a method for improved distribution concentration in the time frequency analysis of multicomponent signals using the l wigner distribution the energy location in the cohen class of time frequency distributions is analyzed if the instantaneous frequency is linear then only the wigner distribution produces the ideal energy concentration the scaled version of the wigner distribution l wigner distribution is used to improve the time frequency representation of signals with nonlinear instantaneous frequencies in the case of multicomponent signals the cross terms appearing in the wigner distribution and in the l wigner distribution can be easily removed or reduced in a computationally very efficient way the theory is illustrated on the numerical examples with multicomponent noisy signals

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

a comparison of the existence of cross terms in the wigner distribution and the squared magnitude of the wavelet transform and the short time fourier transform it is shown that cross terms comparable to those found in the wigner distribution wd exist for the energy distributions of the wavelet transform wt and the short time fourier transform stft the geometry of the cross terms is described by deriving mathematical expressions for the energy distributions of the stft and the wt of a multicomponent signal from those mathematical expressions it is inferred that the stft and the wt cross terms 1 occur at the intersection of the respective transforms of the two signals under consideration whereas the wd cross terms occur at mid time frequency of the two signals 2 are oscillatory in nature as are the wd cross terms and are modulated by a cosine whose argument is a function of the difference in center times and center frequencies of the signals under consideration and 3 can have a maximum amplitude as large as twice the product of the magnitude of the transforms of the two signals in question like wd cross terms it is shown that the presence of these cross terms could lead to problems in analyzing a multicomponent signal the consequences of this effect with respect to speech applications are discussed

absorbing state phase transitions with quenched disorder quenched disorder in the sense of the harris criterion is generally a relevant perturbation at an absorbing state phase transition point here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class for strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point which is isomorph with the fixed point of random quantum ising systems in this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one dimensional systems the renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found for weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder whereas the dynamical correlations are compatible with two possible scenarios either they follow a power law decay with a varying dynamical exponent like in random quantum systems or the dynamical correlations are logarithmically slow even for a weak disorder for models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

structure of the liquid vapor interface using a gaussian column model with a variable interaction range abstract we study properties of the liquid vapor interface using an exactly solvable model consisting of a one dimensional array of columns whose interaction is of variable range and quadratic in the height difference between columns in the limit of infinitely long ranged intercolumn interactions the classical mean field description of the interface is exact there is an intrinsic interface profile of finite width and all pair correlations are short ranged however for realistic short ranged interactions the model is equivalent to the capillary wave model of buff lovett and stillinger here we find long ranged pair correlations parallel to the interface of precisely the form deduced by wertheim the interface profile now depends on system size and strength of an external gravitational field the interface width diverges as the field tends to zero in an infinite system explicit expressions for the pair correlation are inverted to yield the direct correlation function in the interfacial region

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

statistical methods for eliciting probability distributions elicitation is a key task for subjectivist bayesians although skeptics hold that elicitation cannot or perhaps should not be done in practice it brings statisticians closer to their clients and subject matter expert colleagues this article reviews the state of the art reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively and how they respond to questions about that information in a discussion of the elicitation process the first issue to address is what it means for an elicitation to be successful that is what criteria should be used our answer is that a successful elicitation faithfully represents the opinion of the person being elicited it is not necessarily true in some objectivistic sense and cannot be judged in that way we see that elicitation as simply part of the process of statistical modeling indeed in a hierarchical model at which point the likelihood ends and the pr

modeling tangential vector fields on a sphere abstractphysical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences these naturally occurring vector fields are often subject to physical constraints such as being curl free or divergence free we start with constructing parametric models for curl free and divergence free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere using the helmholtz hodge decomposition we then construct a class of simple but flexible parametric models for general tangential vector fields which are represented as a sum of a curl free and a divergence free components we propose a likelihood based parameter estimation procedure and show that fast computation is possible even for large data sets when the observations are on a regular latitude longitude grid characteristics and practical utility of the proposed methodology are illustrated th

directed percolation with a wall or edge we examine the effects of introducing a wall or edge into a directed percolation process scaling ansatze are presented for the density and survival probability of a cluster in these geometries and we make the connection to surface critical phenomena and field theory the results of previous numerical work for a wall can thus be interpreted in terms of surface exponents satisfying scaling relations generalizing those for ordinary directed percolation new exponents for edge directed percolation are also introduced they are calculated in mean field theory and measured numerically in 2c 1 dimensions

