model choice versus model criticism ratmann et al 1 radically modifies the perception of the approximate bayesian computation abc error into a genuine parameter whereas the unification of abc representations in section 2 is immensely valuable however it requires that the data are informative about e which is not necessarily true for instance when then e e x0 e e

inference for stereological extremes in the production of clean steels the occurrence of imperfections so called inclusions is unavoidable the strength of a clean steel block is largely dependent on the size of the largest imperfection that it contains so inference on extreme inclusion size forms an important part of quality control sampling is generally done by measuring imperfections on planar slices leading to an extreme value version of a standard stereological problem how to make inference on large inclusions using only the sliced observations under the assumption that inclusions are spherical this problem has been tackled previously using a combination of extreme value models stereological calculations a bayesian hierarchical model and standard markov chain monte carlo mcmc techniques our objectives in this article are twofold 1 to assess the robustness of such inferences with respect to the assumption of spherical inclusions and 2 to develop an inference procedure that is valid for nonspherical inclusions we inv

asymptotic behaviour of the posterior distribution in overfitted mixture models abstract summary we study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components a situation which is commonly referred to as an overfitted mixture we prove in particular that quite generally the posterior distribution has a stable and interesting behaviour since it tends to empty the extra components this stability is achieved under some restriction on the prior which can be used as a guideline for choosing the prior some simulations are presented to illustrate this behaviour

relevant statistics for bayesian model choice the choice of the summary statistics that are used in bayesian inference and in particular in approximate bayesian computation algorithms has bearings on the validation of the resulting inference those statistics are nonetheless customarily used in approximate bayesian computation algorithms without consistency checks we derive necessary and sufficient conditions on summary statistics for the corresponding bayes factor to be convergent namely to select the true model asymptotically those conditions which amount to the expectations of the summary statistics differing asymptotically under the two models are quite natural and can be exploited in approximate bayesian computation settings to infer whether or not a choice of summary statistics is appropriate via a monte carlo validation

examples of summing integral and nuclear operators on the space c 0 1 x with values in c0 abstract we give necessary and sufficient conditions that some operators on the space c 0 1 x with values in c 0 be as in the title related questions are investigated

alive smc2 bayesian model selection for low count time series models with intractable likelihoods in this article we present a new method for performing bayesian parameter inference and model choice for low count time series models with intractable likelihoods the method involves incorporating an alive particle filter within a sequential monte carlo smc algorithm to create a novel exact approximate algorithm which we refer to as alive smc2 the advantages of this approach over competing methods are that it is naturally adaptive it does not involve between model proposals required in reversible jump markov chain monte carlo and does not rely on potentially rough approximations the algorithm is demonstrated on markov process and integer autoregressive moving average models applied to real biological datasets of hospital acquired pathogen incidence animal health time series and the cumulative number of prion disease cases in mule deer

an interpretation of partial least squares abstract univariate partial least squares pls is a method of modeling relationships between a y variable and other explanatory variables it may be used with any number of explanatory variables even far more than the number of observations a simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations its relationship to multivariate pls in which there are two or more y variables is examined and an example is given in which it is compared by simulation with other methods of forming prediction equations with univariate pls linear combinations of the explanatory variables are formed sequentially and related to y by ordinary least squares regression it is shown that these linear combinations here called components may be viewed as weighted averages of predictors where each predictor holds the residual information in an explanatory variable that is not contained in earlier components and the quantity to be predicted is the vecto

estimation of parameters for macroparasite population evolution using approximate bayesian computation we estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate bayesian computation abc the immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted with very limited data process rates are inferred reasonably precisely modeling involves a three variable markov process for which the observed data likelihood is computationally intractable abc methods are particularly useful when the likelihood is analytically or computationally intractable the abc algorithm we present is based on sequential monte carlo is adaptive in nature and overcomes some drawbacks of previous approaches to abc the algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the markov process model for experimental data the fitted model explains the observed extra binomial variation in terms of a zero one immunity variable which has a short lived presence in the host

boosting bayesian parameter inference of nonlinear stochastic differential equation models by hamiltonian scale separation parameter inference is a fundamental problem in data driven modeling given observed data that is believed to be a realization of some parameterized model the aim is to find parameter values that are able to explain the observed data in many situations the dominant sources of uncertainty must be included into the model for making reliable predictions this naturally leads to stochastic models stochastic models render parameter inference much harder as the aim then is to find a distribution of likely parameter values in bayesian statistics which is a consistent framework for data driven learning this so called posterior distribution can be used to make probabilistic predictions we propose a novel exact and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series the algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer where the measurements are mapped on heavier beads compared to those of the simulated data to arrive at distribution samples we employ a hamiltonian monte carlo approach combined with a multiple time scale integration a separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large furthermore at least for one dimensional problems we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically our approach is applicable to a wide range of inference problems and is highly parallelizable

