An updated discussion on physical and mathematical aspects of the ergodic hypothesis in classical equilibrium statistical mechanics is presented. Then a practical attitude for the justification of the microcanonical ensemble is indicated. It is also remarked that the difficulty in proving the ergodic hypothesis should be expected.

This paper presents hypothesis mixture decoding (HM decoding), a new decoding scheme that performs translation reconstruction using hypotheses generated by multiple translation systems. HM decoding involves two decoding stages: first, each component system decodes independently, with the explored search space kept for use in the next step; second, a new search space is constructed by composing ...

This paper provides a rationalization for using classical one-sided hypothesis tests for approving innovations, such as new drugs or treatment programs. I consider statistical testing as a strategy of the regulator in a game against informed proponents who can profit from the regulator’s acceptance decision even for ineffective innovations. Lower test size deters proponents from attempting cost...

We propose a set of novel methodologies which enable valid statistical hypothesis testing when we have only positive and unlabelled (PU) examples. This type of problem, a special case of semi-supervised data, is common in text mining, bioinformatics, and computer vision. Focusing on a generalised likelihood ratio test, we have 3 key contributions: (1) a proof that assuming all unlabelled exampl...

In this paper we address the problem of identifying differences between populations of trees. Besides the theoretical relevance of this problem, we are interested in testing if trees characterizing protein sequences from different families constitute samples of significantly different distributions. In this context, trees are obtained by modelling protein sequences as Variable Length Markov Cha...

In this paper we show how the present day fast computer could solve non-standard old statistical problems. In most cases statisticians work with approximations of test statistics distributions, and then use respective statistical tables. When approximations do not work the problem is usually tabled. We propose such simulation approach which we do believe could be helpful in many case. The probl...

The word " five " is missing from the third sentence of the fifth paragraph in the online answers to this Endgames article by Philip Sedgwick (BMJ 2014;349:g5310, doi:10.1136/bmj. g5310). The sentence should have read: " For example, the probability of a significant result when there are two, three, four, and five hypothesis tests is 0.

In comparing or assessing methods of treatment it is vital that the appropriate number of patients is selected in order to ensure that the conclusions drawn are statistically viable. This annotation describes the relevance of a statistical power analysis in the context of hypothesis testing to the determination of the optimal sample size of a study. The power of the test indicates how likely it...