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

evaluating probabilities asymmetric scoring rules proper scoring rules are over evaluation measures that reward accurate probabilities specific rules encountered in the literature and used in practice are invariably symmetric in the sense that the expected score for a perfectly calibrated probability assessor or model generating probabilities is minimized at a probability of one half a family of asymmetric scoring rules that provide better measures of the degree of skill inherent in the probabilities and render scores that are more comparable in different situations is developed here one member of this family a quadratic asymmetric rule is applied to evaluate an extensive set of precipitation probability forecasts from the u s national weather service connections to previous characterizations of proper scoring rules are investigated and some relevant issues pertaining to the design of specific asymmetric rules for particular inferential and decision making problems are discussed briefly

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

low density series expansions for directed percolation iv temporal disorder we introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex t x where t is the time and x is the spatial coordinate is independent of x but depends on t using a very efficient algorithm we calculate low density series for bond percolation on the directed square lattice analysis of the series yields estimates for the critical point pc and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased

general notions of statistical depth function statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data here we introduce several general structures for depth functions classify many existing examples as special cases and establish results on the possession or lack thereof of four key properties desirable for depth functions in general roughly speaking these properties may be described as affine invariance maximality at center monotonicity relative to deepest point and vanishing at infinity this provides a more systematic basis for selection of a depth function in particular from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors

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

the discrete gaussian chain with 1 r n interactions exact results we show that the discrete gaussian chain with interactionv r 1 r2 1 4 is self dual at the dual temperaturek b t 1 we calculate the height height correlation function and find that the system is rough a duality relation is established for the temperature dependent correlation function exponent we also consider interactionsv r 1 rn and show that absence of a phase transition for 2 n 3 implies absence of a phase transition for 1 n 2 all these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic forn 2 or power law like forn 2

discontinuous percolation transitions in epidemic processes surface depinning in random media and hamiltonian random graphs discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena to demonstrate this we present and relate the continuous and first order behaviors in two different classes of models the first are generalized epidemic processes that describe in their spatially embedded version either on or off a regular lattice compact or fractal cluster growth in random media at zero temperature a random graph version of these processes is mapped onto a model previously proposed for complex social contagion we compute detailed phase diagrams and compare our numerical results at the tricritical point in d 3 with field theory predictions of janssen et al phys rev e 70 026114 2004 the second class consists of exponential hamiltonian i e formally equilibrium random graph models and includes the strauss and the two star model where chemical potentials control the densities of links triangles or two stars when the chemical potentials in either graph model are o logn the percolation transition can coincide with a first order phase transition in the density of links making the former also discontinuous hysteresis loops can then be of mixed order with second order behavior for decreasing link fugacity and a jump first order when it increases

a method for time frequency analysis a method for time frequency signal analysis is presented the proposed method belongs to the general class of smoothed pseudo wigner distributions it is derived from the analysis of the wigner distribution defined in the frequency domain this method provides some substantial advantages over the wigner distribution the well known cross term effects are reduced or completely removed the oversampling of signal is not necessary in addition the computation time can be significantly shorter the results are demonstrated on two numerical examples with frequency modulated signals

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

one dimensional models with 1 r2 interactions the critical behaviour of a general discrete one dimensional model with inverse square interactions is discussed using renormalisation group methods

a general method for comparing probability assessors a probability assessor or forecaster is a person who assigns subjective probabilities to events which will eventually occur or not occur in this paper a general method for comparing forecasters after a finite number of trials is introduced the general method is proven to include calculating all proper scoring rules as special cases it also includes comparison of forecasters in all simple two decision problems as special cases the relationship between the general method and calibration is also explored the general method is also translated into a method for deciding who will give better forecasts in the future

