Monte Carlo Likelihood Research Articles

Skewing the CMB×LSS: a fast method for bispectrum analysis

Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed.Our results show that for the combination of the Planck satellite and the Dark Energy Spectroscopic Instrument (DESI), the difference in the constraints on bias and cosmological parameters from the skew-spectrum and the bispectrum is at most 17%.We further compare and find agreement between our theoretical skew-spectra and those estimated from N-body simulations, for which it is important to include gravitational non-linearities beyond perturbation theory and the post-Born effect for CMB lensing. We define an algorithm to apply the skew-spectrum estimator to the data and, as a preliminary step, we use the skew-spectra to constrain bias parameters and the amplitude of shot noise from the simulations through a Markov chain Monte Carlo likelihood analysis, finding that it may be possible to reach percent-level estimates for the linear bias parameter b 1.

Handling Missing Values in Information Systems Research: A Review of Methods and Assumptions

Data have never been more essential to the success of decision making. However, data are often messy. A perennial data challenge is missing values, which frequently occur in real-world data, such as unreported data items in public firms’ financial statements and skipped product ratings from consumers. What is the influence of missing values and how should they be handled? Although we are in a big data era, missing values are not ignorable if data are missing for nonrandom reasons. In the case of product ratings, if only people who favor the product provide ratings while others put aside the product and do not respond, then even a simple mean estimation of the product rating would be significantly biased. Such bias challenges the validity of data analysis, and it cannot be eliminated simply by increasing the sample size of the data. To correct the bias arising from nonrandom missing values, it is necessary to examine and model what causes the missing values. We propose and demonstrate the superior performance of a Monte Carlo likelihood approach to correct the bias. Overall, we recommend well-designed data collection processes with documentation of the possible reasons for missing values, cautious adoption of missing value handling methods, and structured missing value reporting practices.

Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers

The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model), and higher-moment spillovers. The matrix exponential transformation guarantees the positive definiteness of the dynamic covariance matrix. We decompose the likelihood function of the RMESV-ALM model into two components: one based on the conventional Kalman filter, and the other evaluated by a Monte Carlo likelihood technique. We consider a two-step quasi-maximum likelihood estimator for maximizing the likelihood function, and examine the finite sample properties of the estimator. The specification enables us to analyze asymmetric and higher-moment spillover effects in the covariance dynamics via news impact curves and impulse response functions. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. Our empirical results suggest the RMESV-ALE specification to be superior, and spillover effects are found from returns or volatility to the remaining volatilities.

Likelihood‐based inference for generalized linear mixed models: Inference with the R package glmm

The R package glmm enables likelihood‐based inference for generalized linear mixed models with a canonical link. No other publicly available software accurately conducts likelihood‐based inference for generalized linear mixed models with crossed random effects. glmm is able to do so by approximating the likelihood function and two derivatives using importance sampling. The importance sampling distribution is an essential piece of Monte Carlo likelihood approximation, and developing a good one is the main challenge in implementing it. The package glmm uses the data to tailor the importance sampling distribution and is constructed to ensure finite Monte Carlo standard errors. In the context of the generalized linear mixed model, the salamander model with crossed random effects has become a benchmark example. We use this model to illustrate the complexities of the likelihood function and to demonstrate the use of the R package glmm.

Accurately weighing neutrinos with cosmological surveys

A promising avenue to measure the total, and potentially individual, mass of neutrinos consists of leveraging cosmological datasets, such as the cosmic microwave background and surveys of the large-scale structure of the universe. In order to obtain unbiased estimates of the neutrino mass, however, many effects ought to be included. Here we forecast, via a Markov Chain Monte Carlo likelihood analysis, whether measurements by two galaxy surveys: DESI and {\it Euclid}, when added to the CMB-S4 experiment, are sensitive to two effects that can alter neutrino-mass measurements. The first is the slight difference in the suppression of matter fluctuations that each neutrino-mass hierarchy generates, at fixed total mass. The second is the growth-induced scale-dependent bias (GISDB) of haloes produced by massive neutrinos. We find that near-future surveys can distinguish hierarchies with the same total mass only at the $1\sigma$ level; thus, while these are poised to deliver a measurement of the sum of neutrino masses, they cannot significantly discern the mass of each individual neutrino in the foreseeable future. We further find that neglecting the GISDB induces up to a $1\sigma$ overestimation of the total neutrino mass, and we show how to absorb this effect via a redshift-dependent parametrization of the scale-independent bias.

