a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

getting it right joint distribution tests of posterior simulators analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments this article develops simple tests of posterior simulators that detect both kinds of errors and uses them to detect and correct errors in two previously published articles the tests exploit the fact that a bayesian model specifies the joint distribution of observables data and unobservables parameters there are two joint distribution simulators the marginal conditional simulator draws unobservables from the prior and then observables conditional on unobservables the successive conditional simulator alternates between the posterior simulator and an observables simulator formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator

generalized quasi variational inequalities for fuzzy mappings abstract we consider the generalized quasi variation inequalities for fuzsy mappings several existence results are derived and potential applications are given

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

bayesian antisparse coding sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing conversely enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as robust encoding in digital communications antisparse regularization can be naturally expressed through an ell infty norm penalty this paper derives a probabilistic formulation of such representations a new probability distribution referred to as the democratic prior is first introduced its main properties as well as three random variate generators for this distribution are derived then this probability distribution is used as a prior to promote antisparsity in a gaussian linear model yielding a fully bayesian formulation of antisparse coding two markov chain monte carlo algorithms are proposed to generate samples according to the posterior distribution the first one is a standard gibbs sampler the second one uses metropolis hastings moves that exploit the proximity mapping of the log posterior distribution these samples are used to approximate maximum a posteriori and minimum mean square error estimators of both parameters and hyperparameters simulations on synthetic data illustrate the performances of the two proposed samplers for both complete and over complete dictionaries all results are compared to the recent deterministic variational fitra algorithm

bayesian reduced rank regression in econometrics abstract the reduced rank regression model arises repeatedly in theoretical and applied econometrics to date the only general treatment of this model have been frequentist this paper develops general methods for bayesian inference with noninformative reference priors in this model based on a markov chain sampling algorithm and procedures for obtaining predictive odds ratios for regression models with different ranks these methods are used to obtain evidence on the number of factors in a capital asset pricing model

the generalized quasi variational inequality problem over non compact sets abstract in this note we shall prove new existence results for the generalized quasi variational inequality problem which includes as particular cases all the existing generalizations of the classical variational inequality problem

a quadratic weight selection algorithm a new algorithm is presented which determines a positive semi definite state weighting matrix in the linear quadratic optimal control design problem the algorithm chooses the weighting matrix by attempting to place dosed loop eigenvalues and eigenvectors near desired locations using optimal feedback gains a simplified flight control design example is used to illustrate the algorithm s capabilities

corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146 corrigendum to bayesian reduced rank regression in econometrics j econometrics 75 1996 121 146

a flexible prior distribution for markov switching autoregressions with student t errors this paper proposes an empirical bayes approach for markov switching autoregressions that can constrain some of the state dependent parameters regression coefficients and error variances to be approximately equal across regimes by flexibly reducing the dimension of the parameter space this can help to ensure regime separation and to detect the markov switching nature of the data the permutation sampler with a hierarchical prior is used for choosing the prior moments the identification constraint and the parameters governing prior state dependence the empirical relevance of the methodology is illustrated with an application to quarterly and monthly real interest rate data

the hessian method highly efficient simulation smoothing in a nutshell abstract i introduce the hessian highly efficient simulation smoothing in a nutshell method for numerically efficient simulation smoothing in state space models with univariate states given a vector of parameters the vector of states 1 n is gaussian and the observed vector y y 1 y n need not be i describe a procedure to construct a close approximation q y to the target density p y it requires code to compute five derivatives of log p y t t with respect to t t 1 n and is not otherwise model specific since q y is proper fully normalised and simulable it can be used as an importance density for importance sampling is or as a proposal density for markov chain monte carlo mcmc hessian is an acronym but it also refers to the sparse hessian matrix of log p y with respect to the hessian method is based on sparse matrix operations rather than the kalman filter i construct q y and a related approximation q y of p y for two stochastic volatility models two stochastic count models and a stochastic duration model i illustrate their use for numerical approximation of likelihood function values and marginal likelihoods using is and for posterior inference using is and mcmc compared with other simulation smoothing methods the hessian method is highly numerically efficient in an is application featuring a student s t stochastic volatility model and n 8851 daily log returns the efficiency of is for numerical approximation of the elements of the posterior mean e y is between 80 and 100

