Including individual as a independent random effect in the latent field is implemented the same way in INLA for all case studies in house sparrow population (Gaussian, binomial and Poisson). Note that in the Gaussian case study we have repeated measurements, i.e. possible several observation for each individual random effect, while in the binomial and Poisson cases there are only one observatio...

Gaussian numbers, also called Gaussian polynomials or q-binomial coefficients are the q-analogs of common binomial coefficients. First introduced by Euler these polynomials have played an important role in many different branches of mathematics. Sylvester discovered the unimodality of their coefficients, using invariant theory. Gauss recognized the connection of the coefficients to proper integ...

For a polynomial with palindromic coefficients, unimodality is equivalent to having a nonnegative g-vector. A sufficient condition for unimodality is having a nonnegative γ-vector, though one can have negative entries in the γ-vector and still have a nonnegative g-vector. In this paper we provide combinatorial models for three families of γ-vectors that alternate in sign. In each case, the γ-ve...

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions , the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total num...

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated in sections 2-4. In particular, it is shown thatˆd N − d = O P (Log N) 3 N , where d = (d 1 , d 2) denotes the long memory parameter.

The ^-binomial coefficient is a polynomial in q . Given an integer t and a residue class r modulo ;, a sieved ^-binomial coefficient is the sum of those terms whose exponents are congruent to r modulo /. In this paper explicit polynomial identities in q are given for sieved ij-binomial coefficients. As a limiting case, generating functions for the sieved partition function are found as multidim...