1 / 57

Stochastic motion rate

Chasing peaks. Stochastic motion rate. Ornstein-Uhlenbeck mean. Continuous state. Brian O’Meara http:// www.brianomeara.info. and/or. Directionally: be pulled towards some value. In what ways can a continuous trait change in an instant of time?.

dalmar
Download Presentation

Stochastic motion rate

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chasing peaks Stochastic motion rate Ornstein-Uhlenbeck mean Continuous state Brian O’Meara http://www.brianomeara.info

  2. and/or Directionally: be pulled towards some value In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance

  3. In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value

  4. In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value

  5. Rate of wiggle In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value

  6. In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value

  7. Adds the entire difference In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value

  8. In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value Allows directional change less than 100% (even zero)

  9. In what ways can a continuous trait change in an instant of time? Randomly: increase or decrease slightly by chance and/or Directionally: be pulled towards some value Ornstein-Uhlenbeck process

  10. Ornstein-Uhlenbeck process

  11. 1 1 1 1 1

  12. 2 2 2 2 2

  13. 3 3 3 3 3

  14. And so forth... 3 3 3 3 3

  15. Brownian rate OU attraction OU mean

  16. Brownian rate OU attraction OU mean

  17. Brownian rate OU attraction OU mean

  18. Hansen 1997

  19. Hansen 1997

  20. Info and collage from Luke Mahler, http://lukemahler.com/. Photos by J. Losos, B.Falk, M. Landestoy, and L. Mahler

  21. Butler & King 2004

  22. Butler & King 2004

  23. ∆ Butler & King 2004

  24. Butler & King 2004

  25. Build up (paint regimes one at a time) Merge SURFACE: Ingram & Mahler 2013

  26. Mahler, Ingram, Revell, Losos 2013 (Science!)

  27. Brownian rate OU attraction OU mean

  28. Brownian rate OU attraction OU mean

  29. Beaulieu, Jhwueng, Boettiger, O'Meara 2012

  30. Beaulieu, Jhwueng, Boettiger, O'Meara 2012

  31. Beaulieu, Jhwueng, Boettiger, O'Meara 2012

  32. Beaulieu, Jhwueng, Boettiger, O'Meara 2012

  33. Beaulieu, Jhwueng, Boettiger, O'Meara 2012

  34. Hansen & Martins 1996

  35. Brownian motion OU or OU-like Hansen & Martins 1996

  36. Some applications of ABC

  37. What is the probability of heads for our coin?

  38. What is the probability of heads for our coin?

  39. What is the probability of heads for our coin?

  40. What is the probability of heads for our coin?

  41. What is the probability of heads for our coin? Sim 1: HTTTTHTT Sim 2: TTHHTTTT Sim 3: TTTHHTHH Sim 4: TTTTTTTT Sim 5: TTTTTTTT Sim 6: THHTTTTH Sim 7: TTHHTTHT Sim 8: TTTTHHHT Sim 9: HTTHTTTT Sim 10: THHHTHTT Let p = 0.2

  42. What is the probability of heads for our coin? Sim 1: HTTTTHTT Sim 2: TTHHTTTT Sim 3: TTTHHTHH Sim 4: TTTTTTTT Sim 5: TTTTTTTT Sim 6: THHTTTTH Sim 7: TTHHTTHT Sim 8: TTTTHHHT Sim 9: HTTHTTTT Sim 10: THHHTHTT Let p = 0.2

  43. What is the probability of heads for our coin? Sim 1: HTTTTHTT Sim 2: TTHHTTTT Sim 3: TTTHHTHH Sim 4: TTTTTTTT Sim 5: TTTTTTTT Sim 6: THHTTTTH Sim 7: TTHHTTHT Sim 8: TTTTHHHT Sim 9: HTTHTTTT Sim 10: THHHTHTT Let p = 0.2 P(data) ≈ 1/10

  44. What is the probability of heads for our coin? True Approximation 200 simulations per p

  45. What is the probability of heads for our coin? True Approximation 2,000 simulations per p

  46. What is the probability of heads for our coin? True Approximation 20,000 simulations per p

  47. What is the probability of heads for our coin? True Approximation 200,000 simulations per p

  48. Discrete time taxa[[i]]$nextstates= taxa[[i]]$states + intrinsicFn(…) + extrinsicFn(…)

More Related