Handling Missing Values in Information Systems Research: A Review of Methods and Assumptions

In today’s big data environment, missing values continues to be a problem that harms the data quality. The bias caused by missing values raises the highest concern as it cannot be eliminated simply by increasing the sample size. Although the statistics literature has developed approaches to handling missing values and formulated assumptions regarding when these approaches generate valid statistical inferences, these prescriptions have yet to be broadly accepted by many social science disciplines including the Information Systems (IS) discipline. By reviewing recently published empirical research in information systems, we find that missing values is indeed an important and pervasive problem. We believe that a review of missing value theory is necessary for the IS community to understand the nature of missing values and to promote more rigorous research practice when missing values is often unavoidable. In addition, the not missing at random (NMAR) mechanism brings in challenges in parameter estimation. We contribute to research practice by proposing and demonstrating the superior performance of a Monte Carlo likelihood approach in correcting bias in parameter estimation. We conclude by suggesting that research validity can be enhanced through reasoned adoption of missing value handling method and missing value reporting practice.

A novel risk analysis approach of casing under complex conditions using copulas

Failure accidents of casings, designed obeying traditional design standards that have been amended for many times, are still happening nowadays, and existing reliability analysis methods mostly have not considered the dependence structures of variables, it's badly necessary to seek other methods to compensate these two problems and defects. This study proposes a copula-based risk analysis framework of casing in a casing-formation composite system (CFCS). Firstly, a mechanical analysis model of casing under CFCS is established and verified by the simulation method. Secondly, random data sets of the formation parameters are obtained by using logging data, meanwhile, the acquisition methods of statistical data of casing are also provided. Thirdly, the best uncertainty parameters in the given five copulas are inferred by using Bayesian-based Markov chain Monte Carlo (MCMC) likelihood algorithm, which are compared with those from other algorithms; the optimal copula is determined by the Bayesian-based MCMC-estimated method and the squared Euclidean distance (SED), respectively; the posterior joint probability isolines of the copulas are depicted, and isolines from the optimal copula are compared with that of the empirical copula method; the correlation coefficients of variables in CFCS, relative to performance function value, are sorted in magnitude. Finally, a division method of safety level is adopted, and based on the optimal copula, the risk analysis of casing is conducted with considering the bivariate dependence. The proposed framework can provide unique insights into the risk analysis of casing in CFCS with correlations considered and can also be programmed to use in risk management and decision-making systems of petroleum engineering.

Multiple particle filtering for tracking wireless agents via Monte Carlo likelihood approximation

The localization of multiple wireless agents via, for example, distance and/or bearing measurements is challenging, particularly if relying on beacon-to-agent measurements alone is insufficient to guarantee accurate localization. In these cases, agent-to-agent measurements also need to be considered to improve the localization quality. In the context of particle filtering, the computational complexity of tracking many wireless agents is high when relying on conventional schemes. This is because in such schemes, all agents’ states are estimated simultaneously using a single filter. To overcome this problem, the concept of multiple particle filtering (MPF), in which an individual filter is used for each agent, has been proposed in the literature. However, due to the necessity of considering agent-to-agent measurements, additional effort is required to derive information on each individual filter from the available likelihoods. This is necessary because the distance and bearing measurements naturally depend on the states of two agents, which, in MPF, are estimated by two separate filters. Because the required likelihood cannot be analytically derived in general, an approximation is needed. To this end, this work extends current state-of-the-art likelihood approximation techniques based on Gaussian approximation under the assumption that the number of agents to be tracked is fixed and known. Moreover, a novel likelihood approximation method is proposed that enables efficient and accurate tracking. The simulations show that the proposed method achieves up to 22% higher accuracy with the same computational complexity as that of existing methods. Thus, efficient and accurate tracking of wireless agents is achieved.

Global multivariate point pattern models for rain type occurrence

We seek statistical methods to study the occurrence of multiple rain types observed by satellite on a global scale. The main scientific interests are to relate rainfall occurrence with various atmospheric state variables and to study the dependence between the occurrences of multiple types of rainfall (e.g. short-lived and intense vs. long-lived and weak; the heights of the rain clouds are also considered). Commonly in point process model literature, the spatial domain is assumed to be a small, and thus planar domain. We consider the log-Gaussian Cox Process (LGCP) models on the surface of a sphere and take advantage of cross-covariance models for spatial processes on a global scale to model the stochastic intensity function of the LGCP models. We present analysis results for rainfall observations from the TRMM satellite and atmospheric state variables from MERRA-2 reanalysis data over the tropical Eastern and Western Pacific Ocean, as well as over the entire tropical and subtropical ocean regions. Statistical inference is done through Monte Carlo likelihood approximation for LGCP models. We employ covariance approximation to deal with massive data.

