Preferences and Production under Uncertainty

The Arrow-Savage-Debreu formalism (state space, consequence space, acts) for modelling a stochastic decision is introduced. Preferences over stochastic outcomes framed as maps (acts) from the state space to the consequence space are studied and related to nonstochastic preference structures. Distance function representations of preferences are developed and their superdifferential correspondences are shown to define subjective probability measures. Structural restrictions including uncertainty aversion, constant absolute uncertainty aversion, and constant relative uncertainty aversion are examined and related to parallel restrictions for nonstochastic preference or production structures. A model of a stochastic technology that has the nonstochastic production model as a special case is introduced, and distance function representations of it are discussed. Structural assumptions on the stochastic technology are discussed.

Análisis de la calidad de la leche en un modelo microeconómico multi-output: El papel de la genética

Economía Agraria y Recursos Naturales ◽

10.7201/earn.2005.10.01 ◽

2011 ◽

Vol 5 (10) ◽

pp. 3 ◽

Cited By ~ 2

Author(s):

Antonio Álvarez ◽

Carlos Arias ◽

David Roibás

Keyword(s):

Panel Data ◽

Milk Production ◽

Distance Function ◽

Dairy Farms ◽

Milk Quality ◽

Production Model ◽

Genetic Traits

In this paper we analyze the influence of genetics on milk quality. For that purpose, we use a multi-output production model in which milk quality is included as an additional output in milk production. A distance function is used to estimate empirically the contribution of genetics to milk quality. For that purpose, we use a panel data of 96 dairy farms in Asturias. This dataset contains indexes measuring the genetic traits of the herd.

On the Outlying Eigenvalues of a Polynomial in Large Independent Random Matrices

International Mathematics Research Notices ◽

10.1093/imrn/rnz080 ◽

2019 ◽

Cited By ~ 1

Author(s):

Serban T Belinschi ◽

Hari Bercovici ◽

Mireille Capitaine

Keyword(s):

Probability Theory ◽

Random Matrices ◽

Empirical Distribution ◽

Free Probability ◽

Probability Measures ◽

Unitary Operators ◽

Free Probability Theory ◽

Wigner Matrix ◽

Asymptotic Eigenvalue ◽

Abstract Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A_N,B_N)$, where $A_N$ and $B_N$ are independent Hermitian random matrices and the distribution of $B_N$ is invariant under conjugation by unitary operators. We assume that the empirical eigenvalue distributions of $A_N$ and $B_N$ converge almost surely to deterministic probability measures $\mu$ and $\nu$, respectively. In addition, the eigenvalues of $A_N$ and $B_N$ are assumed to converge uniformly almost surely to the support of $\mu$ and $\nu ,$ respectively, except for a fixed finite number of fixed eigenvalues (spikes) of $A_N$. It is known that almost surely the empirical distribution of the eigenvalues of $P(A_N,B_N)$ converges to a certain deterministic probability measure $\eta \ (\textrm{sometimes denoted}\ P^\square(\mu,\nu))$ and, when there are no spikes, the eigenvalues of $P(A_N,B_N)$ converge uniformly almost surely to the support of $\eta$. When spikes are present, we show that the eigenvalues of $P(A_N,B_N)$ still converge uniformly to the support of $\eta$, with the possible exception of certain isolated outliers whose location can be determined in terms of $\mu ,\nu ,P$, and the spikes of $A_N$. We establish a similar result when $B_N$ is replaced by a Wigner matrix. The relation between outliers and spikes is described using the operator-valued subordination functions of free probability theory. These results extend known facts from the special case in which $P(X,Y)=X+Y$.

