pseudo-Bayesian Approach Research Articles

Pseudo-Bayesian Approach for Quantile Regression Inference: Adaptation to Sparsity

Pseudo-Bayesian Approach for Quantile Regression Inference: Adaptation to Sparsity

A reduced-rank approach to predicting multiple binary responses through machine learning

This paper investigates the problem of simultaneously predicting multiple binary responses by utilizing a shared set of covariates. Our approach incorporates machine learning techniques for binary classification, without making assumptions about the underlying observations. Instead, our focus lies on a group of predictors, aiming to identify the one that minimizes prediction error. Unlike previous studies that primarily address estimation error, we directly analyze the prediction error of our method using PAC-Bayesian bounds techniques. In this paper, we introduce a pseudo-Bayesian approach capable of handling incomplete response data. Our strategy is efficiently implemented using the Langevin Monte Carlo method. Through simulation studies and a practical application using real data, we demonstrate the effectiveness of our proposed method, producing comparable or sometimes superior results compared to the current state-of-the-art method.

Pseudo-Bayesian Approach for Robust Mode Detection and Extraction Based on the STFT

This paper addresses the problem of disentangling nonoverlapping multicomponent signals from their observation being possibly contaminated by external additive noise. We aim to extract and to retrieve the elementary components (also called modes) present in an observed nonstationary mixture signal. To this end, we propose a new pseudo-Bayesian algorithm to perform the estimation of the instantaneous frequency of the signal modes from their time-frequency representation. In a second time, a detection algorithm is developed to restrict the time region where each signal component behaves, to enhance quality of the reconstructed signal. We finally deal with the presence of noise in the vicinity of the estimated instantaneous frequency by introducing a new reconstruction approach relying on nonbinary band-pass synthesis filters. We validate our methods by comparing their reconstruction performance to state-of-the-art approaches through several experiments involving both synthetic and real-world data under different experimental conditions.

An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography

We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradigm for quantum tomography with attractive theoretical and empirical results. However, the computation of (Pseudo-)Bayesian estimators, due to sampling from complex and high-dimensional distribution, pose significant challenges that hamper their usages in practical settings. To overcome this problem, we present an efficient adaptive MCMC sampling method for the Pseudo-Bayesian estimator by exploring an adaptive proposal scheme together with subsampling method. We show in simulations that our approach is substantially computationally faster than the previous implementation by at least two orders of magnitude which is significant for practical quantum tomography.

A Bayesian network approach incorporating imputation of missing data enables exploratory analysis of complex causal biological relationships.

Bayesian networks can be used to identify possible causal relationships between variables based on their conditional dependencies and independencies, which can be particularly useful in complex biological scenarios with many measured variables. Here we propose two improvements to an existing method for Bayesian network analysis, designed to increase the power to detect potential causal relationships between variables (including potentially a mixture of both discrete and continuous variables). Our first improvement relates to the treatment of missing data. When there is missing data, the standard approach is to remove every individual with any missing data before performing analysis. This can be wasteful and undesirable when there are many individuals with missing data, perhaps with only one or a few variables missing. This motivates the use of imputation. We present a new imputation method that uses a version of nearest neighbour imputation, whereby missing data from one individual is replaced with data from another individual, their nearest neighbour. For each individual with missing data, the subsets of variables to be used to select the nearest neighbour are chosen by sampling without replacement the complete data and estimating a best fit Bayesian network. We show that this approach leads to marked improvements in the recall and precision of directed edges in the final network identified, and we illustrate the approach through application to data from a recent study investigating the causal relationship between methylation and gene expression in early inflammatory arthritis patients. We also describe a second improvement in the form of a pseudo-Bayesian approach for upweighting certain network edges, which can be useful when there is prior evidence concerning their directions.

A-optimal designs for optimum mixture in an additive quadratic mixture model

ABSTRACTIn the analysis of experiments with mixtures, quadratic models have been widely used. The optimum designs for the estimation of optimum mixing proportions in a quadratic mixture model have been studied by Pal and Mandal [Optimum designs for optimum mixtures. Statist Probab Lett. 2006;76:1369–1379] and Mandal et al. [Optimum mixture designs: a pseudo-Bayesian approach. J Ind Soc Agric Stat. 2008;62(2):174–182; Optimum mixture designs under constraints on mixing components. Statist Appl. 2008;6(1&2) (New Series): 189–205], using a pseudo-Bayesian approach. In this paper, a similar approach has been employed to obtain the A-optimal designs for the estimation of optimum proportions in an additive quadratic mixture model, proposed by Darroch and Waller [Additivity and interaction in three-component experiments with mixture. Biometrika. 1985;72:153–163], when the number of components is 3, 4 and 5. It has been shown that the vertices of the simplex are necessarily the support points of the optimum design, and the other support points include barycentres of depth at most 2.