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

the critical behaviour of the long range potts chain from the largest cluster probability distribution abstract we present the numerical study of the one dimensional potts model with power law decaying ferromagnetic interactions the largest cluster probability distribution is obtained by monte carlo simulations using the swendsen wang cluster algorithm with cumulative probabilities the finite size scaling analysis of the largest cluster is used to derive the critical behaviour in the non classical regime of this model for various values of q

logarithmic corrections in the two dimensional ising model in a random surface field in the two dimensional ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point we study this question by extensive monte carlo simulations for various strengths of disorder the calculated effective temperature or size dependent critical exponents fit with the field theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system s critical behaviour

heterogeneous k core versus bootstrap percolation on complex networks we introduce the heterogeneous k core which generalizes the k core and contrast it with bootstrap percolation vertices have a threshold r i that may be different at each vertex if a vertex has fewer than r i neighbors it is pruned from the network the heterogeneous k core is the subgraph remaining after no further vertices can be pruned if the thresholds r i are 1 with probability f or k ensuremath geqslant 3 with probability 1 ensuremath f the process can be thought of as a pruning process counterpart to ordinary bootstrap percolation which is an activation process we show that there are two types of transitions in this heterogeneous k core process the giant heterogeneous k core may appear with a continuous transition and there may be a second discontinuous hybrid transition we compare critical phenomena critical clusters and avalanches at the heterogeneous k core and bootstrap percolation transitions we also show that the network structure has a crucial effect on these processes with the giant heterogeneous k core appearing immediately at a finite value for any fg0 when the degree distribution tends to a power law p q q ensuremath ensuremath gamma with ensuremath gamma l3

two dimensional sir epidemics with long range infection we extend a recent study of susceptible infected removed epidemic processes with long range infection referred to as i in the following from 1 dimensional lattices to lattices in two dimensions as in i we use hashing to simulate very large lattices for which finite size effects can be neglected in spite of the assumed power law p x x 2 for the probability that a site can infect another site a distance vector x apart as in i we present detailed results for the critical case for the supercritical case with 2 and for the supercritical case with 0 2 for the latter we verify the stretched exponential growth of the infected cluster with time predicted by m biskup for 2 we find generic power laws with dependent exponents in the supercritical phase but no kosterlitz thouless kt like critical point as in 1 d instead of diverging exponentially with the distance from the critical point the correlation length increases with an inverse power as in an ordinary critical point finally we study the dependence of the critical exponents on in the regime 0 2 and compare with field theoretic predictions in particular we discuss in detail whether the critical behavior for slightly less than 2 is in the short range universality class as conjectured recently by f linder et al as in i we also consider a modified version of the model where only some of the contacts are long range the others being between nearest neighbors if the number of the latter reaches the percolation threshold the critical behavior is changed but the supercritical behavior stays qualitatively the same

tsallis scaling and the long range ising chain a transfer matrix approach a numerically efficient transfer matrix tm approach is introduced to investigate the long range ising spin chain results obtained within this procedure are primarily used to verify the tsallis scaling hypothesis for long range systems with an ensuremath alpha power law decay of the interaction constants both in the extensive ensuremath alpha g1 and nonextensive ensuremath alpha l1 regimes results for finite size systems taking into account all interactions between spins up to 24 sites apart show that the conjecture is satisfied with a very good precision less than 0 004 for all temperature intervals this tm procedure is further used to investigate several other thermodynamic and critical properties of this system and it may also be extended to similar one dimensional long range systems

space spatial frequency analysis based filtering space invariant filtering of signals that overlap with noise in both space and frequency can be inefficient however the signal and noise may be well separated in the joint space spatial frequency domain then it is possible to benefit from the application of space spatial frequency approaches processing based on these approaches can outperform space or frequency invariant based methods to this aim the concept of nonstationary space varying filtering is introduced in this paper as an extension of the time varying filtering concept the filtering definitions are based on statistical averages although the filtering should commonly be applied knowing only a single noisy signal realization the procedures that can produce good estimates of quantities crucial for efficient filtering based on a single noisy signal realization are considered special attention has been paid to the region of support estimation and cross term effects removal the efficiency of the proposed space spatial frequency filtering concept is tested on the signal forms inspired by the interferograms in optics including real images as disturbances examples demonstrate the superiority of the proposed filtering over the space invariant one for the considered type of signals and noise

