摘要:

The concept of statistical decision theory concerning sequential observations is generalized to decision problems, which are based upon a continuous stochastic process.

ISSN:0090-9491    

DOI:10.1080/17442507508833111

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

ISSN:0090-9491    

DOI:10.1080/17442507508833112

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

摘要:

A short review is given of the necessity for, and evidence of, synaptic facilitation as a mechanism which organises the microcircuitry of the brain as a result of experience. Conditional probability statistics described this process and perceptual learning machines illustrate it. A brief review of animal and machine pattern recognition and learning is given. A simple model is described which simulates learning and pattern recognition. It is suggested that certain brain processes and perceptual learning machines are homologous rather than just analogous.

ISSN:0090-9491    

DOI:10.1080/17442507508833113

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

摘要:

This paper is concerned with the problem of optimalM-alternative determination of quantum statistical states. A review of newest achievement of solving this problem is given. A notion of an effective decision Hilbert space is introduced and necessary and sufficient condkions for optimality of multiple quantum hypothesis testing in this space are formulated. The general solution is found for the case of a two-dimensional decision space. Another problem solved is that of discrimination of quantum pure non-orthogonal states. The result is represented in explicit analytical form for an "equidiagonal" case, which is quite general. In particular, we find explicit solutions of optimal discrimination problem of homogeneous and equiangle sets of pure states. These results are used for theM-ary detection problem in solving for the quantum coherent non-orthogonal signals. It is proved that the simplex signals are optimal elso in quantum case. The optimal estimatesof phaseandamplitude of quantum coherent signals are found. For decision operators a notion of IT-representation is introduced to get a general quasi-classical (optimal in quasi-classical limit)M-ary detection procedure of stochastic fields and particles, which submits to Bose-Einstein statistics. An optimal solution of problem of non-coherent detection of quantum stochastic (including optical) signals are found in the extreme quantum limit (weaknoise and signals with unknown phase).

ISSN:0090-9491    

DOI:10.1080/17442507508833114

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

摘要:

The theory of periodic generators of the Riccati equation is presented, as well as a method for their determination

ISSN:0090-9491    

DOI:10.1080/17442507508833115

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

摘要:

Modifications to the Cramer-von Mises goodness-of-fit test statistic for spectral distributions are discussed. The modifications consist of inserting weight functions into the usual sto¬chastic integral for the test statistic. Conditions on the weight function are given under which the integral of the weighted square of the difference between the empirical and theoretical spectral distribution functions converges in distribution to the corresponding integral of a process related to Brownian Motion. The distributions of the test statistic under certain alternatives to the null hypothesis are also discussed. A discussion is given of the large sample distributions for weight function of the form ψ(t) =atk,k< –2.

ISSN:0090-9491    

DOI:10.1080/17442507508833116

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor

摘要:

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has anaprioriknowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances andn-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.

ISSN:0090-9491    

DOI:10.1080/17442507508833117

出版商:Gordon and Breach Science Publishers, Ltd    

年代:1975

数据来源: Taylor