Nonparametric Model Research Articles

Doubly-robust and heteroscedasticity-aware sample trimming for causal inference

SUMMARY A popular method for variance reduction in causal inference is propensity-based trimming, the practice of removing units with extreme propensities from the sample. This practice has theoretical grounding when the data are homoscedastic and the propensity model is parametric (Yang & Ding, 2018; Crump et al., 2009), but in modern settings where heteroscedastic data are analyzed with non-parametric models, existing theory fails to support current practice. In this work, we address this challenge by developing new methods and theory for sample trimming. Our contributions are three-fold: first, we describe novel procedures for selecting which units to trim. Our procedures differ from previous works in that we trim not only units with small propensities, but also units with extreme conditional variances. Second, we give new theoretical guarantees for inference after trimming. In particular, we show how to perform inference on the trimmed sub-population without requiring that our regressions converge at parametric rates. Instead, we make only fourth-root rate assumptions like those in the double machine learning literature. This result applies to conventional propensity-based trimming as well and thus may be of independent interest. Finally, we propose a bootstrap-based method for constructing simultaneously valid confidence intervals for multiple trimmed sub-populations, which are valuable for navigating the trade-off between sample size and variance reduction inherent in trimming. We validate our methods in simulation, on the 2007-2008 National Health and Nutrition Examination Survey, and on a semi-synthetic Medicare dataset and find promising results in all settings.

Growth of Optimizational Principles in Portfolio Analysis through Discrete Entropic Models

There exists an extensive collection of parametric and non-parametric discrete and continuous information models but still inevitability arises to broaden supplementary parametric models to encourage flexibility in the system under study. Moreover, there appears well-built relation between information entropy and the theory of “Portfolio Analysis”. Further, various approaches of measuring risk in portfolio analysis including entropy method, divergence technique and integrated methodology etc. are accessible in the existing literature of portfolio analysis. In the present communication, our intention is to provide advancement regarding certain well convinced optimizational principles by means of new discrete entropic models, and consequently to deliver their solicitations in portfolio analysis. Additionally, the well-established principle has been enlightened through the assistance of a numerical illustration.

Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, i.e., on large data sets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a threefold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite data set. All methods are implemented in a free C++ software library with high-level Python and R packages. 4

Nonparametric Bayesian estimation in a multidimensional diffusion model with high frequency data

AbstractWe consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $$L^2$$ L 2 -loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over Hölder smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.

MCMC for Bayesian nonparametric mixture modeling under differential privacy

Estimating the probability density of a population while preserving the privacy of individuals in that population is an important and challenging problem that has received considerable attention in recent years. While the previous literature focused on frequentist approaches, in this paper, we propose a Bayesian nonparametric mixture model under differential privacy (DP) and present two Markov chain Monte Carlo (MCMC) algorithms for posterior inference. One is a marginal approach, resembling Neal’s algorithm 5 with a pseudo-marginal Metropolis-Hastings move, and the other is a conditional approach. Although our focus is primarily on local DP, we show that our MCMC algorithms can be easily extended to deal with global differential privacy mechanisms. Moreover, for some carefully chosen mechanisms and mixture kernels, we show how auxiliary parameters can be analytically marginalized, allowing standard MCMC algorithms (i.e., non-privatized, such as Neal’s Algorithm 2) to be efficiently employed. Our approach is general and applicable to any mixture model and privacy mechanism. In several simulations and a real case study, we discuss the performance of our algorithms and evaluate different privacy mechanisms proposed in the frequentist literature.

Deep neural networks for variable selection of higher-order nonparametric spatial autoregressive model

Deep neural networks for variable selection of higher-order nonparametric spatial autoregressive model

The Estimating Parameter and Number of Knots for Nonparametric Regression Methods in Modelling Time Series Data

