Statistics

2411 Submissions

[2] viXra:2411.0080 [pdf] submitted on 2024-11-11 20:56:07

The Fundamental Problem of Causal Inference

Authors: Andrea Berdondini
Comments: 6 Pages.

The fundamental problem of causal inference defines the impossibility of associating a causal link to a correlation, in other words: correlation does not prove causality. This problem can be understood from two points of view: experimental and statistical. The experimental approach tells us that this problem arises from the impossibility of simultaneously observing an event both in the presence and absence of a hypothesis. The statistical approach, on the other hand, suggests that this problem stems from the error of treating tested hypotheses as independent of each other. Modern statistics tends to place greater emphasis on the statistical approach because, compared to the experimental point of view, it also shows us a way to solve the problem. Indeed, when testing many hypotheses, a composite hypothesis is constructed that tends to cover the entire solution space. Consequently, the composite hypothesis can be fitted to any data set by generating a random correlation. Furthermore, the probability that the correlation is random is equal to the probability of obtaining the same result by generating an equivalent number of random hypotheses.
Category: Statistics

[1] viXra:2411.0008 [pdf] submitted on 2024-11-02 07:03:48

A Subsampling Based Neural Network for Spatial Data

Authors: Debjoy Thakur
Comments: 28 Pages.

The application of deep neural networks in geospatial data has become a trending research problem in the present day. A significant amount of statistical research has already been introduced, such as generalized least square optimization by incorporating spatial variance-covariance matrix, considering basis functions in the input nodes of the neural networks, and so on. However, for lattice data, there is no available literature about the utilization of asymptotic analysis of neural networks in regression for spatial data. This article proposes a consistent localized two-layer deep neural network-based regression for spatial data. We have proved the consistency of this deep neural network for bounded and unbounded spatial domains under a fixed sampling design of mixed-increasing spatial regions. We have proved that its asymptotic convergence rate is faster than that of cite{zhan2024neural}'s neural network and an improved generalization of cite{shen2023asymptotic}'s neural network structure. We empirically observe the rate of convergence of discrepancy measures between the empirical probability distribution of observed and predicted data, which will become faster for a less smooth spatial surface. We have applied our asymptotic analysis of deep neural networks to the estimation of the monthly average temperature of major cities in the USA from its satellite image. This application is an effective showcase of non-linear spatial regression. We demonstrate our methodology with simulated lattice data in various scenarios.
Category: Statistics