In EcoFoG/vernabota: Association between vernacular and botanical names for Guyafor data

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Method of association of a vernacular name with a botanical name

Be a tree t with a vernacular name v. This tree can have a known genus, only a known family or no botanical information at all. The associated botanical names follow a categorical distribution $\mathcal{Cat} (\alpha^v)$ where $\alpha^v = [\alpha^v_1, \alpha^v_2,..., \alpha^v_N]$ is the vector of probability of association of between the vernacular name v and each botanical name (so $\sum_{s=1}^N \alpha^v_i =1)$) and N is the number of botanical name present in the inventories taken as a reference and/or the prior knowledge.

To get the vector $\alpha^v$, we use a Dirichlet-categorical scheme to combine a prior information based on expert knowledge that we updated with observed frequencies of association between the vernacular name v and each botanical name in the reference inventories $f^v = [f^v_1, f^v_2,..., f^v_N]$ [@Aubry-Kientz2013].

We consider $\lambda^v$ as hyperparameters of $\alpha^v$, i.e. the parameters of the prior distribution of $\alpha^v$. The prior probability of association of the vernacular v with each botanical name s in [1,N] is $\lambda^v_s$ and is obtained as follows:

• $\lambda^v_s = \frac{1}{m_v}$ if the botanical name s is associated to the vernacular name v AND belongs to the same genus than t (if there is a know genus) and the same family than t (if there is a known family). $m_v$ is the number of botanical names meeting these conditions.
• $\lambda^v_s = \frac{\epsilon}{N-m_v}$ otherwise ($\epsilon$ being a background noise)

The prior distribution of $\alpha^v \sim \mathcal{Dir}(N, \lambda^v)$.

As the Dirichlet distribution is the conjugated prior of the categorical distribution, the posterior distribution of the probabilities of associations $\alpha^v$ can be obtained by updating the expert knowledge with the observed frequency of association $f^v$.

So the posterior distribution of probability of association is $\alpha^v | f^v,\lambda^v \sim \mathcal{Dir} (N, w_p \times \lambda^v_1 + (1-w_p) \times f^v_1,...,w_p \times \lambda^v_N+(1-w_p) \times f^v_N)$ where $w_p$ is the weight given to the prior information.

NB: $\lambda^v$ and $f^v$ are taken as frequencies to give the same weight to give the same weight to the prior and the observations when given an equal weight (i.e. when $w_p=0.5$).

In practice, as we don't want to calculate the vector $\alpha^v$ for each tree, we create a matrix $\alpha$ of $\alpha^v$ that will be used for all trees. We therefore don't have any information on the family or the genus at this stage. We take $\lambda^v_s = 0$ for the botanical names that are not associated to the vernacular name v according to expert knowledge. The matrix $\alpha$ have a lot of 0 (in case when there is no association according to expert knowledge, nor according to the data). When we then consider the tree t, we replace non-null values by 0 when botanical names don't belong to the same genus than t (if there is a known genus) and the same family than t (if there is a known family). We then replace 0 by $\epsilon$ divided by the number of value=0.

Possible types of gapfilling

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Bibliography

EcoFoG/vernabota documentation built on Feb. 15, 2023, 6:40 p.m.