Ecological Archives A025-075-A2

Joe Scutt Phillips, Toby A. Patterson, Bruno Leroy, Graham M. Pilling, and Simon J. Nicol. 2015. Objective classification of latent behavioral states in bio-logging data using multivariate-normal hidden Markov models. Ecological Applications 25:12441258. http://dx.doi.org/10.1890/14-0862.1

Appendix B. Simulation experiments: Full parameter tables for simulations and results from the second, more complex simulation scenario two.

Artificial data sets were generated under two different scenarios, as described in the main article. Full parameters are given in the following tables. A parallel coordinate plot showing the true values and spread of estimated parameters is given in Fig. B1 for scenario two. The corresponding figure for scenario one is given in the main article.

Table B1. Scenario one simulation parameters.

State

Multivariate mean μ

Variance-covariance matrix ∑

Transition probabilities

 

Parameter

True

Estimate Mean

Estimate Stan dev.

Parameter

True

 

Estimate Mean

Estimate Stan dev.

Parameter

True

Estimate Mean

Estimate Stan dev.

State 1- Persistent Shallow State

Depth Amplitude

 

Water Temperature

4

 

 

10

4.000

 

 

9.994

0.11

 

 

0.05

Depth Amplitude

 

Temperature

 

Covariance

2

 

 

0.5

 

0

2.019

 

 

0.585

 

-0.015

0.17

 

 

0.08

 

0.08

1->1

 

1->2

 

0.8

 

0.2

0.752

 

0.248

 

0.04

 

0.04

State 2- Persistent Deep State

Depth Amplitude

 

Water Temperature

6

 

 

6

6.133

 

 

6.025

0.11

 

 

0.18

Depth Amplitude

 

Temperature

 

Covariance

1.5

 

 

3

 

-0.5

1.507

 

 

3.119

 

-0.182

0.17

 

 

0.58

 

0.32

2->1

 

2->2

0.3

 

0.7

0.305

 

0.695

0.04

 

0.04

 

Table B2. Scenario two state distribution parameters.

State

Multivariate mean μ

Variance-covariance matrix ∑

 

Parameter

True

Estimate Mean

Estimate Stan dev.

Parameter

True

 

Estimate Mean

Estimate Stan dev.

State 1- Persistent Shallow State

Depth Amplitude

 

Water Temperature

4

 

 

10

3.931

 

 

10.016

0.14

 

 

0.06

Depth Amplitude

 

Temperature

 

Covariance

2

 

 

0.5

 

0

1.949

 

 

0.517

 

0.021

0.27

 

 

0.06

 

0.10

State 2- Transitive Searching State

Depth Amplitude

 

Water Temperature

6

 

 

6

5.921

 

 

6.478

0.16

 

 

0.51

Depth Amplitude

 

Temperature

 

Covariance

1.5

 

 

3

 

-0.5

1.398

 

 

2.892

 

-0.012

0.27

 

 

0.77

 

0.42

State 3- Persistent Deep State

Depth Amplitude

 

Water Temperature

7

 

 

4

6.989

 

 

4.050

0.09

 

 

0.10

Depth Amplitude

 

Temperature

 

Covariance

0.5

 

 

0.5

 

0

0.564

 

 

0.619

 

0.008

0.11

 

 

0.16

 

0.07

 

Table B3. Scenario two transition matrix parameters.

State

Day-time transition probabilities

Night-time transition probabilities

 

Parameter

True

Estimate Mean

Estimate Stan dev.

Parameter

True

 

Estimate Mean

Estimate Stan dev.

State 1- Persistent Shallow State

1->1

1->2

1->3

 

0.2

0.2

0.6

0.152

0.203

0.645

0.07

0.08

0.08

1->1

1->2

1->3

 

0.8

0.2

0.0

0.780

0.193

0.028

0.05

0.04

0.02

State 2- Transitive Searching State

2->1

2->2

2->3

 

0.04

0.48

0.48

0.084

0.0274

0.642

0.05

0.14

0.14

2->1

2->2

2->3

 

0.4

0.58

0.02

0.402

0.478

0.121

0.08

0.14

0.08

State 3- Persistent Deep State

3->1

3->2

3->3

0.3

0.1

0.6

0.289

0.169

0.542

0.06

0.05

0.08

3->1

3->2

3->3

0.5

0.5

0.0

0.492

0.466

0.042

0.11

0.11

0.05

 

Fig B1

Fig. B1. Parallel coordinate plots showing true and estimated parameter values for 50 repetitions of simulation scenario two.


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