Showing papers in "Scandinavian Journal of Statistics in 2009"
TL;DR: In this paper, a stochastic process driven by diffusions and jumps is considered and a technique for identifying the times when jumps larger than a suitably defined threshold occurred is proposed.
Abstract: We consider a stochastic process driven by diffusions and jumps Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred This allows us to determine a consistent non-parametric estimator of the integrated volatility when the infinite activity jump component is Levy Jump size estimation and central limit results are proved in the case of finite activity jumps Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data
399 citations
TL;DR: A comprehensive Bayesian non‐parametric analysis of random probabilities which are obtained by normalizing random measures with independent increments (NRMI), which allows to derive a generalized Blackwell–MacQueen sampling scheme, which is then adapted to cover also mixture models driven by general NRMIs.
Abstract: . One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. In this paper, we provide a comprehensive Bayesian non-parametric analysis of random probabilities which are obtained by normalizing random measures with independent increments (NRMI). Special cases of these priors have already shown to be useful for statistical applications such as mixture models and species sampling problems. However, in order to fully exploit these priors, the derivation of the posterior distribution of NRMIs is crucial: here we achieve this goal and, indeed, provide explicit and tractable expressions suitable for practical implementation. The posterior distribution of an NRMI turns out to be a mixture with respect to the distribution of a specific latent variable. The analysis is completed by the derivation of the corresponding predictive distributions and by a thorough investigation of the marginal structure. These results allow to derive a generalized Blackwell–MacQueen sampling scheme, which is then adapted to cover also mixture models driven by general NRMIs.
211 citations
TL;DR: A Bayesian semiparametric methodology for quantile regression modelling that allows the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions.
Abstract: . We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non-parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non-parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.
143 citations
TL;DR: In this article, the pointwise asymptotic normality of a kernel estimator (r) over cap(.) of r (.) has been proved in the literature.
Abstract: We consider the functional non-parametric regression model Y = r(chi) + epsilon, where the response Y is univariate, chi is a functional covariate (i.e. valued in some infinite-dimensional space), and the error epsilon satisfies E(epsilon vertical bar chi) = 0. For this model, the pointwise asymptotic normality of a kernel estimator (r) over cap(.) of r (.) has been proved in the literature. To use this result for building pointwise confidence intervals for r (.), the asymptotic variance and bias of (r) over cap(.) need to be estimated. However, the functional covariate setting makes this task very hard. To circumvent the estimation of these quantities, we propose to use a bootstrap procedure to approximate the distribution of (r) over cap(.) - r (.). Both a naive and a wild bootstrap procedure are studied, and their asymptotic validity is proved. The obtained consistency results are discussed from a practical point of view via a simulation study. Finally, the wild bootstrap procedure is applied to a food industry quality problem to compute pointwise confidence intervals.
87 citations
TL;DR: A bound on how close the solution is to a true sparse signal in the case where the number of covariates is large is established and this is applied to a breast cancer data set with gene expression recordings and to the primary biliary cirrhosis clinical data.
Abstract: This paper considers covariate selection for the additive hazards model. This model is particularly simple to study theoretically and its practical implementation has several major advantages to the similar methodology for the proportional hazards model. One complication compared with the proportional model is, however, that there is no simple likelihood to work with. We here study a least squares criterion with desirable properties and show how this criterion can be interpreted as a prediction error. Given this criterion, we define ridge and Lasso estimators as well as an adaptive Lasso and study their large sample properties for the situation where the number of covariates p is smaller than the number of observations. We also show that the adaptive Lasso has the oracle property. In many practical situations, it is more relevant to tackle the situation with large p compared with the number of observations. We do this by studying the properties of the so-called Dantzig selector in the setting of the additive risk model. Specifically, we establish a bound on how close the solution is to a true sparse signal in the case where the number of covariates is large. In a simulation study, we also compare the Dantzig and adaptive Lasso for a moderate to small number of covariates. The methods are applied to a breast cancer data set with gene expression recordings and to the primary biliary cirrhosis clinical data.
59 citations
TL;DR: In this paper, an empirical likelihood method was developed to do inference for the unknown, true parameters (µ0, ν0 ) under very mild conditions on the vector of criterion functions g. In particular, we do not require that g1, gp+q are smooth in µ or ν.