bayesian inference in a correlated random coefficients model modeling causal effect heterogeneity with an application to heterogeneous returns to schooling abstract we consider the problem of causal effect heterogeneity from a bayesian point of view this is accomplished by introducing a three equation system similar in spirit to the work of heckman and vytlacil 1998 describing the joint determination of a scalar outcome an endogenous treatment variable and an individual specific causal return to that treatment we describe a bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population the object which has been the focus of most previous work parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed combining data sets from high school and beyond hsb and the 1980 census we illustrate our methods in practice and investigate heterogeneity in returns to education our analysis decomposes the impact of key hsb covariates on log wages into three parts a direct effect and two separate indirect effects through educational attainment and returns to education our results strongly suggest that the quantity of schooling attained is determined at least in part by the individual s own return to education specifically a one percentage point increase in the return to schooling parameter is associated with the receipt of approximately 0 14 more years of schooling furthermore when we control for variation in returns to education across individuals we find no difference in predicted schooling levels for men and women however women are predicted to attain approximately 1 4 of a year more schooling than men on average as a result of higher rates of return to investments in education

bayesian phylogenetic inference using a combinatorial sequential monte carlo method the application of bayesian methods to large scale phylogenetics problems is increasingly limited by computational issues motivating the development of methods that can complement existing markov chain monte carlo mcmc schemes sequential monte carlo smc methods are approximate inference algorithms that have become very popular for time series models such methods have been recently developed to address phylogenetic inference problems but currently available techniques are only applicable to a restricted class of phylogenetic tree models compared to mcmc in this article we propose an original combinatorial smc csmc method to approximate posterior phylogenetic tree distributions which is applicable to a general class of models and can be easily combined with mcmc to infer evolutionary parameters our method only relies on the existence of a flexible partially ordered set structure and is more generally applicable to sampling problems on combinatorial spaces we demonstrate that the proposed csmc

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

a general theorem of complementarity for the implicit gqvi problem abstract in this paper we prove a basic theory of complementarity for the implicit generalized quasi variational inequality problem our result widely extends many known results established in the literature an application to the quasi equilibrium problem is also given

design of linear quadratic regulators with assigned eigenstructure a recursive design procedure is presented which assigns the closed loop eigenstructure in linear quadratic regulators at each stage the required solution for the steady state riccati matrix which shifts a pole or pole pair to specified values is obtained for pole pair placement a free parameter in the solution permits selection of closed loop eigenvectors the interactive design procedure is summarized and illustrated by an example

some properties of optimal regulators and their applications some properties of linear optimal regulators are discussed first some fundamental relations on the bound of the overshoot of the output are derived then an explicit description of a solution set of linear optimal regulator problems for a linear system and all possible quadratic cost functions is derived as an application of these properties a new design method for a feedback law is proposed which takes into account the requirement on the output overshoot

on successive pole assignment by linear quadratic optimal feedbacks abstract this paper studies a method of shifting poles of linear constant systems via lq optimal feedback by making use of a solution to the so called inverse regulator problem this method enables us to shift poles successively by pairs while maintaining the well known advantages of lq regulators polynomial fractional representation is effectively used both to characterize the maximal pole assignable area which clarifies the theoretical bound of the lq optimal pole shifting and to derive an algorithm a numerical example is given to illustrate the results

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

optimization and pole placement for a single input controllable system given the system xdot ax bu and the cost function j dt relations are to be determined among the open loop characteristic polynomial the closed loop characteristic polynomial and the matrices a and q those relations take a simple form if the system is in the standard controllable form in this case the optimal control law can be found easily without solving the matrix riccati equation while the minimum value of the cost function if it is required can be determined by solving a matrix equation of the form c t x xc d

partial pole placement by lq regulators an inverse problem approach this paper gives a necessary and sufficient condition under which a state feedback control law places part of the closed loop poles exactly at specified points and at the same time is linear quadratic optimal for some quadratic weightings this is made possible by means of a solution to the inverse problem of optimal control a design example is given to illustrate the result