convergence of regression adjusted approximate bayesian computation we present asymptotic results for the regression adjusted version of approximate bayesian computation introduced by beaumont et al 2002 we show that for an appropriate choice of the bandwidth regression adjustment will lead to a posterior that asymptotically correctly quantifies uncertainty furthermore for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases this compares favourably to results for standard approximate bayesian computation where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth one for which the acceptance probability tends to zero and hence for which monte carlo error will dominate

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

model misspecification in approximate bayesian computation consequences and diagnostics we analyze the behavior of approximate bayesian computation abc when the model generating the simulated data differs from the actual data generating process i e when the data simulator in abc is misspecified we demonstrate both theoretically and in simple but practically relevant examples that when the model is misspecified different versions of abc can yield substantially different results our theoretical results demonstrate that even though the model is misspecified under regularity conditions the accept reject abc approach concentrates posterior mass on an appropriately defined pseudo true parameter value however under model misspecification the abc posterior does not yield credible sets with valid frequentist coverage and has non standard asymptotic behavior in addition we examine the theoretical behavior of the popular local regression adjustment to abc under model misspecification and demonstrate that this approach concentrates posterior mass on a completely different pseudo true value than accept reject abc using our theoretical results we suggest two approaches to diagnose model misspecification in abc all theoretical results and diagnostics are illustrated in a simple running example

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

generalized quadratic receivers for orthogonal signals over the gaussian channel with unknown phase fading the orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated pilot tone component which can be used for channel measurement starting from this point of view the quadratic receiver for orthogonal signals over the gaussian channel with unknown phase fading has been shown to be equivalent to a detector estimator receiver the estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal this channel estimate then forms a partially coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal this paper exploits this detector estimator structure of the quadratic receiver and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals the generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver a theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol by symbol receiver for uncoded orthogonal signals over the gaussian channel with unknown phase fading the theory shows that the structure provides a unified and systematic approach to the design of coherent symbol by symbol receivers and shows that the conventional carrier loop type receivers are ad hoc

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

approximate bayesian computation with the wasserstein distance a growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions approximate bayesian computation has become a popular approach to overcome this issue in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values we propose to avoid the use of summaries and the ensuing loss of information by instead using the wasserstein distance between the empirical distributions of the observed and synthetic data this generalizes the well known approach of using order statistics within approximate bayesian computation to arbitrary dimensions we describe how recently developed approximations of the wasserstein distance allow the method to scale to realistic data sizes and we propose a new distance based on the hilbert space filling curve we provide a theoretical study of the method proposed describing consistency as the threshold goes to 0 while the observations are kept fixed and concentration properties as the number of observations grows various extensions to time series data are discussed the approach is illustrated on various examples including univariate and multivariate g and k distributions a toggle switch model from systems biology a queuing model and a levy driven stochastic volatility model

a viterbi type algorithm for efficient estimation of m psk sequences over the gaussian channel with unknown carrier phase a viterbi type algorithm for the efficient estimation of a convolutionally trellis coded or uncoded m psk sequence over the gaussian channel with unknown carrier phase is presented it performs coherent detection of m psk sequences with no explicit recovery of coherent references the metric computations involve only linear operations theoretical and simulated performance results are presented for various carrier phase processes the algorithm is called the suboptimum ml estimator smle its ber in the presence of a time invariant carrier phase is obtained analytically the simulation results for the ber with time invariant as well as time varying carrier phase processes allow a comparison of the performance of the smle with other sequence estimation algorithms and enable the applicability of the smle to burst mode tdma communications to be ascertained

