In the previous lecture we defined the principle of Maximum Likelihood (ML): suppose we have random variables X1, ..., Xn form a random sample from a discrete distribution whose joint probability distribution is P (x | φ) where x = (x1, ..., xn) is a vector in the sample and φ is a parameter from some parameter space (which could be a discrete set of values — say class membership). When P (x | ...

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimatio...

Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical proof of consistency by Wald holds for the MLE of evolutionary tree. Other proofs of consistency under various models were also proposed. Here we will discuss s...

in the last decades, rice yields in south asian countries grew tremendously in one hand and a noticeable yield fluctuation on the other. the objective of this study was to examine the rice yield distributions, estimate yield risks at country level, and compare risks between five countries namely afghanistan, bangladesh, nepal, sri lanka, and pakistan. anderson darling (ad) test was applied to t...

this paper investigates the multiplicative spread spectrum watermarking method for the image. the information bit is spreaded into middle-frequency discrete cosine transform (dct) coefficients of each block of an image using a generated pseudo-random sequence. unlike the conventional signal modeling, we suppose that both signal and noise are distributed with laplacian distribution, because the ...

in order to assess the satellite data for soil investigation, aster digital data 20 june 2006, field study and phisiochemical properties of soil, were analyzed. all landcover classes including soils are classified based onmorphological and physico-chemical characteristics. images were geocorrected and photomorphic units were selected based upon visual interpretation and sampling in study area. ...