A Multiple optimal stopping rule for a buying–selling problem with a deterministic trend

We consider a buying–selling problem with the finite time horizon when several stops of a sequence of independent random variables can be made. The objective is to find an optimal sequential procedure which maximizes the total expected revenue. In this paper, we obtain an optimal stopping rule and the value of a game.13 page(s

Evaluating optimal stopping rules in the multiple best choice problem using the cross-entropy method

Best choice problems can be considered one of the most interesting problems of sequential decision analysis. Problems of this type can arise in a wide variety of fields, including psychological, economical, and ecological applications. In this study, we consider a generalization of the best choice problem when it is possible to make more than one choice. We use the Cross-Entropy method to determine the optimal stopping rules and the value of a game. We include results of numerical experiments illustrating the effectiveness of the approach. We obtain estimates of the thresholds in the optimal stopping rules and compare the accuracy of these estimates with those obtained via asymptotic approximation.8 page(s

A hybrid genetic algorithm for change-point detection in binary biomolecular sequences

Genomes of eukaryotic organisms vary in GC ratio, that is, share of DNA bases such that C or G as contrary to T or A. Statistical identification of segments that are internally homogenous with respect to GC ratio is essential for understanding of evolutionary processes and the different functional characteristics of the genome. It appears that DNA segmentation concerns one of the most important applications involving change-point detection. Problems of this type arise in various areas, such as speech and image processing, biomedical applications, econometrics, industry and seismology. In this study, we develop a hybrid genetic algorithm for detecting change-points in binary sequences. We apply our algorithm to both synthetic and real data sets, and demonstrate that it is more effective than other well-known methods such as Markov chain Monte Carlo, Cross-Entropy and Genetic algorithms.8 page(s

Asymptotic Duration for Optimal Multiple Stopping Problems

We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations

On Asymptotics of Optimal Stopping Times

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions

Analysis of correlation structure in bilateral traits

When studying asymmetry of bilateral traits, it is very important to take into account their correlation structure. The assumption for quadrivariate normal distribution of traits considers possible models of equality of four correlation coefficients between traits using different criteria and approaches on the basis of two large lamina samples (N₁=500, N₂=521) of drooping birch (Betula pendula Roth.). This study has shown that different traits give evidence of different models of correlation structure.17 page(s

Statistical analysis of spatial distribution in populations of microspecies of Alchemilla L

In this paper, we consider Alchemilla vulgaris L. (or common lady's mantle), which is an herbaceous perennial plant. It is known that within this species it is possible to distinguish microspecies, that is, fairly homogeneous groups having minor morphological differences. We study spatial distributions of the microspecies found in various localities as well as possible interaction between different microspecies.4 page(s

The Analysis of ontogenetic spectrum of heterogeneous population

The distribution of discrete ontogenetic states of individuals is usually spatially and temporally different within a population. If a sample from the population sample consists of several subsamples, the comparison of their ontogenetic spectra reveals heterogeneity of samples, i.e. different subsamples cannot be described by the same polynomial distribution. Therefore, the comparison of the samples using the aggregate data is not correct and tends to result in false inferences of biological importance. The paper proposes three methods for comparison of ontogenetic spectra of heterogeneous samples: a randomized variant of ANOVA, principal components analysis and ordinal regression analysis. The following approaches are exemplified in natural populations of cowberry Vaccinium vitis-idaea L. and epiphytic lichens Hypogymnia physodes (L.) Nyl. and Pseudevernia furfuracea (L.) Zopf.19 page(s