A Conway Maxwell Poisson type generalization of the negative hypergeometric distribution

Negative hypergeometric distribution arises as a waiting time distribution when we sample without replacement from a finite population. It has applications in many areas such as inspection sampling and estimation of wildlife populations. However, as is well known, the negative hypergeometric distribution is over-dispersed in the sense that its variance is greater than the mean. To make it more flexible and versatile, we propose a modified version of negative hypergeometric distribution called COM-Negative Hypergeometric distribution (COM-NH) by introducing a shape parameter as in the COM-Poisson and COMP-Binomial distributions. It is shown that under some limiting conditions, COM-NH approaches to a distribution that we call the COM-Negative binomial (COMP-NB), which in turn, approaches to the COM Poisson distribution. For the proposed model, we investigate the dispersion characteristics and shape of the probability mass function for different combinations of parameters. We also develop statistical inference for this model including parameter estimation and hypothesis tests. In particular, we investigate some properties such as bias, MSE, and coverage probabilities of the maximum likelihood estimators for its parameters by Monte Carlo simulation and likelihood ratio test to assess shape parameter of the underlying model. We present illustrative data to provide discussion.

Parameter identification for structural health monitoring based on Monte Carlo method and likelihood estimate

Structural parameters are the most important factors reflecting structural performance and conditions. As a result, their identification becomes the most essential aspect of the structural assessment and damage identification for the structural health monitoring. In this article, a structural parameter identification method based on Monte Carlo method and likelihood estimate is proposed. With which, parameters such as stiffness and damping are identified and studied. Identification effects subjected to three different conditions with no noise, with Gaussian noise, and with non-Gaussian noise are studied and compared. Considering the existence of damage, damage identification is also realized by the identification of the structural parameters. Both simulations and experiments are conducted to verify the proposed method. Results show that structural parameters, as well as the damages, can be well identified. Moreover, the proposed method is much robust to the noises. The proposed method may be prospective for the application of real structural health monitoring.

Modeling Count Data from Dependent Clusters with Poisson Mixed Models


 
 
 
 Responses collected from dependent clusters are affected by the dependence among clusters and it should be taken into account in modeling such responses. In this study, a new approach was evaluated to incorporate cluster dependence in generalized linear Poisson mixed models for count responses from dependent clusters. Performance of this approach was evaluated by using a simulation process under three different designs and different covariates. The Marginal Generalized Quasi-likelihood (GQL) method was used for estimation of parameters with the cluster dependence. Monte Carlo likelihood (MCL) and Penalized Quasi-likelihood (PQL) estimates also were obtained for the purpose of comparison. Proposed approach was tested with a real data set also.
 The proposed approach, with the incorporation of cluster dependence, gives better estimates for both fixed effects and variance of random effects with low standard errors with compared to the estimates obtained by ignoring the cluster dependence. Therefore, the proposed approach can be used for modeling count responses from a dependent cluster set up.
 
 
 

OUP accepted manuscript

SummarySeparability is a common simplifying assumption on the covariance structure of spatiotemporal functional data. We present three tests of separability, one a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two based on quadratic forms. Our tests are based on asymptotic distributions of maximum likelihood estimators and do not require Monte Carlo simulation. The main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators, which can be used to derive many other tests. The main methodological finding is that one of the quadratic form methods, which we call a norm approach, emerges as a clear winner in terms of finite-sample performance in nearly every setting we considered. This approach focuses directly on the Frobenius distance between the spatiotemporal covariance function and its separable approximation. We demonstrate the efficacy of our methods via simulations and application to Irish wind data.

Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study

In this paper, we compare the small sample performances of Quasi Maximum Likelihood (QML) and Monte Carlo Likelihood (MCL) methods through Monte Carlo studies for several multivariate stochastic volatility models, among which we consider two new models that account for leverage effects. Our results confirm previous findings within the literature, namely, that the MCL estimator has better finite sample performance compared to the QML estimator. QML estimator's performance is closer to that of MCL estimator when the volatility processes have higher variance or when the correlations are high and/or time varying, but it performs relatively worse when leverage is introduced. Finally, we include an empirical illustration by estimating an MSV model with leverage using a trivariate data from the major European stock markets.

Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited

In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated by Gegenbauer polynomials and the ARMA structure (GARMA) with both the long-memory and time-dependent innovation variance. We establish the existence and uniqueness of second-order solutions. We also extend this family with innovations to follow GARCH and stochastic volatility (SV). Under certain regularity conditions, we give asymptotic results for the approximate maximum likelihood estimator for the GARMA-GARCH model. We discuss a Monte Carlo likelihood method for the GARMA-SV model and investigate finite sample properties via Monte Carlo experiments. Finally, we illustrate the usefulness of this approach using monthly inflation rates for France, Japan and the United States.