Abstract: Suppose that X1, ..., Xn is a sequence of independent random vectors, identically distributed as a d-dimensional random vector X. Let µ ∈ IR p be a parameter of interest and ν ∈ IR q be some nuisance parameter. The unknown, true parameters (µ0 , ν0 ) are uniquely determined by the system of equations E {g(X, µ0 , ν0 )} = 0, where g = (g1, ..., gp+q ) is a vector of p + q functions. In this paper we develop an empirical likelihood method to do inference for the parameter µ0. The results in this paper are valid under very mild conditions on the vector of criterion functions g. In particular, we do not require that g1,..., gp+q are smooth in µ or ν. This offers the advantage that the criterion function may involve indicators, which are encountered when considering e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed empirical likelihood method for small samples.
57 citations
TL;DR: In this paper, the authors derived the fully efficient Bayes predictor by utilizing all the available data and employed the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor.
Abstract: . Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.
48 citations
TL;DR: In this paper, the authors prove the validity of smooth residual bootstrap versions of procedures that are based on the empirical process of residuals estimated from a non-parametric regression model.
Abstract: . The aim of this paper is to prove the validity of smooth residual bootstrap versions of procedures that are based on the empirical process of residuals estimated from a non-parametric regression model. From this result, consistency of various model tests in non-parametric regression is deduced, such as goodness-of-fit tests for the regression and variance function, tests for equality of regression functions and tests concerning the error distribution.
47 citations
TL;DR: In this article, a class of bias-corrected empirical log-likelihood ratios for the response mean is defined, and the corresponding empirical likelihood confidence interval is constructed, where the range of bandwidths contains the optimal bandwidth for estimating the regression function, since the existing data-driven algorithm is valid for selecting an optimal bandwidth.
Abstract: . A kernel regression imputation method for missing response data is developed. A class of bias-corrected empirical log-likelihood ratios for the response mean is defined. It is shown that any member of our class of ratios is asymptotically chi-squared, and the corresponding empirical likelihood confidence interval for the response mean is constructed. Our ratios share some of the desired features of the existing methods: they are self-scale invariant and no plug-in estimators for the adjustment factor and asymptotic variance are needed; when estimating the non-parametric function in the model, undersmoothing to ensure root-n consistency of the estimator for the parameter is avoided. Since the range of bandwidths contains the optimal bandwidth for estimating the regression function, the existing data-driven algorithm is valid for selecting an optimal bandwidth. We also study the normal approximation-based method. A simulation study is undertaken to compare the empirical likelihood with the normal approximation method in terms of coverage accuracies and average lengths of confidence intervals.
46 citations
TL;DR: In this article, the robust expectation-solution (RES) estimator is proposed for the zero-inflated Poisson regression model, which is a special case of finite mixture models that is useful for count data containing many zeros.
Abstract: . The zero-inflated Poisson regression model is a special case of finite mixture models that is useful for count data containing many zeros. Typically, maximum likelihood (ML) estimation is used for fitting such models. However, it is well known that the ML estimator is highly sensitive to the presence of outliers and can become unstable when mixture components are poorly separated. In this paper, we propose an alternative robust estimation approach, robust expectation-solution (RES) estimation. We compare the RES approach with an existing robust approach, minimum Hellinger distance (MHD) estimation. Simulation results indicate that both methods improve on ML when outliers are present and/or when the mixture components are poorly separated. However, the RES approach is more efficient in all the scenarios we considered. In addition, the RES method is shown to yield consistent and asymptotically normal estimators and, in contrast to MHD, can be applied quite generally.
42 citations
TL;DR: In this article, the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative is investigated and sufficient conditions for consistency are established with priors using certain mixtures of triangular densities.
Abstract: We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.
TL;DR: In this paper, the Cramer-von Mises functional of the empirical copula process and moment-based goodness-of-fit statistics are compared by considering their associated asymptotic local power curves.
Abstract: . The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramer–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramer–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.
TL;DR: Two parameterizations of models for marginal independencies for discrete distributions which are representable by bi‐directed graph models, under the global Markov property are discussed, also known as thenation multivariate logistic transformation and variation‐independent parameters.
Abstract: We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property Such models are useful data analytic tools especially if used in combination with other graphical models The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation-independent parameters An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method
TL;DR: In this article, a calibration of the posterior predictive p-value is proposed to make the resulting calibrated p-values uniformly distributed under the model conditions, allowing for discrepancy measures that can be used for checking properties of the model at all stages.
