There is a vast amount of literature about (spatial) modelling in GIS. I do not know the details of your data, but assuming that your points are actually indicating the presence of a given phenomenon (forest loss), and assuming that you have the possibility to locate with certainty locations featuring the absence of the same phenomenon (i.e., no forest loss), you could try Binary Logistic Regression, in which the Dependent Variable is forest loss presence/absence (coded as 1 and 0 respectively), and your distances would act as Predictors.
This is something that is used, for instance, in landslides studies in order to assess the impact of different predictors in the odds for the positive outcome of an event, in this case presence of a landslide.
As for GIS:
-I would create a point SHAPEFILE representing all the locations under study, that is the ones featuring forest loss and the ones featuring no forest loss;
-Create a field for your DV, which would contain 0 for the point with NO loss, and 1 for points WITH loss.
-Then, extract the values of your Predictors (e.g., distance from road, location of kilns, etc) to your points.
At that point, you can export the table and perform Logistic Regression outside GIS, in R for example. First, you should check if the model is significant, and then, the estimated Betas (coefficients) should inform you about the strength and direction of the "influence" of your predictors on the chances (actually, odds) for forest loss.
You can plug the Betas (and intercept) in the Raster Calculator to produce a forest loss probability maps. If you are not familiar with R (which is free), you can perform Logistic Regression via a quite simple function which is provided by a website that I found just googling a little (http://cainarchaeology.weebly.com/r-function-for-binary-logistic-regression.html).
There are more things to check for and take into account in regression modelling with spatial data: for instance, the spatial autocorrelation among the model's residuals. If that is the case, you could try to subsample from your universe of points in order to increase the distance between your sampling location so alleviating for any existing spatial autocorrelation. Otherwise, you could resort to autoregressive modelling strategies (but I am not so familiar with these).
These are just my two cents. Hope they prove useful.
A couple of good readings:
Zhang, Z. X., Zhang, H. Y., & Zhou, D. W. (2010). Using GIS spatial analysis and logistic regression to predict the probabilities of human-caused grassland fires. Journal of Arid Environments, 74(3), 386–393. https://doi.org/10.1016/j.jaridenv.2009.09.024
Arekhi, S. (2011). Modeling spatial pattern of deforestation using GIS and logistic regression: A case study of northern Ilam forests, Ilam province, Iran. African Journal of Biotechnology, 10(72), 16236–16249. https://doi.org/10.5897/AJB11.1122
Hu, Z., & Lo, C. P. (2007). Modeling urban growth in Atlanta using logistic regression. Computers, Environment and Urban Systems, 31, 667–688. https://doi.org/10.1016/j.compenvurbsys.2006.11.001
Wang, L., Sawada, K., & Moriguchi, S. (2011). Landslide Susceptibility Mapping by Using Logistic Regression Model with Neighborhood Analysis: A Case Study in Mizunami City. International Journal of Geomate, 1(2), 99–104. Retrieved from http://www.gi-j.com/serial 2/99-104-2c-wang.pdf