directed percolation near a wall series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction the percolation threshold is found to be the same as that for the bulk however the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by and respectively on the other hand the exponent characterizing the scale of the cluster size distribution is found to be unchanged by the presence of the wall the parallel connectedness length which is the scale for the cluster length distribution has an exponent which we estimate to be and is also unchanged the exponent of the mean cluster length is related to and by the scaling relation and using the above estimates yields to within the accuracy of our results we conjecture that this value of is exact and further support for the conjecture is provided by the direct series expansion estimate

auto term representation by the reduced interference distributions a procedure for kernel design an analysis of auto term presentation using the reduced interference distributions rid is done comparison with an ideal time frequency signal representation is taken as a basis for this analysis the following distributions are considered choi williams 1989 zao atlas marks born jordan sinc zhang sato see ibid vol 42 no 1 p 54 1994 butterworth spectrogram and the author s recently proposed s method for time frequency analysis various distributions produce different auto term shapes in all cases the condition for cross term reduction is contradictory to the condition for high auto term quality a procedure for designing a kernel that will produce the desired auto term shape is demonstrated an optimal kernel with respect to the auto term quality and cross term suppression is derived

weather forecasting for weather derivatives we take a simple time series approach to modeling and forecasting daily average temperature in u s cities and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market the answer is perhaps surprisingly yes time series modeling reveals conditional mean dynamics and crucially strong conditional variance dynamics in daily average temperature and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises as we argue it also holds promise for producing the long horizon predictive densities crucial for pricing weather derivatives so that additional inquiry into time series weather forecasting methods will likely prove useful in weather derivatives contexts

solving 1d plasmas and 2d boundary problems using jack polynomials and functional relations the general one dimensional log sine gas is defined by restricting the positive and negative charges of a two dimensional coulomb gas to live on a circle depending on charge constrannts this problem is equivalent to different boundary field theories we study the electrically neutral case which is equivalent to a two dimensional free boson with an impurity cosine potential we use two different methods a perturbative one based on jack symmetric functions and a nonperturbative one based on the thermodynamic bethe ansatz and functional relations the first method allows us to find an explicit series expression for all coefficients in the virial expansion of the free energy and the experimentally measurable conductance some results for correlation functions are also presented the second method gives an expression for the full free energy which yields a surprising fluctuation dissipation relation between the conductance and the free energy

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

economic interpretation of probabilities estimated by maximum likelihood or score the conventional method of estimating a probability prediction model by maximum likelihood mle is a form of maximum score estimation with economic meaning of all the probabilities that a given model might have produced those obtained by mle yield maximum in sample betting return to a log utility investor recognition of this affinity between mle and log utility begs the wider methodological question of whether different decision makers benefit in different degrees from different probabilities probabilities produced by mle can be either too conservative or too bold relative to those found by maximizing utility under more risk tolerant or risk averse score functions a very not very risk averse user who bets characteristically small large fractions of wealth based on a conservative forecast is bound to make a rapidly slowly increasing bet as the forecast probability becomes progressively bolder or more distant from the market probability the effect of this interaction between risk aversion and forecast is that a highly risk averse user may need a much bolder forecast to obtain the same certainty equivalent as a more risk tolerant investor it follows more broadly that professional forecasters should anticipate how a client with given risk aversion expects to gain from any given forecast or forecast revision before committing resources toward making a better informed but still honest forecast this paper was accepted by peter wakker decision analysis

