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Mismatch between priors and data

What's the deal with the posteriors.pdf plots for setariaWT?

Vcmax:

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  • Prior in BETY says dist = lnorm, a = 3.75, b = 0.3, n = 12
  • query.trait.data() also shows 3.75, 0.3, 12
  • Prior in Vcmax.model.bug says beta.o ~ dlnorm (3.75, 11.1111111111111)#BBB. This is just because BUGS paramaterizes distributions differentlly
  • None of those are truncated at ~20 like in the plot above

Output of query.trait.data():

2022-09-26 19:03:17 INFO   [query.trait.data] : Vcmax 
2022-09-26 19:03:17 INFO   [query.trait.data] : 
   Median Vcmax : 24.367

This is pretty different from median(rlnorm(100000, 3.75, 0.3)) (42.61)

Output of meta analysis:

------------------------------------------------
starting meta-analysis for:

 Vcmax 

------------------------------------------------
prior for Vcmax
                     (using R parameterization):
lnorm(3.75, 0.3)
data max: 33.587 
data min: 14.572 
mean: 24 
n: 33
stem plot of data points

  The decimal point is at the |

  14 | 67
  16 | 3993
  18 | 024
  20 | 80567
  22 | 14
  24 | 49069
  26 | 235
  28 | 3
  30 | 06758
  32 | 486

stem plot of obs.prec:

  The decimal point is 2 digit(s) to the left of the |

  0 | 00000000111111111111222234
  0 | 55
  1 | 
  1 | 689
  2 | 
  2 | 
  3 | 3
  3 | 
  4 | 2

Read 28 items
Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 66
   Unobserved stochastic nodes: 11
   Total graph size: 231

Initializing model

  |++++++++++++++++++++++++++++++++++++++++++++++++++| 100%
  |**************************************************| 100%

Iterations = 1002:4000
Thinning interval = 2 
Number of chains = 4 
Sample size per chain = 1500 

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

                Mean    SD Naive SE Time-series SE
beta.ghs[2]   5.8939 6.527 0.084269       0.605218
beta.o       22.5960 3.908 0.050453       0.524178
beta.site[1] -1.1988 3.573 0.046125       0.515177
beta.site[2] -3.6076 4.346 0.056111       0.571501
beta.site[3]  1.0050 4.721 0.060941       0.312704
beta.trt[2]   9.0024 1.685 0.021759       0.051840
beta.trt[3]  -3.2650 2.429 0.031353       0.038937
beta.trt[4]   0.2434 1.813 0.023410       0.044398
sd.site       4.5082 5.840 0.075394       0.576771
sd.trt        7.9614 8.151 0.105231       0.106347
sd.y          4.5453 0.318 0.004106       0.004568

2. Quantiles for each variable:

                 2.5%     25%     50%     75%   97.5%
beta.ghs[2]  -11.7959  3.7225  7.6125  9.9905 14.4939
beta.o        17.7133 19.9710 21.3688 24.4605 32.3529
beta.site[1] -10.7692 -2.1732 -0.0981  0.5913  3.7577
beta.site[2] -14.5592 -5.9696 -1.9854 -0.2457  0.8886
beta.site[3]  -7.2625 -0.7105  0.1354  2.0609 13.1585
beta.trt[2]    5.7321  7.8513  8.9890 10.1680 12.2848
beta.trt[3]   -7.9935 -4.8725 -3.2776 -1.6559  1.5000
beta.trt[4]   -3.2401 -0.9942  0.2183  1.4505  3.7676
sd.site        0.1239  0.7684  2.4657  6.1013 20.1850
sd.trt         2.8689  4.6978  6.4385  9.1335 22.2883
sd.y           3.9386  4.3262  4.5382  4.7598  5.1978


2022-09-26 19:17:33 WARN   [check_consistent] : 
   CHECK THIS: Vcmax data and prior are inconsistent: 
2022-09-26 19:17:33 INFO   [check_consistent] : 
   Vcmax P[X<x] = 0.0107234090491143