This research aims to explore and compare several nonparametric regression techniques, including smoothing splines, natural cubic splines, B-splines, and penalized spline methods. The focus is on estimating parameters and determining the optimal number of knots to forecast cyclic and nonlinear patterns, applying these methods to simulated and real-world datasets, such as Thailand’s coal import data. Cross-validation techniques are used to control and specify the number of knots, ensuring the curve fits the data points accurately. The study applies nonparametric regression to forecast time series data with cyclic patterns and nonlinear forms in the dependent variable, treating the independent variable as sequential data. Simulated data featuring cyclical patterns resembling economic cycles and nonlinear data with complex equations to capture variable interactions are used for experimentation. These simulations include variations in standard deviations and sample sizes. The evaluation criterion for the simulated data is the minimum average mean square error (MSE), which indicates the most efficient parameter estimation. For the real data, monthly coal import data from Thailand is used to estimate the parameters of the nonparametric regression model, with the MSE as the evaluation metric. The performance of these techniques is also assessed in forecasting future values, where the mean absolute percentage error (MAPE) is calculated. Among the methods, the natural cubic spline consistently yields the lowest average mean square error across all standard deviations and sample sizes in the simulated data. While the natural cubic spline excels in parameter estimation, B-splines show strong performance in forecasting future values.

B-043 Q-nab™ Igg kit: verification and validation of a novel cell-free quantitative neutralizing antibody assay

Abstract Background As the world exits the COVID-19 pandemic era, it is very important to assess population-level and individual seroprotectivity against multiple circulating and emerging SARS-CoV-2 strains, especially in vulnerable populations. Current serological measurements for neutralizing antibodies (NAbs) are either done using complex and time-intensive pseudovirus- or micro-neutralization assays or as a high throughput competitive ELISA assay. These assays, by design, cannot be multiplexed to measure NAb titers against multiple strains and suffer from a limited dynamic range. The Q-NAb IgG Tests, which rely on blocking the non-neutralizing antibodies (NNAbs) using a novel fusion protein, were developed and validated to quantitatively measure NAb titer against the SARS-CoV-2 strains used to develop the first two mRNA vaccines viz. ancestral and BA.4/5 strains. Methods The Q-NAb assay measures the NAb titer in a sample by first sequestering the NNAbs using the fusion protein (made by covalently coupling SARS-CoV-2 BA.4/5 RBD and h-ACE2 protein) thereby enriching the NAbs in the sample. Variant-specific NAbs are then detected using an indirect ELISA where the wells are coated with the variant RBD and yield a signal that is directly proportional to the concentration of NAb. Clinical samples from subjects that have either had a SARS-CoV-2 infection (N=27), taken the initial vaccine series (N=123) and/or the bivalent booster (N=151) and pre-pandemic samples (N=29) were commercially sourced. Q-NAb NAb titers were measured using the ancestral and BA.4/5 kits and were compared against corresponding MN50 values using both parametric and non-parametric models. Single-site precision, low-end sensitivity, dilutional linearity, and interference screening of Q-NAb IgG Kits were evaluated in accordance with appropriate CLSI guidelines. Traceability and total uncertainty of the Q-NAb IgG Kits (Ancestral and BA.4/5) to WHO International Standard 21/340 and 21/338 respectively was established using a calibration hierarchy adapted from ISO 17511:2020. Results Both the ancestral and BA.4/5 Q-NAb IgG Test Kits correlated with MN50 titers with a Spearman correlation coefficient of 0.90 and 0.89 respectively. The total uncertainty in traceability of calibration to WHO International standards 21/340 and 21/338 was found to be less than 10% for both tests. Single site precision across the assay range for BA.4/5 kit was found to be 6-10% with a limit of quantitation of 312 IU/mL. Assays exhibited dilutional linearity across their respective dynamic range and had no significant interference from common endogenous and exogenous substances. Conclusions We have successfully validated the novel Q-NAb IgG neutralization assay platform as individual assays for measuring neutralizing titers against ancestral and BA.4/5 SARS-CoV-2 strains. The assays have expanded dynamic range, excellent analytical performance and correlation to accepted gold-standard microneutralization assays. Both assays are calibrated and traceable to WHO international standards, thereby enabling the compilation and comparison of data from multiple clinical cohorts run across multiple laboratories. The design of the Q-NAb IgG Test kit makes it amenable to multiplexing (for example, on an MSD platform) to assess neutralization titers against multiple variants at the same time. Such a multiplexed platform can be used to assess vaccine efficacy and seroprotection against multiple variants including emerging variants.

