Showing papers on "Conditional probability distribution published in 1989"

Testing for the Constancy of Parameters over Time

Abstract: Tests are proposed for detecting possible changes in parameters when the observations are obtained sequentially in time. While deriving the tests the alternative one has in mind specifies the parameter process as a martingale. The distribution theory of these tests relies on the large-sample results; that is, only the limiting null distributions are known (except in very special cases). The main tool in establishing these limiting distributions is weak convergence of stochastic processes. Suppose that we have vector-valued observations x 1, …, x n obtained sequentially in time (or ordered in some other linear fashion). Their joint distribution is described by determining the initial distribution for x 1 and the conditional distribution for each x k given the past up to x k–1. Suppose further that these distributions depend on a p-dimensional parameter vector θ. At least locally (i.e., in a short time period) this may be more or less legitimate. In the long run, however, the possibility of some ch...

Asymptotic techniques for use in statistics

Abstract: Preliminary notions.- Some basic limiting procedures.- Asymptotic expansions.- Edgeworth and allied expansions.- Miscellany on multivariate distributions.- Multivariate asymptotic expansions.- Expansions for conditional distributions.- Postscript.

The Conditional Beta Distribution as a Stochastic Production Function

Abstract: The conditional beta distribution is proposed as a parametric model of the probability distribution of agricultural output. A two-stage maximum likelihood estimation procedure is shown to produce consistent, asymptotically efficient and normal estimates of maximum output and the parameters of the conditional distribution. Application of the procedure to data on corn yield response to fertilizers shows that fertilizers have a significant impact on each of the first three moments of the distribution of corn yield. Corn yield distributions are found to be negatively skewed, implying that above average yields are more probable than below average yields.

Compatible Conditional Distributions

Abstract: Consider two families of candidate conditional densities (or probability mass functions), {f(x | y);y ∈ S y} and {f(y | x): x ∈ S x}. This article investigates necessary and sufficient conditions for the existence of a joint density (or joint probability mass function) f(x, y) with the given families as its associated conditional densities. This supplements previous work that has addressed the question of uniqueness of f(x, y) assuming its existence.

Conditional Probabilities and Compounds of Conditionals

Abstract: Tjrnest Adams (1965, 1975) has advanced a probabilistic acL count of conditionals, according to which the probability of a simple English indicative conditional is the conditional probability of the consequent given the antecedent. The theory describes what English speakers assert and accept with unfailing accuracy, yet the theory has won only limited acceptance. A principal reason for this has been that the theory is so limited in its scope. While the theory does a marvelous job of accounting for how we use simple conditionals, it tells us nothing about compound conditionals or about Boolean combinations of conditionals. In view of the Lewis Triviality Theorem (which we shall discuss below), this limitation has been thought to be insuperable, so that Adams's theory has appeared to be a dead end, highly accurate in a narrowly specialized domain, but isolated from the rest of logical theory and unable to overcome that isolation. Adams's theory has also seemed to be isolated from probability theory, since it tells us nothing about the probabilities of Boolean compounds of conditionals, and the laws governing the probabilities of Boolean compounds lie at the very center of classical probability theory. Since the laws of probability cannot be meaningfully applied to the numerical values Adams assigns to conditionals, there has seemed to be little point in referring to these numerical values as "probabilities." The numerical values accurately measure the assertability and acceptability of conditionals, but they are, as Lewis (1976, p. 135) puts it, "probabilities only in name." In the present paper, I shall attempt to meet these difficulties

Linear inverse problems for generalised random variables

Abstract: In a statistical inverse theory both the unknown quantity and the measurement are random variables. The solution of the inverse problem is then the conditional distribution of the unknown variable with the measurement supposed to be known. Both variables often have their values in spaces of functions or generalised functions while the statistical theory of conditional distributions has only been fully developed for Polish spaces. Also, the mappings representing the solution of linear inverse problems with Gaussian priors and noises are usually only defined on a subset of the spaces used. This problem has previously been correctly handled only for Hilbert-space-valued variables. The existence of a regular version of the conditional distribution of random variables with values in spaces of generalised functions is shown and the inverse problem is solved in the linear Gaussian case.