Bayesian optimal cluster designs

Designing cluster trials depends on the knowledge of the intracluster correlation coefficient. To overcome the issue of parameter dependence, Bayesian designs are proposed for two level models with and without covariates. These designs minimize the variance of the treatment contrast under certain cost constraints. A pseudo Bayesian design approach is advocated that integrates and averages the objective function over a prior distribution of the intracluster correlation coefficient. Theoretical results on the Bayesian criterion are noted when the intracluster correlation follows a uniform distribution. Two data sets based on educational surveys conducted in schools are used to illustrate the proposed methodology.

Sampling designs on stream networks using the pseudo-Bayesian approach

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.

Honey Bee Location- and Time-Linked Memory Use in Novel Foraging Situations: Floral Color Dependency

Learning facilitates behavioral plasticity, leading to higher success rates when foraging. However, memory is of decreasing value with changes brought about by moving to novel resource locations or activity at different times of the day. These premises suggest a foraging model with location- and time-linked memory. Thus, each problem is novel, and selection should favor a maximum likelihood approach to achieve energy maximization results. Alternatively, information is potentially always applicable. This premise suggests a different foraging model, one where initial decisions should be based on previous learning regardless of the foraging site or time. Under this second model, no problem is considered novel, and selection should favor a Bayesian or pseudo-Bayesian approach to achieve energy maximization results. We tested these two models by offering honey bees a learning situation at one location in the morning, where nectar rewards differed between flower colors, and examined their behavior at a second location in the afternoon where rewards did not differ between flower colors. Both blue-yellow and blue-white dimorphic flower patches were used. Information learned in the morning was clearly used in the afternoon at a new foraging site. Memory was not location-time restricted in terms of use when visiting either flower color dimorphism.

Optimum Designs for Estimation of Optimum Amount and Proportions in a Mixture-Amount Model

This article studies a mixture-amount model, which is quadratic both in the proportions of mixing components and the amount of mixture. Using the pseudo-Bayesian approach of Pal and Mandal (2006), it attempts to find the A-optimal design for the estimation of the optimum mixing proportions and the optimum amount.

A New Pseudo-Bayesian Model with Implications for Financial Anomalies and Investors’ Behavior

Barberis, Shleifer, and Vishny [1998] and others have developed Bayesian models to explain investors’ behavioral biases by using conservative heuristics and representative heuristics in making decisions. To extend their work, Lam, Liu, and Wong [2010] have developed a model of weight assignments using a pseudo-Bayesian approach that reflects investors’ behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors’ conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors’ behavioral biases. This paper extends their work further by developing a theory to explain some market anomalies, including short-term underreaction, long-term overreaction, and excess volatility. We also explain in detail the linkage between these market anomalies and investors’ behavioral biases.

Pseudo-Bayesian [formula omitted]-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model

In the analysis of experiments with mixture, quadratic models have been widely used. Several authors considered finding optimum designs for the estimation of the parameters of the model. The optimum designs for the estimation of optimum mixing proportions in Scheffé’s quadratic mixture model has been studied by Pal and Mandal (2006) and Mandal et al. (2008a,b) using a pseudo-Bayesian approach. In this paper, we consider an additive quadratic mixture model, proposed by Darroch and Waller (1985), when the amount of mixture is taken into account, and obtain the A-optimal designs for the estimation of optimum proportions, adopting the approach of Pal and Mandal (2006). We show that, besides other support points, the origin and the vertices of the simplex are necessarily the support points of the optimum design.

A Pseudo-Bayesian Model for Stock Returns In Financial Crises

Recently, there has been a considerable interest in the Bayesian approach for explaining investors' behaviorial biases by incorporating conservative and representative heuristics when making financial decisions, (see, for example, Barberis, Shleifer and Vishny (1998)). To establish a quantitative link between some important market anomalies and investors' behaviorial biases, Lam, Liu, and Wong (2010) introduced a pseudo-Bayesian approach for developing properties of stock returns, where weights induced by investors' conservative and representative heuristics are assigned to observations of the earning shocks and stock prices. In response to the recent global financial crisis, we introduce a new pseudo-Bayesian model to incorporate the impact of a financial crisis. Properties of stock returns during the financial crisis and recovery from the crisis are established. The proposed model can be applied to investigate some important market anomalies including short-term underreaction, long-term overreaction, and excess volatility during financial crisis. We also explain in some detail the linkage between these market anomalies and investors' behavioral biases during financial crisis.