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

on a notion of data depth based on random simplices for a distribution f on mathbb r p and a point x in mathbb r p the simplical depth d x is introduced which is the probability that the point x is contained inside a random simplex whose vertices are p 1 independent observations from f mathematically and heuristically it is argued that d x indeed can be viewed as a measure of depth of the point x with respect to f an empirical version of d cdot gives rise to a natural ordering of the data points from the center outward the ordering thus obtained leads to the introduction of multivariate generalizations of the univariate sample median and l statistics this generalized sample median and l statistics are affine equivariant

one dimensional ising spin glass model with long range interactions an ising chain with hamiltonian h j sigma i j epsilon ijsisj mod i j mod 1 sigma 2 is considered where the epsilon ij are independent random variables according to kotliar et al 1983 this model has a phrase transition with non mean field exponents when 1 3 sigma 1 and mean field exponents beyond the upper critical value of sigma 1 3 by means of an epsilon expansion about the lower critical value of sigma 1 the model is shown to be replica symmetric as epsilon to 0 and it is speculated that this result holds for 1 3 sigma 1

reexamination of the long range potts model a multicanonical approach we investigate the critical behavior of the one dimensional q state potts model with long range lr interaction 1 r d sigma using a multicanonical algorithm the recursion scheme initially proposed by berg is improved so as to make it suitable for a large class of lr models with unequally spaced energy levels the choice of an efficient predictor and a reliable convergence criterion is discussed we obtain transition temperatures in the first order regime which are in far better agreement with mean field predictions than in previous monte carlo studies by relying on the location of spinodal points and resorting to scaling arguments we determine the threshold value sigma c q separating the first and second order regimes to two digit precision within the range 3 leq q leq 9 we offer convincing numerical evidence supporting sigma c q 1 0 for all q by virtue of an unusual finite size effect namely finite size scaling predicts a continuous transition in the thermodynamic limit despite the first order nature of the transition at finite size a qualitative account in terms of correlation lengths is provided finally we find the crossover between the lr and short range regimes to occur inside a narrow window 1 0 sigma 1 2 thus lending strong support to sak s scenario

strict definiteness of integrals via complete monotonicity of derivatives let k be a nonnegative integer and let 0 r be a c function with k k completely monotone and not constant if 6 0 is a signed measure on any euclidean space rd with vanishing moments up to order k 1 then the integral rd rd x y 2 d x d y is strictly positive whenever it exists for general d no larger class of continuous functions seems to admit the same conclusion examples and applications are indicated a section on bilinear integrability might be of independent interest

phase transitions in cooperative coinfections simulation results for networks and lattices we study the spreading of two mutually cooperative diseases on different network topologies and with two microscopic realizations both of which are stochastic versions of a susceptible infected removed type model studied by us recently in mean field approximation there it had been found that cooperativity can lead to first order transitions from spreading to extinction however due to the rapid mixing implied by the mean field assumption first order transitions required nonzero initial densities of sick individuals for the stochastic model studied here the results depend strongly on the underlying network first order transitions are found when there are few short but many long loops i no first order transitions exist on trees and on 2 d lattices with local contacts ii they do exist on erd s renyi er networks on d dimensional lattices with d 4 and on 2 d lattices with sufficiently long ranged contacts iii on 3 d lattices with local contacts the results depend on the microscopic details of the implementation iv while single infected seeds can always lead to infinite epidemics on regular lattices on er networks one sometimes needs finite initial densities of infected nodes v in all cases the first order transitions are actually hybrid i e they display also power law scaling usually associated with second order transitions on regular lattices our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs finally the detailed results mentioned above hold only when both diseases propagate along the same network of links if they use different links results can be rather different in detail but are similar overall

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

low density series expansions for directed percolation ii the square lattice with a wall a new algorithm for the derivation of low density expansions has been used to greatly extend the series for moments of the pair connectedness on the directed square lattice near an impenetrable wall analysis of the series yields very accurate estimates for the critical point and exponents in particular the estimate for the exponent characterizing the average cluster length near the wall 1 1 00014 2 appears to exclude the conjecture 1 1 the critical point and the exponents and have the same values as for the bulk problem

effective scoring rules for probabilistic forecasts this paper studies the use of a scoring rule for the elicitation of forecasts in the form of probability distributions and for the subsequent evaluation of such forecasts given a metric distance function on a space of probability distributions a scoring rule is said to be effective if the forecaster s expected score is a strictly decreasing function of the distance between the elicited and true distributions two simple well known rules the spherical and the quadratic are shown to be effective with respect to suitable metrics examples and a practical application in foreign exchange rate forecasting are also provided