2 absolutely summing operators on the space c t x abstract we give for some banach spaces x and y examples of linear and continuous operators u c t x y such that u as2 x y for each c t and u c t as2 x y is a 2 absolutely summing operator with respect to the 2 absolute norm on as2 x y but u is not 2 absolutely summing

maximum likelihood digital data sequence estimation over the gaussian channel with unknown carrier phase we consider the problem of simultaneous ml estimation of data and carrier phase from a linear suppressed carrier modulated signal received in the presence of additive white gaussian noise the ml detector of the data sequence is derived and its error probability performance is analyzed the result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length a suboptimum decision aided subsequence by subsequence detector whose complexity does not increase exponentially with sequence length is proposed and its performance is analyzed

approximate bayesian computation a nonparametric perspective approximate bayesian computation is a family of likelihood free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism in a nutshell approximate bayesian computation proceeds by computing summary statistics sobs from the data and simulating summary statistics for different values of the parameter the posterior distribution is then approximated by an estimator of the conditional density g sobs in this paper we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment additionally we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling we find that they can achieve better performance

operator valued operators that are associated to vector valued operators this paper is motivated by a long standing conjecture of dinculeanu from 1967 let x and y be banach spaces and let be a compact hausdorff space dinculeanu conjectured that there exist operators s l c l x y s l c l x y which are not associated to any u l c x y u l c x y we study this existence problem systematically on three possible levels of generality the classical case c x c x of continuous vector valued functions p continuous vector valued functions and tensor products on each level we establish necessary and sufficient conditions for an l x y l x y valued operator to be associated to a y valued operator among others we see that examples proving dinculeanu s conjecture come out on the all three levels of generality

integral mappings between banach spaces abstract we consider the classes of grothendieck integral g integral and pietsch integral p integral linear and multilinear operators see definitions below and we prove that a multilinear operator between banach spaces is g integral resp p integral if and only if its linearization is g integral resp p integral on the injective tensor product of the spaces together with some related results concerning certain canonically associated linear operators as an application we give a new proof of a result on the radon nikodym property of the dual of the injective tensor product of banach spaces moreover we give a simple proof of a characterization of the g integral operators on c k x spaces and we also give a partial characterization of p integral operators on c k x spaces

estimating ocean circulation an mcmc approach with approximated likelihoods via the bernoulli factory we provide a bayesian analysis of ocean circulation based on data collected in the south atlantic ocean the analysis incorporates a reaction diffusion partial differential equation that is not solvable in closed form this leads to an intractable likelihood function we describe a novel markov chain monte carlo approach that does not require a likelihood evaluation rather we use unbiased estimates of the likelihood and a bernoulli factory to decide whether or not proposed states are accepted the variates required to estimate the likelihood function are obtained via a feynman kac representation this lifts the common restriction of selecting a regular grid for the physical model and eliminates the need for data preprocessing we implement our approach using the parallel graphic processing unit gpu computing environment

variance bounding and geometric ergodicity of markov chain monte carlo kernels for approximate bayesian computation approximate bayesian computation has emerged as a standard computational tool when dealing with intractable likelihood functions in bayesian inference we show that many common markov chain monte carlo kernels used to facilitate inference in this setting can fail to be variance bounding and hence geometrically ergodic which can have consequences for the reliability of estimates in practice this phenomenon is typically independent of the choice of tolerance in the approximation we prove that a recently introduced markov kernel can inherit the properties of variance bounding and geometric ergodicity from its intractable metropolis hastings counterpart under reasonably weak conditions we show that the computational cost of this alternative kernel is bounded whenever the prior is proper and present indicative results for an example where spectral gaps and asymptotic variances can be computed as well as an example involving inference for a partially and discretely observed time homogeneous pure jump markov process we also supply two general theorems one providing a simple sufficient condition for lack of variance bounding for reversible kernels and the other providing a positive result concerning inheritance of variance bounding and geometric ergodicity for mixtures of reversible kernels

asymptotic properties of approximate bayesian computation approximate bayesian computation abc is becoming an accepted tool for statistical analysis in models with intractable likelihoods with the initial focus being primarily on the practical import of abc exploration of its formal statistical properties has begun to attract more attention in this paper we consider the asymptotic behavior of the posterior obtained from abc and the ensuing posterior mean we give general results on i the rate of concentration of the abc posterior on sets containing the true parameter vector ii the limiting shape of the posterior and iii the asymptotic distribution of the abc posterior mean these results hold under given rates for the tolerance used within abc mild regularity conditions on the summary statistics and a condition linked to identification of the true parameters using simple illustrative examples that have featured in the literature we demonstrate that the required identification condition is far from guaranteed the implications of the theoretical results for practitioners of abc are also highlighted

bayesian monte carlo testing with one dimensional measures of evidence abstract bayesian hypothesis testing procedures are constructed by means of test statistics which are functions of the posterior distribution usually the whole sample vector is selected to form the sufficient empirical part of the posterior distribution but in certain problems one may prefer to use well established one dimensional sufficient statistics in place of the sample vector this paper introduces a bayesian monte carlo procedure specially designed for such cases it is shown that the performance of this new approach is arbitrarily close to the exact bayesian test in addition for arbitrary desired precisions we develop a theoretical rule of thumb for choosing the minimum number m 0 of monte carlo simulations surprisingly m 0 does not depend on the shape of loss cost functions when those are used to compound the test statistic the method is illustrated for testing mean vectors in high dimension and for detecting spatial clusters of diseases in aggregated maps