Abstract: . The present work focuses on extensions of the posterior predictive p-value (ppp-value) for models with hierarchical structure, designed for testing assumptions made on underlying processes. The ppp-values are popular as tools for model criticism, yet their lack of a common interpretation limit their practical use. We discuss different extensions of ppp-values to hierarchical models, allowing for discrepancy measures that can be used for checking properties of the model at all stages. Through analytical derivations and simulation studies on simple models, we show that similar to the standard ppp-values, these extensions are typically far from uniformly distributed under the model assumptions and can give poor power in a hypothesis testing framework. We propose a calibration of the p-values, making the resulting calibrated p-values uniformly distributed under the model conditions. Illustrations are made through a real example of multinomial regression to age distributions of fish.
TL;DR: Empirical likelihood (EL) pointwise confidence regions for the time-dependent regression coefficients via local partial likelihood smoothing and simultaneous confidence bands for a linear combination of the coefficients are derived based on the strong approximation methods.
Abstract: The Cox model with time-dependent coefficients has been studied by a number of authors recently. In this paper, we develop empirical likelihood (EL) pointwise confidence regions for the time-dependent regression coefficients via local partial likelihood smoothing. The EL simultaneous confidence bands for a linear combination of the coefficients are also derived based on the strong approximation methods. The empirical likelihood ratio is formulated through the local partial log-likelihood for the regression coefficient functions. Our numerical studies indicate that the EL pointwise/simultaneous confidence regions/bands have satisfactory finite sample performances. Compared with the confidence regions derived directly based on the asymptotic normal distribution of the local constant estimator, the EL confidence regions are overall tighter and can better capture the curvature of the underlying regression coefficient functions. Two data sets, the gastric cancer data and the Mayo Clinic primary biliary cirrhosis data, are analyzed using the proposed method.
TL;DR: In this article, a non-parametric test for the proportionality of the regression function and the scale function in a nonparametric context is proposed. But the test is based on the difference between two nonparameterized estimators of the distribution of regression error.
Abstract: Several classical time series models can be written as a regression model between the components of a strictly stationary bivariate process. Some of those models, such as the ARCH models, share the property of proportionality of the regression function and the scale function, which is an interesting feature in econometric and financial models. In this article, we present a procedure to test for this feature in a non-parametric context. The test is based on the difference between two non-parametric estimators of the distribution of the regression error. Asymptotic results are proved and some simulations are shown in the paper in order to illustrate the finite sample properties of the procedure.
TL;DR: In this article, a regression analysis for multiple events data with major interest in a non-terminal event such as disease progression is proposed, under flexible model assumptions on the two types of events.
Abstract: Multiple events data are commonly seen in medical applications. There are two types of events, namely terminal and non-terminal. Statistical analysis for non-terminal events is complicated due to dependent censoring. Consequently, joint modelling and inference are often needed to avoid the problem of non-identifiability. This article considers regression analysis for multiple events data with major interest in a non-terminal event such as disease progression. We generalize the technique of artificial censoring, which is a popular way to handle dependent censoring, under flexible model assumptions on the two types of events. The proposed method is applied to analyse a data set of bone marrow transplantation.
TL;DR: In this paper, the authors show that retrospective change point detection policies based on Shiryayev-Roberts statistics are non-asymptotically optimal in the context of most powerful testing.
Abstract: . Since the middle of the twentieth century, the problem of making inferences about the point in a surveyed series of observations at which the underlying distribution changes has been extensively addressed in the economics, biostatistics and statistics literature. Cumulative sum-type statistics have commonly been thought to play a central role in non-sequential change point detections. Alternatively, we present and examine an approach based on the Shiryayev–Roberts scheme. We show that retrospective change point detection policies based on Shiryayev–Roberts statistics are non-asymptotically optimal in the context of most powerful testing.
TL;DR: In this paper, the authors focus on locally stationary processes and develop tests of the hypothesis that the time-varying spectral density has a semiparametric structure, including the interesting case of a time varying autoregressive moving-average (tvARMA) model.