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

should scoring rules be effective a scoring rule is a reward function for eliciting or evaluating forecasts expressed as discrete or continuous probability distributions a rule is strictly proper if it encourages the forecaster to state his true subjective probabilities and effective if it is associated with a metric on the set of probability distributions recently the property of effectiveness which is stronger than strict properness has been proposed as a desideratum for scoring rules for continuous forecasts for reasons of monotonicity in keeping the forecaster close to his true probabilities since in practice the forecast must be chosen from a low dimensional set of admissible distributions it is shown in this paper that what effectiveness implies beyond strict properness is not a monotonicity property but a transitivity property which is difficult to justify behaviorally the logarithmic scoring rule is shown to violate the transitivity property and hence is not effective the l1 and l metrics are shown to allow no effective scoring rules some potential difficulties in interpreting admissible forecasts are also discussed

discrimination slope and integrated discrimination improvement properties relationships and impact of calibration discrimination slope defined as the slope of a linear regression of predicted probabilities of event derived from a prognostic model on the binary event status has recently gained popularity as a measure of model performance it is as a building block for the integrated discrimination improvement that equals the difference in discrimination slopes between the two models being compared several authors have pointed out that it does not make sense to apply the integrated discrimination improvement and discrimination slope when working with mis calibrated models whereas others have raised concerns about the ability of improving discrimination slope without adding new information in this paper we show that under certain assumptions the discrimination slope is asymptotically related to two other r squared measures one of which is a rescaled version of the brier score known to be proper furthermore we illustrate how a simple recalibration makes the slope equal to the rescaled brier r squared metric we also show that the discrimination slope can be interpreted as a measure of reduction in expected regret for the gini brier regret function using theoretical and practical examples we illustrate how all of these metrics are affected by different levels of model mis calibration in particular we demonstrate that simple recalibration ascertaining calibration in the large and calibration slope equal to 1 are not sufficient to correct for some forms of mis calibration we conclude that r squared metrics including the discrimination slope offer an attractive choice for quantifying model performance as long as one accounts for their sensitivity to model calibration copyright 2016 john wiley sons ltd

an analysis of instantaneous frequency representation using time frequency distributions generalized wigner distribution this paper presents an analysis of the representation of instantaneous frequency using time frequency distributions of energy density domain similarity to the ideal instantaneous frequency presentation is chosen as a criterion for comparison of various distributions although all the commonly used distributions suffer from the artifacts along frequency axis it is shown that the wigner distribution is the best among them with respect to this criterion the generalization of wigner distribution lwd is introduced to decrease the artifacts the properties of the lwd are analyzed it is shown that at the expense of an insignificant increase in computation time much better results are obtained the theory is illustrated by a numerical example with the frequency modulated signals

critical behavior and griffiths effects in the disordered contact process we study the nonequilibrium phase transition in the one dimensional contact process with quenched spatial disorder by means of large scale monte carlo simulations for times up to 10 9 and system sizes up to 10 7 sites in agreement with recent predictions of an infinite randomness fixed point our simulations demonstrate activated exponential dynamical scaling at the critical point the critical behavior turns out to be universal even for weak disorder however the approach to this asymptotic behavior is extremely slow with crossover times of the order of 10 4 or larger in the griffiths region between the clean and the dirty critical points we find power law dynamical behavior with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder

critical behaviour near multiple junctions and dirty surfaces in the two dimensional ising model the authors consider m two dimensional semi infinite planes of ising spins joined together through surface spins and study the critical behaviour near to the junction the m 0 limit of the model according to the replica trick corresponds to the semi infinite ising model in the presence of a random surface field rsfi using conformal mapping second order perturbation expansion around the weak and strong coupled planes limits and a differential renormalization group they show that the surface critical behaviour of the rsfi model is described by ising critical exponents with logarithmic corrections to scaling while at multiple junctions m 2 the transition is of first order there is a spontaneous junction magnetization at the bulk critical point