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

estimation and accuracy after model selection classical statistical theory ignores model selection in assessing estimation accuracy here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account the methodology involves bagging also known as bootstrap smoothing to tame the erratic discontinuities of selection based estimators a useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators two examples nonparametric and parametric are carried through in detail a regression model where the choice of degree linear quadratic cubic is determined by the cp criterion and a lasso based estimation problem

chernoff bounds on pairwise error probabilities of space time codes we derive chernoff bounds on pairwise error probabilities of coherent and noncoherent space time signaling schemes first general chernoff bound expressions are derived for a correlated ricean fading channel and correlated additive gaussian noise then we specialize the obtained results to the cases of space time separable noise white noise and uncorrelated fading we derive approximate chernoff bounds for high and low signal to noise ratios snrs and propose optimal signaling schemes we also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space time codes

on α nuclear operators with applications to vector valued function spaces abstract let x be a banach space and let y be a closed subspace of a banach space z let be a tensor norm our main result is as follows assume that x or z has the approximation property if there is a bounded linear extension operator from y to z then any bounded linear operator t x y is nuclear whenever t is nuclear from x to z using this result we characterize the space c p x respectively uc p x of continuous functions from a compact hausdorff space into a banach space x whose range is p compact respectively unconditionally p compact

on the asymptotic efficiency of approximate bayesian computation estimators many statistical applications involve models for which it is difficult to evaluate the likelihood but from which it is relatively easy to sample approximate bayesian computation is a likelihood free method for implementing bayesian inference in such cases we present results on the asymptotic variance of estimators obtained using approximate bayesian computation in a large data limit our key assumption is that the data is summarized by a fixed dimensional summary statistic that obeys a central limit theorem we prove asymptotic normality of the mean of the approximate bayesian computation posterior this result also shows that in terms of asymptotic variance we should use a summary statistic that is the same dimension as the parameter vector p and that any summary statistic of higher dimension can be reduced through a linear transformation to dimension p in a way that can only reduce the asymptotic variance of the posterior mean we look at how the monte carlo error of an importance sampling algorithm that samples from the approximate bayesian computation posterior affects the accuracy of estimators we give conditions on the importance sampling proposal distribution such that the variance of the estimator will be the same order as that of the maximum likelihood estimator based on the summary statistics used this suggests an iterative importance sampling algorithm which we evaluate empirically on a stochastic volatility model

monte carlo methods of inference for implicit statistical models a prescribed statistical model is a parametric specification of the distribution of a random vector whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism this paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable the kernel method of probability density estimation is advocated for estimating a log likelihood from simulations of such a model the development and testing of an algorithm for maximizing this estimated log likelihood function is described an illustrative example involving a stochastic model for quantal response assays is given possible applications of the maximization algorithm to ad hoc methods of parameter estimation are noted briefly and illustrated by an example involving a model for the spatial pattern of displaced amacrine cells in the retina of a rabbit

binary orthogonal signaling over the gaussian channel with unknown phase fading new results and interpretations the problem of binary orthogonal signaling over a gaussian noise channel with unknown phase fading is considered by viewing the problem in a rotated coordinate system the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement for data detection the optimum matched filter envelope detector is shown to be identical to a novel detector estimator receiver in which the detector performs partially coherent detection using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot tone component of the orthogonal signal structure this detector estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver it also leads to the development of new approaches for analyzing the error probability of the receiver an exponential chernoff upper bound is obtained for the rician channel

the bartle dunford schwartz and the dinculeanu singer theorems revisited abstract let x and y be banach spaces and let be a compact hausdorff space by the classical bartle dunford schwartz theorem any operator s l c y admits an integral representation with respect to a y valued measure by the dinculeanu singer theorem each operator u l c x y admits an integral representation with respect to an l x y valued measure we establish an integral representation for any operator s l c l x y with respect to an l x y valued measure this far reaching extension of the bartle dunford schwartz theorem serves as a departure point for a general integral representation theory developed in the present paper in particular it is an efficient tool that enables us to give an alternative simple proof to the dinculeanu singer theorem the latter theorem is proved in a more general context of x valued continuous functions with p compact range among others useful formulas which connect different vector measures are deduced