On large deviations of empirical measures in the τ-topology

10.1017/s0021900200106977 ◽

1994 ◽

Vol 31 (A) ◽

pp. 41-47 ◽

Cited By ~ 3

Author(s):

A. De Acosta

Keyword(s):

Large Deviations ◽

State Space ◽

The State ◽

Probability Measures ◽

Empirical Measures

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

A family of densities derived from the three-parameter Dirichlet process

10.1239/jap/1037816017 ◽

2002 ◽

Vol 39 (4) ◽

pp. 764-774 ◽

Cited By ~ 4

Author(s):

Matthew A. Carlton

Keyword(s):

State Space ◽

Density Function ◽

Dirichlet Process ◽

Dirichlet Distribution ◽

The State ◽

Measurable Partition ◽

Multivariate Distributions ◽

The Family ◽

Multivariate Density ◽

The traditional Dirichlet process is characterized by its distribution on a measurable partition of the state space - namely, the Dirichlet distribution. In this paper, we consider a generalization of the Dirichlet process and the family of multivariate distributions it induces, with particular attention to a special case where the multivariate density function is tractable.

THE BANACH-LIE -ALGEBRA OF MULTIPLICATION OPERATORS ON A W-ALGEBRA

Asian-European Journal of Mathematics ◽

10.1142/s1793557111000198 ◽

2011 ◽

Vol 04 (02) ◽

pp. 235-261

Author(s):

Maysaa Alqurashi ◽

Najla A. Altwaijry ◽

C. Martin Edwards ◽

Christopher S. Hoskin

Keyword(s):

State Space ◽

Lie Algebra ◽

The State ◽

Multiplication Operators ◽

Dual Cone ◽

Positive Real ◽

Linear Isometry ◽

Real Linear ◽

The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a formula is obtained for the norm of an element of [Formula: see text] in terms of a centre-valued 'norm' on A, which is similar to that previously obtained by non-order-theoretic methods.

Periodic strong ergodicity in non-homogeneous Markov systems

10.2307/3214740 ◽

1991 ◽

Vol 28 (1) ◽

pp. 58-73 ◽

Cited By ~ 7

Author(s):

Ioannis I. Gerontidis

Keyword(s):

State Space ◽

Manpower Planning ◽

Practical Aspect ◽

Periodic Case ◽

Convergence Properties ◽

Markov Systems ◽

Numerical Examples ◽

The Individual ◽

Special Case ◽

Theoretical Results

This paper presents a unified treatment of the convergence properties of nonhomogeneous Markov systems under different sets of assumptions. First the periodic case is studied and the limiting evolution of the individual cyclically moving subclasses of the state space of the associated Markov replacement chain is completely determined. A special case of the above result is the aperiodic or strongly ergodic convergence. Two numerical examples from the literature on manpower planning highlight the practical aspect of the theoretical results.

On large deviations of empirical measures in the τ-topology

10.2307/3214947 ◽

1994 ◽

Vol 31 (A) ◽

pp. 41-47 ◽

Cited By ~ 8

Author(s):

A. De Acosta

Keyword(s):

Large Deviations ◽

State Space ◽

The State ◽

Probability Measures ◽

Empirical Measures

We prove a generalization of Sanov's theorem in which the state space S is arbitrary and the set of probability measures on S is endowed with the τ -topology.

BUGS in Bayesian stock assessments

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f99-043 ◽

1999 ◽

Vol 56 (6) ◽

pp. 1078-1087 ◽

Cited By ~ 96

Author(s):

Renate Meyer ◽

Russell B Millar

Keyword(s):

State Space ◽

Stock Assessment ◽

State Space Model ◽

Production Model ◽

Posterior Density ◽

Convergence Diagnostics ◽

Surplus Production Model ◽

Nonlinear State Space Models ◽

Age Structured ◽

Joint Posterior Density

This paper illustrates the ease with which Bayesian nonlinear state-space models can now be used for practical fisheries stock assessment. Sampling from the joint posterior density is accomplished using Gibbs sampling via BUGS, a freely available software package. By taking advantage of the model representation as a directed acyclic graph, BUGS automates the hitherto tedious calculation of the full conditional posterior distributions. Moreover, the output from BUGS can be read directly into the software CODA for convergence diagnostics and statistical summary. We illustrate the BUGS implementation of a nonlinear nonnormal state-space model using a Schaefer surplus production model as a basic example. This approach extends to other assessment methodologies, including delay difference and age-structured models.