# Mismatch between priors and data What's the deal with the posteriors.pdf plots for setariaWT? ## Vcmax: ![](https://i.imgur.com/1pflijf.png) - 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: <details> ``` ------------------------------------------------ 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 ``` </details> ``` 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 ![](https://i.imgur.com/QCtRG9t.png) - 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: <details> ``` ################################################ ------------------------------------------------ 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 ``` </details> ``` 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? 1. 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" ?