A Pseudo‐Bayesian Shrinkage Approach to Regression with Missing Covariates

We consider the linear regression of outcome Y on regressors W and Z with some values of W missing, when our main interest is the effect of Z on Y, controlling for W. Three common approaches to regression with missing covariates are (i) complete-case analysis (CC), which discards the incomplete cases, and (ii) ignorable likelihood methods, which base inference on the likelihood based on the observed data, assuming the missing data are missing at random (Rubin, 1976b), and (iii) nonignorable modeling, which posits a joint distribution of the variables and missing data indicators. Another simple practical approach that has not received much theoretical attention is to drop the regressor variables containing missing values from the regression modeling (DV, for drop variables). DV does not lead to bias when either (i) the regression coefficient of W is zero or (ii) W and Z are uncorrelated. We propose a pseudo-Bayesian approach for regression with missing covariates that compromises between the CC and DV estimates, exploiting information in the incomplete cases when the data support DV assumptions. We illustrate favorable properties of the method by simulation, and apply the proposed method to a liver cancer study. Extension of the method to more than one missing covariate is also discussed.

A New Pseudo Bayesian Model for Stock Returns In Financial Crisis

Barberis, Shleifer and Vishny (1998) and others have developed Bayesian models to explain investors' behavioral biases by using the conservatism heuristics and the representativeness heuristics in making decisions. To extend their work, Lam, Liu, and Wong (2010) have developed a model of weight assignments using a pseudo-Bayesian approach that reflects investors' behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors' conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors' behavioral biases. This paper extends their work further by developing properties for the stock return during financial crisis and recovery from the crisis, which could then be used to study some market anomalies including short-term underreaction, long-term overreaction, and excess volatility during financial crisis. We also explain in details the linkage between these market anomalies and investors' behavioral biases during financial crisis.

A New Pseudo-Bayesian Model with Implications to Financial Anomalies and Investors’ Behaviors

Barberis, Shleifer and Vishny (1998) and others have developed Bayesian models to explain investors’ behavioral biases by using the conservatism heuristics and the representativeness heuristics in making decisions. To extend their work, Lam, Liu, and Wong (2010) have developed a model of weight assignments using a pseudo-Bayesian approach that reflects investors’ behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors’ conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors’ behavioral biases. This paper extends their work further by developing properties to explain some market anomalies including short-term underreaction, long-term overreaction, and excess volatility. We also explain in details the linkage between these market anomalies and investors’ behavioral biases.

A pseudo-Bayesian model in financial decision making with implications to market volatility, under- and overreaction

This paper develops a model of weight assignments using a pseudo-Bayesian approach that reflects investors’ behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors’ conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors’ behavioral biases. The seriousness of an anomaly can be quantitatively assessed by investigating into its dependency on weights. New results other than the short-run underreaction and long-run overreaction can be derived and new hypotheses can be formed.

Optimum designs for estimation of optimum point under cost constraint

In this paper, we consider the estimation of the optimum factor combination in a response surface model. Assuming that the response function is quadratic concave and there is a linear cost constraint on the factor combination, we attempt to find the optimum design using the trace optimality criterion. As the criterion function involves the unknown parameters, we adopt a pseudo-Bayesian approach to resolve the problem.

A Quantitative Behavioral Model and its Implications for Market Volatility, Underreaction, and Overreaction

This paper develops a model of weight assignments using a pseudo-Bayesian approach that reflects investors' behavioral biases. In this parsimonious model of investor sentiment, weights induced by investors' conservative and representative heuristics are assigned to observations of the earning shocks of stock prices. Such weight assignments enable us to provide a quantitative link between some market anomalies and investors' behavioral biases. Using this model, we can show that while learning may contribute to market anomalies, anomalies still exist even after the learning process has been completed. In particular, we can deduce the following: (1) Excess market volatility will result from investors' biased heuristics. It is the representative heuristic, rather than the conservative heuristic, which contributes to excess volatility in the market. In addition, excess volatility is more prominent when the discount rate is small. (2) Through a misapplication of Bayes' rule, investors' behavioral biases lead to short-term underreaction and long-term overreaction in the market. The more conservative/representative the heuristic, the larger the magnitude of the return auto-correlation and the larger is the contrarian/momentum trading profit. Further analysis shows that the representative heuristic contributes to the contrarian trading profit and the conservative heuristic contributes to the momentum trading profit. In addition, the smaller the discount rate, the larger the contrarian/momentum profit. (3) Investors' behavioral biases induce a magnitude effect in the under- and overreaction phenomena, i.e., the more severe the earnings shock, the larger the market autocorrelation and the larger the momentum/contrarian trading profit. (4) The magnitude effect described in (3) is convex in nature.

Optimum Mixture Design Using Deficiency Criterion

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006, 2007) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing designs.