pooling parameters

[ktoddbrown]

The overall goal of soil decomposition model development is to have a global set of parameters that can be applied to any location on Earth to predict soil heterotrophic respiration (CO2 flux out due to decay) and/or soil carbon stocks. This parameter set includes: decay rates of the pools, transfer:respiration ratios of the exiting flux, and environmental sensitivities. In theory the initial allocation of carbon between the pools is determined by the allocation of the inputs (which is dependent on litter type and environmental variables), in practice with soil incubation the initial soil carbon stock is set and allowed to vary between treatments and/or sites. That being said there are HUGE heterogeneity in soils at pretty much every scale; many incubation studies try to address this by sieving the soils to remove rocks/large litter pieces, mixing the samples, and then 'repacking' the soil cores.

I think we should leave the environmental sensitivity alone for now and assume that the incubations were under the same moisture/temperature conditions (future project!). I would expect that between replicates the initial soil carbon distribution and parameter set are drawn from the same distribution. Between sites/treatments I would expect different initial soil carbon distributions to explain most of the differences between CO2 fluxes.

How would the affect the parameter representation in the model?

[milkha]

in practice with soil incubation the initial soil carbon stock is set and allowed to vary between treatments and/or sites. That being said there are HUGE heterogeneity in soils at pretty much every scale; many incubation studies try to address this by sieving the soils to remove rocks/large litter pieces, mixing the samples, and then 'repacking' the soil cores.

In our current models, we assume that the gamma parameter (which identifies the initial ratio of Carbon in each pool) is common among all replications (i.e., no hierarchical structure). Therefore the model agrees with the practice of mixing the samples to get homogenous soil. Another way to do it is to assume a hierarchical structure (so that gamma differs for each replication) and then give it a hyper-prior to model the heterogeneity. I think this second approach is more accurate and more sensible and I will implement this one.

I think we should leave the environmental sensitivity alone for now and assume that the incubations were under the same moisture/temperature conditions (future project!).

Yes, that makes sense to me.

I would expect that between replicates the initial soil carbon distribution and parameter set are drawn from the same distribution.

Yes, that's exactly the hierarchical structure we implement. We assume that there are some global parameter distribution for each site/treatment, and then the parameters for the replicates are drawn from that distribution.

Between sites/treatments I would expect different initial soil carbon distributions to explain most of the differences between CO2 fluxes.

Just a nomenclature clarification - by site/treatment, do you mean a collection of replications from the same sample?

How would the affect the parameter representation in the model?

We can have the hierarchical structure at different levels. Parameters for different replications can come from a common distribution. At a higher level, the parameters for different sites can in turn have their own common distribution.

[bob-carpenter]

On Jan 23, 2017, at 10:51 AM, Milad Kharratzadeh notifications@github.com wrote:

in practice with soil incubation the initial soil carbon stock is set and allowed to vary between treatments and/or sites. That being said there are HUGE heterogeneity in soils at pretty much every scale; many incubation studies try to address this by sieving the soils to remove rocks/large litter pieces, mixing the samples, and then 'repacking' the soil cores.

In our current models, we assume that the gamma parameter (which identifies the initial ratio of Carbon in each pool) is common among all replications (i.e., no hierarchical structure). Therefore the model agrees with the practice of mixing the samples to get homogenous soil. Another way to do it is to assume a hierarchical structure (so that gamma differs for each replication) and then give it a hyper-prior to model the heterogeneity. I think this second approach is more accurate and more sensible and I will implement this one.

Exactly what I was suggesting. Just hard-coding complete pooling will reduce model-based posterior uncertainty, but at the cost of losing calibration! We need calibration first, basically 50% of simulated true values fall in the posterior 50% intervals. More precisely, we gt a hypothesis test with a binomial(N, p) being the distribution of the number out of N parameters that fall in any posterior p interval.

I think we should leave the environmental sensitivity alone for now and assume that the incubations were under the same moisture/temperature conditions (future project!).

Yes, that makes sense to me.

Agreed.

I would expect that between replicates the initial soil carbon distribution and parameter set are drawn from the same distribution.

Yes, that's exactly the hierarchical structure we implement.

Just what I was going to say.

We assume that there are some global parameter distribution for each site/treatment, and then the parameters for the replicates are drawn from that distribution.

Between sites/treatments I would expect different initial soil carbon distributions to explain most of the differences between CO2 fluxes.

Just a nomenclature clarification - by site/treatment, do you mean a collection of replications from the same sample?

How would the affect the parameter representation in the model?

We can have the hierarchical structure at different levels. Parameters for different replications can come from a common distribution. At a higher level, the parameters for different sites can in turn have their own common distribution.

Please do read either the radon or binomial trial case studies. They both go over how this works for simple examples and why it helps. The binomial trial one that I wrote goes over calibration with real and held out data.

• Bob