Drilling Deeper: Non-Linear, Non-Parametric Natural Gas Price and Volatility Forecasting

This paper studies the forecast accuracy and explainability of a battery of dayahead (Henry Hub and Title Transfer Facility (TTF)) natural gas price and volatility models. The results demonstrate the dominance of non-linear, non-parametric models with deep structure relative to various competing model specifications. By employing the explainable artificial intelligence (XAI) approach, we document that the price of natural gas is formed strategically based on crude oil and electricity prices. While the conditional volatility of natural gas returns is driven by long-memory dynamics and crude oil volatility, the informativeness of the electricity predictor has improved over the most recent volatile time period. Although we reveal that predictive non-linear relationships are inherently complex and time-varying, our findings in general support the notion that natural gas, crude oil and electricity are interconnected. Focusing on the periods when markets experienced sharp structural breaks and extreme volatility (e.g., the COVID-19 pandemic and the Russia-Ukraine conflict), we show that deep learning models provide better adaptability and lead to significantly more accurate forecast performance.

A Novel Method for Nonparametric Statistical Inference for Niche Overlap in Multiple Species.

The understanding of species interactions and ecosystem dynamics hinges upon the study of ecological niches. Quantifying the overlap of Hutchinsonian-niches has garnered significant attention, with many recent publications addressing the issue. Prior work on estimating niche overlap often did not provide confidence intervals or assumed multivariate normality, seriously limiting applications in ecology, and biodiversity research. This paper extends a nonparametric approach, previously applied to the two-species case, to multiple species. For estimation, a consistent plug-in estimator based on rank sums is proposed and its asymptotic distribution is derived under weak conditions. The novel methodology is then applied to a study comparing the ecological niches of the Eurasian eagle owl, common buzzard, and red kite. These species share a habitat in Central Europe but exhibit distinct population trends. The analysis explores their breeding habitat preferences, considering the intricate competition dynamics and utilizing the nonparametric approach to niche overlap estimation. Our proposed method provides a valuable inferential tool for the quantitative evaluation of differences and overlap between niches.

Variable selection of nonparametric spatial autoregressive models via deep learning

With the development of deep learning techniques, the application of neural networks to statistical inference has dramatically increased in popularity. In this paper, we extend the deep neural network-based variable selection method to nonparametric spatial autoregressive models. Our approach incorporates feature selection and parameter learning by introducing Lasso penalties in a residual network structure with spatial effects. We transform the problem into a constrained optimization task, where optimizing an objective function with constraints. Without specifying sparsity, we are also able to obtain a specific set of selected variables. The performance of the method with finite samples is demonstrated through an extensive Monte Carlo simulation study. Finally, we apply the method to California housing price data, further validating its superiority in terms of variable selection and predictive performance.

Context-Based Meta-Reinforcement Learning With Bayesian Nonparametric Models.

Deep reinforcement learning agents usually need to collect a large number of interactions to solve a single task. In contrast, meta-reinforcement learning (meta-RL) aims to quickly adapt to new tasks using a small amount of experience by leveraging the knowledge from training on a set of similar tasks. State-of-the-art context-based meta-RL algorithms use the context to encode the task information and train a policy conditioned on the inferred latent task encoding. However, most recent works are limited to parametric tasks, where a handful of variables control the full variation in the task distribution, and also failed to work in non-stationary environments due to the few-shot adaptation setting. To address those limitations, we propose MEta-reinforcement Learning with Task Self-discovery (MELTS), which adaptively learns qualitatively different nonparametric tasks and adapts to new tasks in a zero-shot manner. We introduce a novel deep clustering framework (DPMM-VAE) based on an infinite mixture of Gaussians, which combines the Dirichlet process mixture model (DPMM) and the variational autoencoder (VAE), to simultaneously learn task representations and cluster the tasks in a self-adaptive way. Integrating DPMM-VAE into MELTS enables it to adaptively discover the multi-modal structure of the nonparametric task distribution, which previous methods using isotropic Gaussian random variables cannot model. In addition, we propose a zero-shot adaptation mechanism and a recurrence-based context encoding strategy to improve the data efficiency and make our algorithm applicable in non-stationary environments. On various continuous control tasks with both parametric and nonparametric variations, our algorithm produces a more structured and self-adaptive task latent space and also achieves superior sample efficiency and asymptotic performance compared with state-of-the-art meta-RL algorithms.