Abstract: . Many time series in applied sciences obey a time-varying spectral structure. In this article, we focus on locally stationary processes and develop tests of the hypothesis that the time-varying spectral density has a semiparametric structure, including the interesting case of a time-varying autoregressive moving-average (tvARMA) model. The test introduced is based on a L2-distance measure of a kernel smoothed version of the local periodogram rescaled by the time-varying spectral density of the estimated semiparametric model. The asymptotic distribution of the test statistic under the null hypothesis is derived. As an interesting special case, we focus on the problem of testing for the presence of a tvAR model. A semiparametric bootstrap procedure to approximate more accurately the distribution of the test statistic under the null hypothesis is proposed. Some simulations illustrate the behaviour of our testing methodology in finite sample situations.
TL;DR: This paper develops a non-concave penalized likelihood approach and adopts the idea behind the oracle procedure for variable selection in the context of regression analysis of panel count data, and presents an algorithm for this process.
Abstract: . Variable selection is an important issue in all regression analyses, and in this paper we discuss this in the context of regression analysis of panel count data. Panel count data often occur in long-term studies that concern occurrence rate of a recurrent event, and their analysis has recently attracted a great deal of attention. However, there does not seem to exist any established approach for variable selection with respect to panel count data. For the problem, we adopt the idea behind the non-concave penalized likelihood approach and develop a non-concave penalized estimating function approach. The proposed methodology selects variables and estimates regression coefficients simultaneously, and an algorithm is presented for this process. We show that the proposed procedure performs as well as the oracle procedure in that it yields the estimates as if the correct submodel were known. Simulation studies are conducted for assessing the performance of the proposed approach and suggest that it works well for practical situations. An illustrative example from a cancer study is provided.
TL;DR: In this paper, several testing procedures are proposed that can detect change-points in the error distribution of non-parametric regression models, where the change-point either occurs at some time point or at some value of the covariate.
Abstract: Several testing procedures are proposed that can detect change-points in the error distribution of non-parametric regression models. Different settings are considered where the change-point either occurs at some time point or at some value of the covariate. Fixed as well as random covariates are considered. Weak convergence of the suggested difference of sequential empirical processes based on non-parametrically estimated residuals to a Gaussian process is proved under the null hypothesis of no change-point. In the case of testing for a change in the error distribution that occurs with increasing time in a model with random covariates the test statistic is asymptotically distribution free and the asymptotic quantiles can be used for the test. This special test statistic can also detect a change in the regression function. In all other cases the asymptotic distribution depends on unknown features of the data-generating process and a bootstrap procedure is proposed in these cases. The small sample performances of the proposed tests are investigated by means of a simulation study and the tests are applied to a data example.
TL;DR: In this article, a model of recurrent events with competing risks and a terminal event was introduced to compare the occurrence rates of two types of events, and two tests were proposed to detect if the occurrence rate of a given type of event increases with time.
Abstract: . We consider a data set on nosocomial infections of patients hospitalized in a French intensive care facility. Patients may suffer from recurrent infections of different types and they also have a high risk of death. To deal with such situations, a model of recurrent events with competing risks and a terminal event is introduced. Our aim was to compare the occurrence rates of two types of events. For this purpose, we propose two tests: one to detect if the occurrence rate of a given type of event increases with time; a second to detect if the instantaneous probability of experiencing an event of a given type is always greater than the one of another type. The asymptotic properties of the test statistics are derived and Monte Carlo methods are used to study the power of the tests. Finally, the procedures developed are applied to the French nosocomial infections data set.
TL;DR: This paper suggests some new measures of conflict based on tail probabilities of the so‐called integrated posterior distributions introduced in the recent paper, equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters.
Abstract: . In a recent paper we extended and refined some tools introduced by O'Hagan for criticism of Bayesian hierarchical models. Especially, avoiding double use of data by a data-splitting approach was a main concern. Such tools can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. As O'Hagan, we investigated a Gaussian model of one-way analysis of variance. Through extensive Markov chain Monte Carlo simulations it was shown that our method detects model misspecification about as well as the one of O'Hagan, when this is properly calibrated, while retaining the desired false warning probability for data generated from the assumed model. In the present paper, we suggest some new measures of conflict based on tail probabilities of the so-called integrated posterior distributions introduced in our recent paper. These new measures are equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters. A general linear normal model with known covariance matrices is considered in detail.
TL;DR: In this paper, the authors define a relatively simple predictive distribution function giving improved prediction intervals, which is defined as a first-order unbiased modification of the plug-in predictive distribution functions based on the constrained maximum likelihood estimator.
