Tree-Structured Regression Model Using a Projection Pursuit Approach

In this paper, we propose a new tree-structured regression modelthe projection pursuit regression tree.a new tree-structured regression model—the projection pursuit regression tree—is proposed. It combines the projection pursuit classification tree with the projection pursuit regression. The main advantage of the projection pursuit regression tree is exploring the independent variable space in each range of the dependent variable. Additionally, it retains the main properties of the projection pursuit classification tree. The projection pursuit regression tree provides several methods of assigning values to the final node, which enhances predictability. It shows better performance than CART in most cases and sometimes beats random forest with a single tree. This development makes it possible to find a better explainable model with reasonable predictability.

Projection Pursuit Regression (PPR) on Statistical Downscaling Modeling for Daily Rainfall Forecasting

Rainfall forecasting has an important role in people's lives. Rainfall forecasting in Indonesia has complex problems because it is located in a tropical climate. Rainfall prediction in Indonesia is difficult due to the complex topography and interactions between the oceans, land and atmosphere. With these conditions, an accurate rainfall forecasting model on a local scale is needed, of course taking into account the information about the global atmospheric circulation obtained from the General Circulation Model (GCM) output. GCM may still be used to provide local or regional scale information by adding Statistical Downscaling (SD) techniques. SD is a regression-based model in determining the functional relationship between the response variable and the predictor variable. Rainfall observations obtained from the Meteorology Climatology and Geophysics Council (BMKG) are a response variable in this study. The predictor variable used in this study is the global climate output from GCM. This research was conducted in a place, namely Kupang City, East Nusa Tenggara because it has low rainfall. The Projection Pursuit Regression (PPR) will be used in this SD method for this study. In PPR modeling, optimization needs to be done and model validation is carried out with the smallest Root Mean Square Error (RMSE) criteria. The expected results must have a pattern between the results of forecasts and observations showing or approaching the observational data. The PPR model is a good model for predicting rainfall because The results of the forecast and observation show that the results of the rainfall forecast are observational data.

Water–sediment separation efficiency prediction of gill-piece separation device

As the key piece of equipment of a micro-irrigation system, the filter can prevent clogging of the emitter and ensure normal operation of the micro-irrigation system. A gill-piece separation device is used for the removal of viscous sediment, which helps to reduce the sediment concentration and decrease the burden on the filter. In this study, using the water–sediment separation efficiency as an evaluation index, a uniform orthogonal experiment was conducted to study the flow rate, sediment concentration, and gill-piece spacing using a physical model. Based on the experimental results of the physical model, multiple linear regression and projection pursuit regression were used for analysis. The results showed that the order of the factors affecting the water-sediment separation efficiency was as follows: flow rate at muddy water inlet > gill-piece spacing > sediment concentration. The correlation coefficients of the water–sediment separation efficiency models established using multiple linear regression and projection pursuit regression were 0.93 and 0.98, respectively. Both models could predict the water–sediment separation efficiency and determine the optimal working conditions of the gill-piece separation device.

Impact of measurement errors on the inferred stellar asteroseismic ages

Aims. We aim to perform a theoretical investigation on the direct impact of measurement errors in the observational constraints on the recovered age for stars in main sequence (MS) and red giant branch (RGB) phases. We assumed that a mix of classical (effective temperature Teff and metallicity [Fe/H]) and asteroseismic (Δν and νmax) constraints were available for the objects. Methods. Artificial stars were sampled from a reference isochrone and subjected to random Gaussian perturbation in their observational constraints to simulate observational errors. The ages of these synthetic objects were then recovered by means of a Monte Carlo Markov chains approach over a grid of pre-computed stellar models. To account for observational uncertainties the grid covers different values of initial helium abundance and mixing-length parameter, that act as nuisance parameters in the age estimation. Results. The obtained differences between the recovered and true ages were modelled against the errors in the observables. This procedure was performed by means of linear models and projection pursuit regression models. The first class of statistical models provides an easily generalizable result, whose robustness is checked with the second method. From linear models we find that no age error source dominates in all the evolutionary phases. Assuming typical observational uncertainties, for MS the most important error source in the reconstructed age is the effective temperature of the star. An offset of 75 K accounts for an underestimation of the stellar age from 0.4 to 0.6 Gyr for initial and terminal MS. An error of 2.5% in νmax resulted the second most important source of uncertainty accounting for about −0.3 Gyr. The 0.1 dex error in [Fe/H] resulted particularly important only at the end of the MS, producing an age error of −0.4 Gyr. For the RGB phase the dominant source of uncertainty is νmax, causing an underestimation of about 0.6 Gyr; the offset in the effective temperature and Δν caused respectively an underestimation and overestimation of 0.3 Gyr. We find that the inference from the linear model is a good proxy for that from projection pursuit regression models. Therefore, inference from linear models can be safely used thanks to its broader generalizability. Finally, we explored the impact on age estimates of adding the luminosity to the previously discussed observational constraints. To this purpose, we assumed – for computational reasons – a 2.5% error in luminosity, much lower than the average error in the Gaia DR2 catalogue. However, even in this optimistic case, the addition of the luminosity does not increase precision of age estimates. Moreover, the luminosity resulted as a major contributor to the variability in the estimated ages, accounting for an error of about −0.3 Gyr in the explored evolutionary phases.