Asymptotically faster estimation of high‐dimensional additive models using subspace learning

AbstractAs a commonly used nonparametric model to overcome the curse of dimensionality, the additive model continually attracts attentions of researchers. Our recent work (He et al., 2022) proposed to reduce the number of unknown functions to be estimated through learning an adaptive subspace shared by the additive component functions. Equipped with an efficient algorithm, our proposed reduced additive model outperforms the state‐of‐the‐art alternatives in numerical studies. However, the asymptotic properties of the proposed estimators have not been explored and the empirical findings are short of theoretical explanation. In this work, we fill in the theoretical gap by showing the resulting estimator has faster convergence rate than the estimation without subspace learning; and this is true even when the reduced additive model is only an approximation, provided that the subspace approximation error is small. Moreover, the proposed method is able to consistently identify the relevant predictors. The developed theoretical results back up the earlier empirical findings.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

Estimation of the Hubble constant using Gaussian process regression and viable alternatives

A well-known problem in cosmology is the ‘Hubble tension’ problem, i.e. different estimates for the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} are not concordant with each other. This work investigates different statistical methods for estimating this value using cosmic chronometer, type Ia supernova and baryonic acoustic data. We start by making use of methods already established in the literature for this purpose, namely Gaussian process regression and Markov chain Monte Carlo (MCMC) methods based on the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. We also consider two novel approaches; the first makes use of non-parametric MCMC inference on the hyperparameters of a Gaussian process kernel, independently of any cosmological model. The second approach is Student’s t-process regression, which is a generalised version of Gaussian process regression that makes use of the multivariate Student’s t-distribution instead of the multivariate Gaussian distribution. We also consider variants of these two methods which account for heteroscedasticity within the data. A comparison of the different approaches is made. In particular, the model-independent techniques investigated mostly agree with predictions based on the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. Moreover, Gaussian process regression is highly sensitive to the prior specification, while Student’s t-process regression and the heteroscedastic variants of both methods are more robust to this. Student’s t-process regression and both heteroscedastic models suggest a lower value of the Hubble constant. Across all the estimates obtained for the Hubble constant within this work, the median value is H^0med=68.85±1.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{H}_0^{med} = 68.85 \\pm 1.67$$\\end{document} km s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} Mpc-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}.

Fast simulation mapping: From standard to modified gravity cosmologies using the bias assignment method

Context. We assess the effectiveness of a non-parametric bias model in generating mock halo catalogues for modified gravity (MG) cosmologies, relying on the distribution of dark matter from either MG or Λ cold dark matter (ΛCDM) simulations. Aims. We aim to generate halo catalogues that effectively capture the distinct impact of MG, ensuring high accuracy in both two- and three-point statistics for a comprehensive analysis of large-scale structures. We investigated the inclusion of MG in non-local bias to directly map the tracers onto ΛCDM fields, which would significantly reduce computational costs. Methods. We employed the bias assignment method (BAM) to model halo distribution statistics by leveraging seven high-resolution COLA simulations of MG cosmologies. Taking cosmic-web dependences into account when learning the bias relations, we designed two experiments to map the MG effects: one utilising the consistent MG density fields and the other employing the benchmark ΛCDM density field. Results. BAM generates MG halo catalogues from both calibration experiments with excellent summary statistics, achieving a ~1% accuracy in the power spectrum across a wide range of k modes, with minimal differences well below 10% for modes subject to cosmic variance, particularly below k < 0.07 h Mpc−1. The reduced bispectrum remains consistent with the reference catalogues within 10% for the studied configuration. Our results demonstrate that a non-linear and non-local bias description can model the effects of MG starting from a ΛCDM field.