Probability for statistics

Abstract: I:Elementary Probability and Statistics.- 1 Relative frequency.- 2 Sample spaces.- * 3 Some rules about sets (see footnote).- 4 The counting function for finite sets.- 5 Probability on finite sample spaces.- * 6 Ordered selections.- * 7 Unordered selections.- 8 Some uniform probability spaces.- 9 Conditional probability/independence.- * 10 Bayes' rule.- 11 Random variables.- 12 Expectation.- 13 A hypergeometric distribution.- * 14 Sampling and simulation.- 15 Testing simple hypotheses.- * 16 An acceptance sampling plan.- 17 The binomial distribution.- * 18 Matching and catching.- 19 Confidence intervals for a Bernoulli ?.- 20 The Poisson distribution.- * 21 The negative binomial distribution.- II:Probability and Expectation.- 1 Some set theory.- 2 Basic probability theory.- 3 The cumulative distribution function.- 4 Some continuous CDFs.- 5 The normal distribution.- 6 Some algebra of random variables.- 7 Convergence of sequences of random variables.- 8 Convergence almost surely and in probability.- 9 Integration-I.- * 10 Integration-II.- 11 Theorems for expectation.- 12 Stieltjes integrals.- 13 Product measures and integrals.- III:Limiting Distributions.- 1 Joint distributions: discrete.- 2 Conditional distributions: discrete.- 3 Joint distributions: continuous.- 4 Conditional distributions: continuous.- 5 Expectation: examples.- 6 Convergence in mean, in distribution.- * 7 Other relations in modes of convergence.- 8 Laws of large numbers.- 9 Convergence of sequences of distribution functions.- 10 Convergence of sequences of integrals.- 11 On the sum of random variables.- 12 Characteristic functions-I.- 13 Characteristic functions-II.- 14 Convergence of sequences of characteristic functions.- 15 Central limit theorems.- References.

Large deviation estimates for a conditional probability distribution. Applications to random interaction Gibbs measures

Abstract: Let (X i ,Y i ) ∈ℤ d , be independent identically distributed random variables with arbitrary distribution. We show that, for almost every(Y i ) i , the conditional law of the empirical field given(Y i ) i satisfies to large deviation inequalities. This applies to the study of Gibbs measures with random interaction, in the case of some mean-field models as well as of short range summable interaction. We show that the pressure is nonrandom, and is given by a variational formula. These random Gibbs measures have the same large deviation rate, which does not depend on the particular realization of the interaction; their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula.

A Multivariate Distribution with Weibull Connections

Abstract: A simple form of multivariate distribution is defined which, for certain parameter values, has Weibull marginals. The distribution has a single parameter governing association between the variates, which may be positive, negative or zero. The simple forms for marginal and conditional distributions, hazard functions and densities make it attractive for practical application and interpretation.

Sensitivity Analysis of Seasonal Adjustments: Empirical Case Studies

Abstract: Three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior. Analyses are performed within a semi-Bayesian framework where inferences for target quantities of interest, such as seasonally adjusted values, are obtained as posterior distributions conditional on observed data and fitted parameter values. Such an approach is similar to previous model-based methods of seasonal analysis, but new models and algorithms are used and, more important, a sensitivity analysis is performed to determine the extent to which conclusions vary across a range of plausible fitted models. It is found that sensitivity to variation across plausible models is not unusual in practice. The logical conclusion of the investigation is that a fully Bayesian analysis is required that averages conditional posteriors over a posterior distribution for the model parameters. Such an analysis is necessarily sensitive to the choice of...

Modelling of reference values for size at birth.

Abstract: Data from the Swedish Medical Birth Registration, 1977-1981 were used to apply methods of constructing reference standards for size at birth. Using clinical information a 'healthy' sub-population was extracted. The conditional distributions of birthweight (BW) and birthlength (BL) for each week of Gestational age, and the conditional distribution of birthweight given birthlength were modelled using truncated Normal distributions, after making use of Box-Cox power transformations. Spline functions were then used in conjunction with a multiplicative method to obtain appropriate percentage point curves. Examples of this analysis are given.

Conditional distributions and the bivariate normal distribution

Abstract: An alaysis of the extent to which conditional distributions of a bivariate vector characterize bivariate normality is given.

A Review of Stochastic Models for Petroleum Reservoirs

Abstract: The stochastic methods used to model petroleum reservoirs can be subdivided into two categories: “object-based” (or Boolean) methods generate discrete sand bodies of random shape at random locations in space, whereas “sequence-based” methods generate distributions of permeability or lithofacies values that satisfy a certain variogram or conditional probability distribution. Object-based methods take into account geological knowledge about the likely shape and size of the sand bodies. Sequence-based methods include geostatistical conditional simulations as well as fractal and Markov techniques, and they incorporate information about the relationships between properties at neighbouring locations.