Recent Developments in Approximated-Likelihood Inference Methods for Latent Variable Models

In this paper we describe some developments on likelihood-based inference for latent variable models (LVMs). The latent variable approach is wide and frequently used in social sciences with the aim of knowing more about some unobservable features, such as attitudes, beliefs or abilities. The definition of LVMs is broad, and a unique definition is not possible. However, all LVMs can be considered powerful tools to take into account the dependence within complex data structure that cannot be fully explained through the observed variables. Nevertheless, despite this flexibility, they could cause some inferential problems, mainly when some independence assumptions are relaxed. A full maximum likelihood approach, although it is the most efficient estimation method statistically, is not always the most efficient computationally. In this paper we provide an overview on some existing approaches developed to solve difficult computational problems, focusing on some particular classes of LVMs. We summarize and compare the main features of three estimation methods: composite likelihood, Monte Carlo likelihood and variational approach. It is not possible to conclude which is the best estimation method; it mainly depends on the data structure (and consequently on the latent variable model used). Thus, we outline some practical guidelines that could help the reader to choose the best estimation method for the latent variable model involved.

Forecasts on neutrino mass constraints from the redshift-space two-point correlation function

We provide constraints on the accuracy with which the neutrino mass fraction, $f_{\nu}$, can be estimated when exploiting measurements of redshift-space distortions, describing in particular how the error on neutrino mass depends on three fundamental parameters of a characteristic galaxy redshift survey: density, halo bias and volume. In doing this, we make use of a series of dark matter halo catalogues extracted from the BASICC simulation. The mock data are analysed via a Markov Chain Monte Carlo likelihood analysis. We find a fitting function that well describes the dependence of the error on bias, density and volume, showing a decrease in the error as the bias and volume increase, and a decrease with density down to an almost constant value for high density values. This fitting formula allows us to produce forecasts on the precision achievable with future surveys on measurements of the neutrino mass fraction. For example, a Euclid-like spectroscopic survey should be able to measure the neutrino mass fraction with an accuracy of $\delta f_{\nu} \approx 6.7\times10^{-4}$, using redshift-space clustering once all the other cosmological parameters are kept fixed to the $\Lambda$CDM case.

Monte Carlo likelihood estimation of mixed-effects state space models with application to HIV dynamics

The statistical inference for generalized mixed-effects state space models (MESSM) are investigated when the random effects are unknown. Two filtering algorithms are designed both of which are based on mixture Kalman filter. These algorithms are particularly useful when the longitudinal measurements are sparse. The authors also propose a globally convergent algorithm for parameter estimation of MESSM which can be used to locate the initial value of parameters for local while more efficient algorithms. Simulation examples are carried out which validate the efficacy of the proposed approaches. A data set from the clinical trial is investigated and a smaller mean square error is achieved compared to the existing results in literatures.

Searching for modified gravity: scale and redshift dependent constraints from galaxy peculiar velocities

We present measurements of both scale- and time-dependent deviations from the standard gravitational field equations. These late-time modifications are introduced separately for relativistic and non-relativistic particles, by way of the parameters $G_{\rm matter}(k,z)$ and $G_{\rm light}(k,z)$ using two bins in both scale and time, with transition wavenumber $0.01$ Mpc$^{-1}$ and redshift 1. We emphasize the use of two dynamical probes to constrain this set of parameters, galaxy power spectrum multipoles and the direct peculiar velocity power spectrum, which probe fluctuations on different scales. The multipole measurements are derived from the WiggleZ and BOSS Data Release 11 CMASS galaxy redshift surveys and the velocity power spectrum is measured from the velocity sub-sample of the 6-degree Field Galaxy Survey. We combine with additional cosmological probes including baryon acoustic oscillations, Type Ia SNe, the cosmic microwave background (CMB), lensing of the CMB, and the temperature--galaxy cross-correlation. Using a Markov Chain Monte Carlo likelihood analysis, we find the inferred best-fit parameter values of $G_{\rm matter}(k,z)$ and $G_{\rm light}(k,z)$ to be consistent with the standard model at the $95\%$ confidence level. Furthermore, accounting for the Alcock-Paczynski effect, we perform joint fits for the expansion history and growth index gamma; we measure $\gamma = 0.665 \pm 0.0669$ ($68\%$ C.L) for a fixed expansion history, and $\gamma = 0.73^{+0.08}_{-0.10}$ ($68\%$ C.L) when the expansion history is allowed to deviate from $\Lambda$CDM. With a fixed expansion history the inferred value is consistent with GR at the $95\%$ C.L; alternatively, a $2\sigma$ tension is observed when the expansion history is not fixed, this tension is worsened by the combination of growth and SNe data.

Practical likelihood analysis for spatial generalized linear mixed models

We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. TheRhizoctonia root rotand theRongelapare, respectively, examples of binomial and count datasets modeled by spatial generalized linear mixed models. Our results show that the Laplace approximation provides similar estimates to Markov Chain Monte Carlo likelihood, Monte Carlo expectation maximization, and modified Laplace approximation. Some advantages of Laplace approximation include the computation of the maximized log‐likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning of algorithms and convergence analysis, commonly required by simulation‐based methods. Copyright © 2015 John Wiley & Sons, Ltd.