A random measure ~ defined on some measurable space (S,S) is said to be symmetrically distributed with respect to some fixed measure w on S, if the distribution of (~Al, ... ,~Ak) for kEN and disjoint AI" .. ,AkES only depends on (wAl, ... ,wAk). The first purpose of the present paper is to extend to such random measures (and then even improve) the results on convergence in distribution and alm...

Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T . We prove that T is exact: ∩ k=1 σ(T (S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scal...

Let Sn, n ∈ N be the simple random walk on Z, d ≥ 3. We denote by Px and Ex the probability measure and the expectation, respectively, of the random walk starting from position x. Independently of the random walk, we give ourselves a family of non-negative random variables V (x, ω), x ∈ Z that we call the potentials. We suppose that the potentials are independent and identically distributed, wi...

Statistical methodology is presented for the analysis of multiple events with random eeects and measurement error. We model multiple events in a general space using a random measure, and deene point process regression models with residual random eeects. Our approach to parameter estimation and signiicance testing is to start with a simple naive model of Poisson process regression, and then to a...

Random ferns is a very simple yet powerful classification method originally introduced for specific computer vision tasks. In this paper, I show that this algorithm may be considered as a constrained decision tree ensemble and use this interpretation to introduce a series of modifications allowing one to use Random ferns in a general machine learning problems. Moreover, I extend the method with...

There are several tasks where is preferable not responding than responding incorrectly. This idea is not new, but despite several previous attempts there isn’t a commonly accepted measure to assess non-response. We study here an extension of accuracy measure with this feature and a very easy to understand interpretation. The measure proposed (c@1) has a good balance of discrimination power, sta...

Measures of class separability can provide valuable insights into data, and suggest promising classification algorithms and approaches in data mining. We compare three simple class separability measures used in supervised machine learning. Their relative effectiveness is evaluated through their functional relationships and their random projections of data onto R for visualization. We conclude t...