Cuticular cond

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  • Prior in BETY says dist = lnorm, a = 8.4, b = 0.9, n = 0
  • query.trait.data() reports the same
  • Prior in model.bug is beta.o ~ dlnorm (8.4, 1.23456790123457)#BBB This is just because BUGS paramaterizes distributions differentlly

Output of query.trait.data()

2022-09-26 19:03:17 INFO   [query.trait.data] : cuticular_cond 
2022-09-26 19:03:17 INFO   [query.trait.data] : 
   Median cuticular_cond : 30546

median(rlnorm(100000, 8.4, 0.9)) = 4431.404, an order of magnitude less

  • Less informative prior needed?

Output of meta analysis:

################################################
------------------------------------------------
starting meta-analysis for:

 cuticular_cond 

------------------------------------------------
prior for cuticular_cond
                     (using R parameterization):
lnorm(8.4, 0.9)
data max: 105286 
data min: 157 
mean: 32900 
n: 33
stem plot of data points

  The decimal point is 4 digit(s) to the right of the |

   0 | 084556799
   2 | 1111390112225599
   4 | 36625
   6 | 22
   8 | 
  10 | 5

stem plot of obs.prec:

  The decimal point is 9 digit(s) to the left of the |

  0 | 000000000000000000000000000000000

Read 28 items
Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 66
   Unobserved stochastic nodes: 11
   Total graph size: 231

Initializing model

  |++++++++++++++++++++++++++++++++++++++++++++++++++| 100%
  |**************************************************| 100%

Iterations = 1002:4000
Thinning interval = 2 
Number of chains = 4 
Sample size per chain = 1500 

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

                   Mean      SD Naive SE Time-series SE
beta.ghs[2]   1.825e-01    10.1   0.1304         0.1299
beta.o        1.553e+04 10486.2 135.3768      1007.7992
beta.site[1]  2.600e+04 11239.3 145.0992      1010.9316
beta.site[2]  7.271e+03 10597.0 136.8070       937.4097
beta.site[3]  8.260e+03 10811.5 139.5762       951.8293
beta.trt[2]  -1.115e+04  4717.3  60.9001       144.4650
beta.trt[3]  -3.642e+03  5625.9  72.6298        93.2426
beta.trt[4]   2.564e+03  4297.7  55.4836        91.3477
sd.site       2.490e+04 21849.1 282.0704      1034.1102
sd.trt        1.104e+04  9343.6 120.6258       154.6123
sd.y          1.262e+04   505.0   6.5189         6.5158

2. Quantiles for each variable:

                  2.5%        25%        50%       75%    97.5%
beta.ghs[2]     -19.16     -6.726      0.177     7.072    19.84
beta.o         1203.97   5806.015  14446.242 24365.430 35362.76
beta.site[1]   5083.49  16996.834  27032.461 35526.081 43717.37
beta.site[2] -12779.60  -1089.941   7629.391 15865.911 25207.22
beta.site[3] -11850.49   -215.555   8666.317 16828.692 27305.50
beta.trt[2]  -20145.56 -14353.173 -11193.095 -8054.345  -688.12
beta.trt[3]  -15721.92  -7243.949  -3241.985    27.388  6609.38
beta.trt[4]   -5969.73   -140.868   2530.423  5330.714 11091.92
sd.site        5112.03  12145.340  19794.892 30371.012 76585.94
sd.trt         1897.80   6038.866   8948.105 13057.602 33412.90
sd.y          11656.55  12278.028  12616.671 12960.389 13629.63


2022-09-26 19:17:33 INFO   [check_consistent] : 
   OK!  cuticular_cond data and prior are consistent: 
2022-09-26 19:17:33 INFO   [check_consistent] : 
   cuticular_cond P[X<x] = 0.896820628855657

Questions:

  1. Which step in the workflow do these plots come from?
  2. What is the difference between post and approx in these plots?
  3. Which of them is being used in the model?
  4. Is this related to "data contains untransformed statistics" ?
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Eric R Scott
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