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

surface critical behavior in systems with nonequilibrium phase transitions we study the surface critical behavior of branching annihilating random walks with an even number of offspring barw and directed percolation dp using a variety of theoretical techniques above the upper critical dimensions d c with d c 4 dp and d c 2 barw we use mean field theory to analyze the surface phase diagrams using the standard classification into ordinary special surface and extraordinary transitions for the case of barw at or below the upper critical dimension d d c we use field theoretic methods to study the effects of fluctuations as in the bulk the field theory suffers from technical difficulties associated with the presence of a second critical dimension however we are still able to analyze the phase diagrams for barw in d 1 and 2 which turn out to be very different from their mean field analog furthermore for the case of barw only and not for dp we find two independent surface beta 1 exponents in d 1 arising from two distinct definitions of the order parameter using an exact duality transformation on a lattice barw model in d 1 we uncover a relationship between these two surface beta 1 exponents at the ordinary and special transitions many of our predictions are supported using monte carlo simulations of two different models belonging to the barw universality class

k core bootstrap percolation on complex networks critical phenomena and nonlocal effects we develop the theory of the k core bootstrap percolation on uncorrelated random networks with arbitrary degree distributions we show that the k core percolation is an unusual hybrid phase transition with a jump emergence of the k core as at a first order phase transition but also with a critical singularity as at a continuous transition we describe the properties of the k core explain the meaning of the order parameter for the k core percolation and reveal the origin of the specific critical phenomena we demonstrate that a so called corona of the k core plays a crucial role corona is a subset of vertices in the k core which have exactly k neighbors in the k core it turns out that the k core percolation threshold is at the same time the percolation threshold of finite corona clusters the mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point we show that a random removal of even one vertex from the k core may result in the collapse of a vast region of the k core around the removed vertex the mean size of this region diverges at the critical point we find an exact mapping of the k core percolation to a model of cooperative relaxation this model undergoes critical relaxation with a divergent rate at some critical moment

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

on the local frequency group shift and cross terms in some multidimensional time frequency distributions a method for multidimensional time frequency analysis presents an analysis of the representation of local frequency and group shift using multidimensional time frequency distributions in the second part of the correspondence the authors extend the analysis to the multicomponent signals and cross terms effects on the basis of that analysis an efficient method derived from the analysis of the multidimensional wigner distribution defined in the frequency domain is proposed this method provides some substantial advantages over the wigner distribution the well known cross terms effects are reduced or completely removed the oversampling of signals is shown to be unnecessary and the computation time can be significantly reduced as well the theory is illustrated by a two dimensional numerical example

mixed order phase transition of the contact process near multiple junctions we have studied the phase transition of the contact process near a multiple junction of m semi infinite chains by monte carlo simulations as opposed to the continuous transitions of the translationally invariant m 2 and semi infinite m 1 system the local order parameter is found to be discontinuous for m 2 furthermore the temporal correlation length diverges algebraically as the critical point is approached but with different exponents on the two sides of the transition in the active phase the estimate is compatible with the bulk value while in the inactive phase it exceeds the bulk value and increases with m the unusual local critical behavior is explained by a scaling theory with an irrelevant variable which becomes dangerous in the inactive phase quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results

high resolution spectral analysis of images using the pseudo wigner distribution several methods for the computation of the discrete wigner distribution dwd through the use of two dimensional 2 d analytic signals have been proposed depending of the direction of the phase shift most of the methods cope with the problem of aliasing of the dwd by low pass prefiltering the spectrum but reducing spatial frequency support a new method for 2 d dwd free of aliasing and simultaneously increasing the spatial frequency support is proposed through the use of a new analytic signal in this way local spectral analysis for small window sizes can be accomplished improving the resolution but reducing cross terms and other interferences inherent in the dwd computation for the three analytic images used in the comparison the method proposed here also performs better than the other two for such tasks

scoring rules generalized entropy and utility maximization information measures arise in many disciplines including forecasting where scoring rules are used to provide incentives for probability estimation signal processing where information gain is measured in physical units of relative entropy decision analysis where new information can lead to improved decisions and finance where investors optimize portfolios based on their private information and risk preferences in this paper we generalize the two most commonly used parametric families of scoring rules and demonstrate their relation to well known generalized entropies and utility functions shedding new light on the characteristics of alternative scoring rules as well as duality relationships between utility maximization and entropy minimization in particular we show that weighted forms of the pseudospherical and power scoring rules correspond exactly to measures of relative entropy divergence with convenient properties and they also correspond exactly to the solutions of expected utility