Software Reliability Prediction by Adaptive Gated Recurrent Unit‐Based Encoder‐Decoder Model With Ensemble Empirical Mode Decomposition

ABSTRACTAccurate software reliability prediction is significant to software quality assurance. However, the rapid development and evolution of modern software pose more challenges for accurate software quality assessment. With the rapid development of machine learning and intelligent algorithms, data‐driven nonparametric models have gradually attracted increasing attention with outstanding prediction performance. However, we found that there may exist some prediction lags caused by the autocorrelation and nonstationarity of software fault data in the prediction of nonparametric models affecting their performance. To address this problem, we proposed an adaptive gated recurrent unit‐based encoder‐decoder model (ED‐GRU) with ensemble empirical mode decomposition (EEMD), effectively reducing prediction lags and performing accurate software fault number prediction. The autocorrelation and nonstationarity of fault data are first reduced by using first‐order difference and EEMD to clearly characterize the changing trend of the data. The frequency‐specific ED‐GRU networks are then combined to adaptively learn the nonlinear fluctuation trend of fault data under different frequency scales and obtain accurate prediction final results after aggregation. Experiments on eight public datasets showed that the proposed EEMD‐ED‐GRU‐PF model could effectively reduce the prediction lags and achieve the best prediction performance compared with four nonparametric and five parametric baseline methods in all datasets. Therefore, the proposed method can effectively and stably reduce the prediction lag to significantly improve the prediction accuracy. In this way, developers can accurately evaluate the current quality of the software and provide valuable guidance for software development and maintenance.

Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

Nonparametric and Continuous Variable-Based Stratigraphic Modelling from Sparse Boreholes using Signed Distance Function and Bayesian Compressive Sensing

An accurate stochastic interpretation of subsurface stratigraphy with quantified uncertainty can benefit the subsequent risk management of geotechnical infrastructure. Traditional approaches to developing geological cross-sections from sparse boreholes typically require the calibration or definition of empirical model parameters and functions, which may introduce subjectivity and bias. In this study, a non-parametric and continuous variable-based spatial predictor that leverages the signed distance function and Bayesian compressive sensing (BCS) is proposed for subsurface stratigraphic modelling. The proposed method transforms sparse categorical borehole data from a low-dimensional space into continuous variables in a high-dimensional space, enabling a comprehensive representation of more implicit characteristics of intricate geological patterns. This transformation facilitates the use of the continuous-variable-based BCS for non-parametric spatial prediction. The most probable geological cross-section and uncertainty qualification plot are derived after transforming spatially interpreted fields of continuous variables back into soil types. The performance of the proposed method is demonstrated using synthetic and real-world cases. Results indicate that the proposed approach can handle intricate stratigraphic scenarios characterized by complex geological structures, such as crossed-inclined, folded, inclined-folded, and interbedded strata, in a data-driven and non-parametric manner. The advantages of the proposed method over existing spatial predictors for developing geological cross-sections are also demonstrated.

Measuring psychache as a suicide risk variable: A Mokken analysis of the Holden's Psychache Scale

BackgroundThe Psychache Scale (PAS) is a questionnaire measuring trait-level psychological pain with satisfactory internal consistency and a strong correlation with suicidal ideation severity. However, inconsistent results have been reported for the PAS dimensionality. In the present study we used a non-parametric item response theory model, called Mokken Scale Analysis (MSA), to refine an unidimensional version of the PAS. MethodsThe sample was composed of 400 Italian adults (312 females and 88 males) nonrandomly recruited from the general population. ResultsA final set of 10 items satisfied the unidimensionality, local independence, and monotonicity assumptions, although it did not satisfy the double monotonicity assumption. The internal consistency of the PAS-10 was satisfactory (ordinal alpha = 0.98, ω = 0.97, and AVE = 0.82), and ROC curves analysis indicated good discriminant validity when differentiating participants with higher suicide risk from those with lower suicide risk. LimitationsStructural invariance between nonclinical and clinical samples was not investigated, and the presence of suicide ideation and behaviors was assessed with self-report measures with potential under-reporting of the phenomenon. ConclusionThe PAS-10 resulted to be a potentially valid and unidimensional measure of psychological pain (i.e., psychache) that could be used to screen adults at higher risk for suicide. Future studies are needed to investigate psychometric properties of the PAS-10 in clinical samples and to replicate results in independent samples.