a note on multiple imputation under complex sampling summary multiple imputation is popular for handling item nonresponse in survey sampling current multiple imputation techniques with complex survey data assume that the sampling design is ignorable in this paper we propose a new multiple imputation procedure for parametric inference without this assumption instead of using the sample data likelihood we use the sampling distribution of the pseudo maximum likelihood estimator to derive the posterior distribution of the parameters the asymptotic properties of the proposed method are investigated a simulation study confirms that the new procedure provides unbiased point estimation and valid confidence intervals with correct coverage properties whether or not the sampling design is ignorable

approximate bayesian computation by subset simulation a new approximate bayesian computation abc algorithm for bayesian updating of model parameters is proposed in this paper which combines the abc principles with the technique of subset simulation for efficient rare event simulation first developed in s k au and j l beck probabilistic engrg mech 16 2001 pp 263 277 it has been named abc subsim the idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space the efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real world applications of abc we show that the proposed algorithm outperforms other recent sequential abc algorithms in terms of computational efficiency while achieving the same or better measure of accuracy in the posterior distribution we also show that abc subsim readily provides an estimate of the evidence marginal likelihood for posterior model class assessment as a by product

frequentist accuracy of bayesian estimates in the absence of relevant prior experience popular bayesian estimation techniques usually begin with some form of uninformative prior distribution intended to have minimal inferential influence bayes rule will still produce nice looking estimates and credible intervals but these lack the logical force attached to experience based priors and require further justification this paper concerns the frequentist assessment of bayes estimates a simple formula is shown to give the frequentist standard deviation of a bayesian point estimate the same simulations required for the point estimate also produce the standard deviation exponential family models make the calculations particularly simple and bring in a connection to the parametric bootstrap

bayesian analysis of accumulated damage models in lumber reliability abstractwood products that are subjected to sustained stress over a period of long duration may weaken and this effect must be considered in models for the long term reliability of lumber the dam

adaptive approximate bayesian computation sequential techniques can be adapted to the abc algorithm to enhance its efficiency for instance when sisson et al 2007 introduced the abc prc algorithm the goal was to improve upon existing abc mcmc algorithms marjoram et al 2003 while the abc prc method is based upon the theoretical developments of del moral et al 2006 the application to the setting of approximate bayesian computation induces a bias in the approximation to the posterior distribution of interest as we demonstrate in this paper via both theoretical reasoning and experimental results it is however possible to devise an alternative version based on genuine importance sampling arguments that we call abc pmc in connection with the population monte carlo method introduced in cappe et al 2004 furthermore the abc pmc algorithm is simpler than the abc prc algorithm in that it does not require any backward transition kernel and proposes an automatic scaling of the forward kernel in this paper we demonstrate the applicability of abc pmc and compare its performances with abc prc

generalized quadratic receivers for unitary space time modulation over rayleigh fading channels we propose the generalized quadratic receivers gqrs for unitary space time modulation over flat rayleigh fading channels the gqrs realize the performance improvement potential known to be approximately 2 4 db between the quadratic receiver qr and the coherent receiver cr by performing channel estimation without the help of additional training signals that consume additional bandwidth they are designed for various unitary space time constellations ustc in which signal matrices may or may not contain explicit inherent training blocks and may be orthogonal or nonorthogonal to one another as the channel memory span exploited for channel estimation increases the error probability of the gqrs reduces from that of the qr to that of the cr the gqrs work well for both slow and fast fading channels and the performance improvement increases as the channel fade rate decreases for a class of ustc with the orthogonal design structure the gqr is simplified to a form whose complexity can be less than the complexity of the qr or even that of the simplified form of the qr

constructing summary statistics for approximate bayesian computation semi automatic approximate bayesian computation summary many modern statistical applications involve inference for complex stochastic models where it is easy to simulate from the models but impossible to calculate likelihoods approximate bayesian computation abc is a method of inference for such models it replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values and comparing summary statistics of the simulated data with summary statistics of the observed data here we show how to construct appropriate summary statistics for abc in a semi automatic manner we aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible theoretical results show that optimal summary statistics are the posterior means of the parameters although these cannot be calculated analytically we use an extra stage of simulation to estimate how the posterior means vary as a function of the data and we then use these estimates of our summary statistics within abc empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate abc analyses than the ad hoc choices of summary statistics that have been proposed in the literature we also demonstrate advantages over two alternative methods of simulation based inference

