| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 97 === The problem of regression which alike linear regression is very important since remotest time.
This paper is about using Bayesian method to estimate increasing regression curve.Because of continuous functions be approached by Bernstein polynomails which can be found the coefficient to show that it is increasing and approach all of the insreasing continuous functions.On the other hand, it's easy to have the prior and is helpful in calculate the posterior by using Bernstein polynomials.So the model using Bernstein polynomials to describe the graph of increasing curve is more complicate than using linear regression,without saying, it's also more difficult to estimate the M.L.E.
Above all,we decide to use Bayesian method and calculate the posterior by using Markov Chain Monte Carlo(M.C.M.C.) method. We have introduction on model algorithm and the theorem of reduction completely in this paper.And using the package software Matlab writing the program to get the estimator can be very nice.
The theorem is in 4. It's really complicate by using M.L.E. mothod.We may use this to be our research title in the future.Compare with our estimation,the paper also can be expended to estimation of 2-dimention surface regression,all of them can be direction of research in our future.
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