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Landslides are among the most dangerous natural processes. Debris avalanches and debris flows in particular have often caused casualties and severe damage to infrastructures in a wide range of environments. The assessment of susceptibility to these phenomena may help policy makers in mitigating the associated risk and thus it has attracted special attention in the last decades. In this experiment, we assessed susceptibility to debris-avalanche and -flow landslides by using a stochastic approach. Two different modeling techniques were employed: i) Multivariate Adaptive Regression Splines (MARS) and ii) Logistic Regression (LR). Both MARS and LR allow for calculating the probability of landslide occurrence by building statistical relationships between a set of environmental variables and the target variable, i.e. presence/absence of the landslide event. The target variable was extracted from an inventory of debris-avalanche and - flow landslides which were triggered by the tropical storm that hit the area of Mocoa (Colombia) on 1 April 2017. As predictor variables, we employed nine terrain attributes derived from a 5-m resolution DEM (i.e. elevation, slope angle, northness, eastness, upslope slope angle, convergence index, topographic position index, valley depth and topographic wetness index), in addition to lithology, distance from faults and presence/absence of soil creep processes. In our experiment, we used three different landslide datasets which contain i) the highest point of each recognized landslide crown-lines (dataset LIP), ii) the highest 10% of cells of each landslide area (dataset SOURCE), and iii) the entire landslide areas, which include initiation and accumulation zones (dataset MASS). In order to evaluate their predictive ability, LR and MARS models were submitted to k-fold spatial cross-validation strategy, which consists in extracting random training and test subsets from k spatially disjoint sub-areas. The results of model validation, expressed in terms of Area Under the ROC Curve (AUC), demonstrate better predictive performance of MARS models with respect to LR models, for all the three landslide datasets. The mean AUC values calculated for the datasets LIP, SOURCE and MASS of the MARS models are 0.776, 0.788 and 0.768, respectively, whereas AUC values of the LR models are 0.748, 0.751 and 0.703, respectively. Model validation also shows that the predictive skill of the models is better when landslide data are sampled from the highest portions of the landslides (dataset SOURCE). Maps of susceptibility to debris-avalanche and -flow landslides for the Mocoa area were produced by using both LR and MARS and the three landslide datasets. The analysis of the distribution of events versus the susceptibility classes of the maps confirm that MARS and the dataset SOURCE provide the best ability to discriminate between event and non-event cells.