Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Semi-intensive shrimp farming system of Kerala, India: a production function analysis

An analysis of the factor-product relationship in the semi-intensive shrimp farming system of Kerala, farm basis and hectare basis, we are attempted and the results reported in this paper. The Cobb-Douglas model, in which the physical relationship between input and output is estimated, and the marginal analysis then employed to evaluate the producer behaviour, was used for the analysis. The study was based on empirical data collected during November 1994 to May 1996, covering three seasons, from 21 farms spread over Alappuzha, Ernakulam and Kasaragod districts of the state. The sample covered a total area of 61.06 ha. Of the 11 explanatory variables considered in the model, the size of the farm, casual labour and chemical fertilizers were found statistically significant. It was also observed that the factors such as age of pond, experience of the farmer, feed, miscellaneous costs, number of seed stocked and skilled labour contributed positively to the output. The estimated industry production function exhibited unitary economies of scale. The estimated mean output was 3937 kg/ha. The test of multi-co-linearity showed that there is no problem of dominant variable. On the basis of the marginal product and the given input-output prices, the optimum amounts of seed, feed and casual labour were estimated. They were about 97139 seed, 959 kg of feed and 585 man-days of casual labour per farm. This indicated the need for reducing the stocking density and amount of feed from the present levels, in order to maximise profit. Based on the finding of the study, suggestions for improving the industry production function are proposed.