Abstract: The plug-in solution is usually not entirely adequate for computing prediction intervals, as their coverage probability may differ substantially from the nominal value. Prediction intervals with improved coverage probability can be defined by adjusting the plug-in ones, using rather complicated asymptotic procedures or suitable simulation techniques. Other approaches are based on the concept of predictive likelihood for a future random variable. The contribution of this paper is the definition of a relatively simple predictive distribution function giving improved prediction intervals. This distribution function is specified as a first-order unbiased modification of the plug-in predictive distribution function based on the constrained maximum likelihood estimator. Applications of the results to the Gaussian and the generalized extreme-value distributions are presented.
TL;DR: In this article, a wavelet-based method for deconvolving a density is proposed, which combines the ideas of non-linear wavelet thresholding with periodized Meyer wavelets and estimation by information projection.
Abstract: This paper proposes a new wavelet-based method for deconvolving a density. The estimator combines the ideas of non-linear wavelet thresholding with periodized Meyer wavelets and estimation by information projection. It is guaranteed to be in the class of density functions, in particular it is positive everywhere by construction. The asymptotic optimality of the estimator is established in terms of the rate of convergence of the Kullback–Leibler discrepancy over Besov classes. Finite sample properties are investigated in detail, and show the excellent empirical performance of the estimator, compared with other recently introduced estimators.
TL;DR: A new class of nonlinear autoregressive models for vector time series, where the current vector depends on single‐indexes defined on the past lags and the effects of different lags have an additive form is studied.
Abstract: We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selec- tion of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Nino phenomenon, the unusual warming of water in the Pacific Ocean.
TL;DR: An in‐depth investigation of diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for generalized linear models and develops specific strategies for incorporating missing data into goodness‐of‐fit statistics in order to increase the power of detecting model missespecification.
Abstract: In this paper, we carry out an in-depth investigation of diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for generalized linear models. Our diagnostic measures include case-deletion measures and conditional residuals. We use the conditional residuals to construct goodness-of-fit statistics for testing possible misspecifications in model assumptions, including the sampling distribution. We develop specific strategies for incorporating missing data into goodness-of-fit statistics in order to increase the power of detecting model misspecification. A resampling method is proposed to approximate the p-value of the goodness-of-fit statistics. Simulation studies are conducted to evaluate our methods and a real data set is analysed to illustrate the use of our various diagnostic measures.
TL;DR: This work generalizes the canonical Gaussian model and proposes a more general selection of λ and ν by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing and investigates some asymptotic properties in parametric and non‐parametric settings.
Abstract: For the problem of estimating a sparse sequence of coefficients of a parametric or non-parametric generalized linear model, posterior mode estimation with a Subbotin(λ,ν) prior achieves thresholding and therefore model selection when ν ∈ [0,1] for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator (ν = 0), its approximate convexification called lasso (ν = 1) and ridge regression (ν = 2). Rather than fixing ν, selecting the two hyperparameters λ and ν adds flexibility for a better fit, provided both are well selected from the data. Considering first the canonical Gaussian model, we generalize the Stein unbiased risk estimate, SURE(λ,ν), to the situation where the thresholding function is not almost differentiable (i.e. ν 1). We then propose a more general selection of λ and ν by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing. We investigate some asymptotic properties in parametric and non-parametric settings. Simulations and applications to real data show excellent performance.
TL;DR: The procedure is shown to control the false discovery exceedance and to be competitive in terms of power and how to apply the idea of GAUGE to achieve control of other error measures is shown.
Abstract: A new multiple testing procedure, the generalized augmentation procedure (GAUGE), is introduced The procedure is shown to control the false discovery exceedance and to be competitive in terms of power It is also shown how to apply the idea of GAUGE to achieve control of other error measures Extensions to dependence are discussed, together with a modification valid under arbitrary dependence We present an application to an original study on prostate cancer and on a benchmark data set on colon cancer
TL;DR: In this paper, the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distributions in ill-posed inverse problems are investigated, and sufficient conditions are provided to ensure geometric ergodicity of RSM samplers of the posterior distribution.
Abstract: In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distributions in ill-posed inverse problems. We provide an accessible set of sufficient conditions, in terms of the observational model and the prior, to ensure geometric ergodicity of RSM samplers of the posterior distribution. We illustrate how these conditions can be checked in an application to the inversion of oceanographic tracer data.