On conditional weak convergence

Abstract: In this paper we discuss a number of technical issues associated with conditional weak convergence. The main modes of convergence of conditional probability distributions areuniform, probability, andalmost sure convergence in the conditioning variable. General results regarding conditional convergence are obtained, including details of sufficient conditions for each mode of convergence, and characterization theorems for uniform conditional convergence.

A Multivariate Distribution with Weibull Connections

Abstract: SUMMARY A simple form of multivariate distribution is defined which, for certain parameter values, has Weibull marginals. The distribution has a single parameter governing association between the variates, which may be positive, negative or zero. The simple forms for marginal and conditional distributions, hazard functions and densities make it attractive for practical application and interpretation.

A Characterization of the Gamma Process by Conditional Moments

Abstract: The gamma process is determined by the form of conditional expectations and conditional variances. Also a new characterization of the gamma law is obtained and then applied to characterize the gamma process among the processes with independent increments.

Can the first two conditional moments identify a mean square differentiable process

Abstract: Following a general theorem concerning the relationship between the first two conditional moments of some random variables and the distribution of the conditioning random vector, we derive differential equations which involve the conditional regression and covariance of the mean square derivative of the process {Wt} and the finite dimensional densities of this process We use these equations to define a subclass of ms differentiable processes having smooth conditional moments and finite dimensional densities and having the property that the first two conditional moments identify a given process completely Among these are processes having linear first moments We show that under some differentiability assumptions these processes have elliptically contoured distributions

Assumed Density Filter with Application to Homing Missile Guidance

Abstract: A maximum likelihood estimation method is developed for a class of problems where the dynamics are linear and the measurement function is nonlinear. In this method, called the "assumed density filter,' the form of the conditional probability density function is selected to be a function of a finite number of quantities. These quantities, which describe the approximate shape of conditional probability density function around the mode, are propagated through each measurement interval. At the measurement, the conditional probability density function is updated using Bayes theorem, and its mode, computed numerically, is defined to be the best estimate of the state. The posteriori conditional probability density function is then approximated by a Taylor series expansion about its mode to preserve the assumed functional form. The numerical results for a target-intercept problem indicate that the assumed density filter is superior to the extended Kalman filter. However, the assumed density filter has a negative range bias. It is analytically proved, with some approximations, that the maximum likelihood range estimates are smaller than the mean range estimates.

Time series formed from the superposition of discrete renewal processes

Abstract: The superposition of independent, discrete, renewal processes produces a counting process which is also a discrete time series. The conditional distribution and correlation structure of this kind of time series may be obtained. In suitable conditions the conditional distribution has a spectrum which is exactly or approximately rational. When this is so, an ARMA can be found which matches the spectrum of the superposition. ARMA TIME SERIES; BOX-JENKINS

Statistical mechanical theory of polar fluids for all densities

Abstract: We present results for the structure and thermodynamics of a polar fluid obtained from a recently developed theory which is based on the method of conditional distribution. Within the framework of the method the concept of the average force potentials is used to develop a truncation procedure for an arbitrary equation of the chain. A closed system of integral equations for the average force potential is formulated. The Helmholtz free energy, the pressure, structural properties and the static dielectric constant are calculated in terms of the binary distribution function. We compare our results with experimental data and find that the theory gives realistic results. Comparisons are also made for self-diffusion coefficients obtained from molecular dynamics simulations.

Continuity properties of optimal stopping value

Abstract: On etudie les proprietes de continuite de la valeur d'arret optimal d'une suite (finie ou infinie) de variables aleatoires integrables

Nonlinear data fusion

Abstract: Consideration is given to a random process whose state is observed by N distributed sensors. Each sensor's measurements are supplied to a nearby local station. Each station processes its observation history to produce a local conditional density function. A coordinator must reconstruct the centralized (global) conditional density of the state process, conditioned on the distributed noise-corrupted observation histories of all the stations. The coordinator can only access the local conditional densities, not the observation histories themselves. The local processors' models can differ from the coordinator's model of the distributed observation dynamics. By constraining the choice of the local models, the coordinator reconstructs exactly the centralized conditional density (as if it has access to all the measurement histories). A nonlinear distributed estimation problem is solved using reduced-order local models that lessen the local processors' complexities or computational loads. >

Estimation of a Probability Density Function with Applications to Nonparametric Inference in Econometrics

Abstract: In this paper we present a class of nonparametric estimates of densities which are asymptotically unbiased and consistent. We point out various applications of these density estimates in econometrics. Some illustrative examples, using economic data, are also given.