Bayesian Prior Distribution Research Articles

(R.Q) inventory problem with unknown mean demand and learning

AbstractWe address a single product, continuous review model with stationary Poisson demand. Such a model has been effectively studied when mean demand is known. However, we are concerned with managing new items for which only a Bayesian prior distribution on the mean is available. As demand occurs, the prior is updated and our control parameters are revised. These include the reorder point (R) and reorder quantity (Q).Deemer, taking a clue from some earlier RAND work, suggested using a model appropriate for known mean, but using a Compound Poisson distribution for demand rather than Poisson to reflect uncertainty about the mean. Brown and Rogers also used this approach but within a periodic review context.In this paper we show how to compute optimum reorder points for a special problem closely related to the problem of real interest. In terms of the real problem, subject to a qualification to be discussed, the reorder points found are upper bounds for the optimum. At the same time, the reorder points found can never exceed those found by the Compound Poisson (Deemer) approach. And they can be smaller than those found when there is no uncertainty about the mean.As a check, the Compound Poisson and proposed approach are compared by simulation.

A Bayesian approach to model inadequacy for polynomial regression

A method is presented which, in many cases, appears to be an improvement over the standard approach to the polynomial regression problem. This improvement is achieved by focusing attention on the deviation of the polynomial representation from the true underlying function. By fully utilizing the nature of this deviation, a model is constructed in which its properties are represented in terms of a Bayesian prior distribution. The model is analyzed to give parameter estimates and predictions of further observations. Comparisons are made with standard least squares procedures when the true underlying model is (a) quadratic and (b) linear and quadratic with a superimposed sine wave.

Bayessche sehätzungen und vorhersagen bei stochastischen linearen bliferenzengleichiingssystemen

For a system of stochastic linear differnce equations where the random disturbances U is a timely non-independent GAUssian process we derive BAYESian estimators for A, B and the unknown parameters the convariance function of U t and conditions for the consistance this estimators. Further we derive BAYEsian predictors of X(T + 1) by the observation of and the recursive form the BAYEsian estimators for time independent random disturbances U t . For the derivation of the BAYEsian estimators and predictors conjugate prior distributions are used.

Bayesian Prior Distributions for Systems with Exponential Failure-time Data

In this paper, confidence bounds on the reliability of a serial system composed of exponential subsystems are considered. Both the classical and the Bayesian analyses are discussed. The main result is that for the case in which there are no previous data, then there are no prior distributions on the subsystem reliabilities that are independent of current data and that yield the uniformly most accurate unbiased confidence bounds available through classical techniques.

Bayesian prior distributions for multi‐component systems

Bayesian prior distributions for multi‐component systems

Technical Note—Approximations to the Renewal Function m(t)

Models of queuing, inventory, and reliability processes often have a useful renewal process imbedded in the fundamental stochastic process. The number of renewals is sufficient to determine performance measures such as the total cost, shortages, etc. The limit theorems of renewal theory are unsatisfactory in obtaining the expected values of these performance measures over a finite time horizon. This paper compares an accurate numerical technique for calculating the expected number of renewals with an approximation that uses the asymptotic expansion of the dominating residues of the Laplace transform M(θ). Furthermore, when a parameter of the renewal process is uncertain except for its Bayesian prior distribution, an approximation that uses a modified exponential renewal process appears better.