watermarking in the space spatial frequency domain using two dimensional radon wigner distribution a two dimensional 2 d signal with a variable spatial frequency is proposed as a watermark in the spatial domain this watermark is characterized by a linear frequency change it can be efficiently detected by using 2 d space spatial frequency distributions the projections of the 2 d wigner distribution the 2 d radon wigner distribution are used in order to emphasize the watermark detection process the watermark robustness with respect to some very important image processing attacks such as for example the translation rotation cropping jpeg compression and filtering is demonstrated and tested by using stirmark 3 1

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

critical dynamics of the contact process with quenched disorder we study critical spreading in monte carlo simulations of the two dimensional contact process cp with quenched disorder in the form of random dilution in the pure model spreading from a single particle at the critical point ensuremath lambda c follows power laws with the critical exponents of directed percolation with disorder critical spreading is logarithmic not power law below ensuremath lambda c there is a griffiths phase in which the time dependence is governed by nonuniversal power laws the effects of disorder are also apparent above ensuremath lambda c in the active phase where the relaxation of the survival probability is algebraic rather than exponential as in the pure model our results support the conjecture by bramson durrett and schonmann ann prob 19 960 1991 that in two or more dimensions the disordered cp has only a single phase transition

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

roughening behavior of a one dimensional crystal surface with inverse square potential abstract the discrete gaussian chain with inverse square potential which models a one dimensional crystal surface is studied by monte carlo methods the system is found to undergo a roughening transition and the temperature dependent correlation function exponent t is shown to be discontinous at the critical point these results can be transposed to the metal insulator transition of a one dimensional plasma of logarithmically interacting charges

probabilistic forecasts calibration and sharpness summary probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions we propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only a simple theoretical framework allows us to distinguish between probabilistic calibration exceedance calibration and marginal calibration we propose and study tools for checking calibration and sharpness among them the probability integral transform histogram marginal calibration plots the sharpness diagram and proper scoring rules the diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the stateline wind energy centre in the us pacific northwest in combination with cross validation or in the time series context our proposal provides very general nonparametric alternatives to the use of information criteria for model diagnostics and model selection

simple model for the dna denaturation transition we study pairs of interacting self avoiding walks mathit ensuremath omega 1 mathit ensuremath omega 2 on the 3d simple cubic lattice they have a common origin mathit ensuremath omega 0 1 mathit ensuremath omega 0 2 and are allowed to overlap only at the same monomer position along the chain mathit ensuremath omega i 1 ensuremath ne mathit ensuremath omega j 2 for i ensuremath ne j while mathit ensuremath omega i 1 mathit ensuremath omega i 2 is allowed the latter overlaps are indeed favored by an energetic gain ensuremath epsilon this is inspired by a model introduced long ago by poland and sheraga j chem phys 45 1464 1966 for the denaturation transition in dna where however self avoidance was not fully taken into account for both models there exists a temperature t m above which the entropic advantage to open up overcomes the energy gained by forming tightly bound two stranded structures numerical simulations of our model indicate that the transition is of first order the energy density is discontinuous but the analog of the surface tension vanishes and the scaling laws near the transition point are exactly those of a second order transition with crossover exponent ensuremath varphi 1 numerical and exact analytic results show that the transition is second order in modified models where the self avoidance is partially or completely neglected

compatible weighted proper scoring rules many proper scoring rules such as the brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution recent work has motivated weighted proper scoring rules which have an additional baseline parameter to date two families of weighted proper scoring rules have been introduced the weighted power and pseudospherical scoring families these families are compatible with the log scoring rule when the baseline maximizes the log scoring rule over some set of distributions the baseline also maximizes the weighted power and pseudospherical scoring rules over the same set we characterize all weighted proper scoring families and prove a general property every proper scoring rule is compatible with some weighted scoring family and every weighted scoring family is compatible with some proper scoring rule