A Markov chain model for juvenile salmon E. A. Steel and P. Guttorp (2001): Modeling juvenile salmon migration using a simple Markov chain. Journal of Agricultural, Biological and Environmental Statistics 6: 80-88. Scientific issue: As few as 15% of hatchery salmon survive to the first dam. Need to understand fish movement and the role of covariates, such as river speed Data: radio tags at 129 yearling chinook in Snake River read at 12 receiving stations Travel time calculated at each segment (between stations). 7– 31 observations/segment Missing data due to signal strength, antenna orientation, tag failure
26
Embed
A Markov chain model for juvenile salmon E. A. Steel and P. Guttorp (2001): Modeling juvenile salmon migration using a simple Markov chain. Journal of.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
A Markov chain model for juvenile salmon
E. A. Steel and P. Guttorp (2001): Modeling juvenile salmon migration using a simple Markov chain. Journal of Agricultural, Biological and Environmental Statistics 6: 80-88.
Scientific issue: As few as 15% of hatchery salmon survive to the first dam. Need to understand fish movement and the role of covariates, such as river speedData: radio tags at 129 yearling chinook in Snake River read at 12 receiving stationsTravel time calculated at each segment (between stations). 7– 31 observations/segmentMissing data due to signal strength, antenna orientation, tag failure
The model
Each fish make 10 decisions per hour (to move 1km or to stay)
It is observed after it has traveled Li km.
A wait time is defined as a 1-0-0-0...-0-1 transition. The expected value and variance can be computed as a function of the transition probabilities.
Total travel time for a segment is the sum of the wait times (independent)
Estimated parameters
Stretch Obs Length p00 p11
1 31 41 .988 .992
4 16 25 .946 .947
7 21 6 .973 .886
10 20 1 .9996 .932
11 20 7 .9999 .989
Model intepretation
Long runs of staying or of moving
Implication for time spent moving and staying?
Fish behavior different in different parts of the river.
Confounded with river speed. Length of movement can be made depend on average speed. Clearer differences between different parts of river, higher precision of estimates.
p̂00 ≈p̂11
Tornado model
C. Marzban, M. Drton and P. Guttorp (2003): A Markov chain model of tornadic activity. Monthly Weather Review 131: 2941-2953.
Scientific issue: Tornado prediction
Data: 49 years of daily indicators of occurrence of a tornado in continental US
Varies with time of year
Time-dependent transition probabilities
Tornado alley
Regional differences
Why is it so?
Frontal systems stay in a region for several days, conducive to tornado activity. So then p11 > p01.
In southern Tornado alley frontal systems cease around mid-May, decreasing p11, but p01 continues to increase for another month due to lots of moisture and weak upper atmosphere systems
SE tornado activity related also to tropical storms, so lasts longer, less pronounced peaks
Quality of forecast
Precipitation modeling
J. P. Hughes and P. Guttorp (1994): Incorporating spatial dependence and atmospheric data in a model of precipitation. Journal of Applied Meteorology 33: 1503-1515. IPCC SAR.
Scientific problem: Downscaling climate models to model regional precipitation
A spatial Markov model
Three sites, A, B and C, each observing 0 or 1. Notation: AB = (A=1,B=1,C=0)