maximum likelihood carrier phase recovery for coherently orthogonal cpfsk signals ml estimation of carrier phase for coherently orthogonal continuous phase frequency shift keying cocpfsk signals is considered although the estimator in general is nonimplementable its high and low signal to noise ratio approximations both lead to linear readily implementable receiver structures the high snr approximation yields a da receiver whereas the low snr approximation yields an nda receiver the performance of both receivers in term of bit error probability is analyzed the existence of an unmodulated component in the sufficient statistical representation of a cocpfsk signal is pointed out and it is shown how this component enters directly into maximum like carrier recovery this leads to interpretation of the nda receiver as a generalization of the conventional matched filter envelope detector receiver the insights gained here are useful to the problem of ml carrier recovery for viterbi decoding of continuous phase modulation signals

estimating functions in indirect inference summary there are models for which the evaluation of the likelihood is infeasible in practice for these models the metropolis hastings acceptance probability cannot be easily computed this is the case for instance when only departure times from a g g 1 queue are observed and inference on the arrival and service distributions are required indirect inference is a method to estimate a parameter in models whose likelihood function does not have an analytical closed form but from which random samples can be drawn for fixed values of first an auxiliary model is chosen whose parameter can be directly estimated next the parameters in the auxiliary model are estimated for the original data leading to an estimate the parameter is also estimated by using several sampled data sets simulated from the original model for different values of the original parameter finally the parameter which leads to the best match to is chosen as the indirect inference estimate we analyse which properties an auxiliary model should have to give satisfactory indirect inference we look at the situation where the data are summarized in a vector statistic t and the auxiliary model is chosen so that inference on is drawn from t only under appropriate assumptions the asymptotic covariance matrix of the indirect estimators is proportional to the asymptotic covariance matrix of t and componentwise inversely proportional to the square of the derivative with respect to of the expected value of t we discuss how these results can be used in selecting good estimating functions we apply our findings to the queuing problem

bayesian computation via empirical likelihood approximate bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable however the well established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate bayesian computation parameters summary statistics distance tolerance while being convergent in the number of observations furthermore bypassing model simulations may lead to significant time savings in complex models for instance those found in population genetics the bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size the method is illustrated using several examples including estimation of standard distributions time series and population genetics models

p summing operators on injective tensor products of spaces the final version of this paper appears in proceedings of the royal society of edinburgh section b 120a 1992 283 296 print

a new pod based approximate bayesian computation method to identify parameters for formed ahss abstract forming has significant influence on the material properties which are critical for the accuracy of simulations however at present most of the existing works took the uniform raw mechanical properties of plate as the one after forming which inevitably resulted in the inaccuracy simulation in this study in order to figure out the material properties of formed dp590 comprehensive experiments based on micro indentation tests and digital image correlation dic are presented the versatile approximate bayesian computation abc inverse method is utilized to identify material parameters due to its difficulty of selection of summary statistics a new flexible and feasible proper orthogonal decomposition pod based abc framework is proposed the pod can project the high dimensional observations into a much lower dimensional coefficient vector thus we can make use of comparisons between simulated and observed coefficient vector of pod to determine the material parameters with the pod the abc can circumvent the complex selection of summary statistics in the computational process the neural network nn is used to construct the nonlinear connection between material properties and its pod coefficient vector thus the coefficient vector with given material properties can be determined efficiently with the well constructed nn instead of time consuming finite element fe simulations

component wise approximate bayesian computation via gibbs like steps approximate bayesian computation methods are useful for generative models with intractable likelihoods these methods are however sensitive to the dimension of the parameter space requiring exponentially increasing resources as this dimension grows to tackle this difficulty we explore a gibbs version of the abc approach that runs component wise approximate bayesian computation steps aimed at the corresponding conditional posterior distributions and based on summary statistics of reduced dimensions while lacking the standard justifications for the gibbs sampler the resulting markov chain is shown to converge in distribution under some partial independence conditions the associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution experiments also demonstrate the gain in efficiency brought by the gibbs version over the standard solution

convergence rates of posterior distributions for non i i d observations we consider the asymptotic behavior of posterior distributions and bayes estimators based on observations which are required to be neither independent nor identically distributed we give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion we then specialize our results to independent nonidentically distributed observations markov processes stationary gaussian time series and the white noise model we apply our general results to several examples of infinite dimensional statistical models including nonparametric regression with normal errors binary regression poisson regression an interval censoring model whittle estimation of the spectral density of a time series and a nonlinear autoregressive model