat 1)-3) with different criteria.
  59. 59. 4) Repeat 1)-3) with different criteria.
  60. 60. 4) Repeat 1)-3) with different criteria.
  61. 61. 4) Repeat 1)-3) with different criteria.
  62. 62. 4) Repeat 1)-3) with different criteria.
  63. 63. 5) You reconstruct the distribution of samples.6) You estimate d’.
  64. 64. 5) You reconstruct the distribution of samples.6) You estimate d’.
  65. 65. 5) You reconstruct the distribution of samples.6) You estimate d’.
  66. 66. 5) You reconstruct the distribution of samples.6) You estimate d’.
  67. 67. 5) You reconstruct the distribution of samples.6) You estimate d’.
  68. 68. 5) You reconstruct the distribution of samples.6) You estimate d’.
  69. 69. 5) You reconstruct the distribution of samples.6) You estimate d’.
  70. 70. How do you change the criteria?
  71. 71. How do you change the criteria?1) Confidence rating (Human study)
  72. 72. How do you change the criteria?1) Confidence rating (Human study)
  73. 73. How do you change the criteria?1) Confidence rating (Human study) No Yes
  74. 74. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure
  75. 75. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure2) By changing value or probability (animal study)
  76. 76. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure2) By changing value or probability (animal study)
  77. 77. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure2) By changing value or probability (animal study)
  78. 78. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure2) By changing value or probability (animal study)
  79. 79. How do you change the criteria?1) Confidence rating (Human study) Very sure Sure Uncertain Uncertain Sure Very sure2) By changing value or probability (animal study)

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