On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Let S be a countable set and let Q = (q(ij), i, j is an element of S) be a conservative q-matrix over S with a single instantaneous state b. Suppose that we are given a real number mu >= 0 and a strictly positive probability measure m = (m(j), j is an element of S) such that Sigma(i is an element of S) m(i)q(ij) = -mu m(j), j 0 b. We prove that there exists a Q-process P(t) = (p(ij) (t), i, j E S) for which m is a mu-invariant measure, that is Sigma(i is an element of s) m(i)p(ij)(t) = e(-mu t)m(j), j is an element of S. We illustrate our results with reference to the Kolmogorov 'K 1' chain and a birth-death process with catastrophes and instantaneous resurrection.

MULTIPRED: A computational system for prediction of promiscuous HLA binding peptides

MULTIPRED is a web-based computational system for the prediction of peptide binding to multiple molecules ( proteins) belonging to human leukocyte antigens (HLA) class I A2, A3 and class II DR supertypes. It uses hidden Markov models and artificial neural network methods as predictive engines. A novel data representation method enables MULTIPRED to predict peptides that promiscuously bind multiple HLA alleles within one HLA supertype. Extensive testing was performed for validation of the prediction models. Testing results show that MULTIPRED is both sensitive and specific and it has good predictive ability ( area under the receiver operating characteristic curve A(ROC) > 0.80). MULTIPRED can be used for the mapping of promiscuous T-cell epitopes as well as the regions of high concentration of these targets termed T-cell epitope hotspots. MULTIPRED is available at http:// antigen.i2r.a-star.edu.sg/ multipred/.

Predicting the solvent accessibility of transmembrane residues from protein sequence

In this study, we propose a novel method to predict the solvent accessible surface areas of transmembrane residues. For both transmembrane alpha-helix and beta-barrel residues, the correlation coefficients between the predicted and observed accessible surface areas are around 0.65. On the basis of predicted accessible surface areas, residues exposed to the lipid environment or buried inside a protein can be identified by using certain cutoff thresholds. We have extensively examined our approach based on different definitions of accessible surface areas and a variety of sets of control parameters. Given that experimentally determining the structures of membrane proteins is very difficult and membrane proteins are actually abundant in nature, our approach is useful for theoretically modeling membrane protein tertiary structures, particularly for modeling the assembly of transmembrane domains. This approach can be used to annotate the membrane proteins in proteomes to provide extra structural and functional information.

Segmenting eukaryotic genomes with the generalized Gibbs sampler

Eukaryotic genomes display segmental patterns of variation in various properties, including GC content and degree of evolutionary conservation. DNA segmentation algorithms are aimed at identifying statistically significant boundaries between such segments. Such algorithms may provide a means of discovering new classes of functional elements in eukaryotic genomes. This paper presents a model and an algorithm for Bayesian DNA segmentation and considers the feasibility of using it to segment whole eukaryotic genomes. The algorithm is tested on a range of simulated and real DNA sequences, and the following conclusions are drawn. Firstly, the algorithm correctly identifies non-segmented sequence, and can thus be used to reject the null hypothesis of uniformity in the property of interest. Secondly, estimates of the number and locations of change-points produced by the algorithm are robust to variations in algorithm parameters and initial starting conditions and correspond to real features in the data. Thirdly, the algorithm is successfully used to segment human chromosome 1 according to GC content, thus demonstrating the feasibility of Bayesian segmentation of eukaryotic genomes. The software described in this paper is available from the author's website (www.uq.edu.au/similar to uqjkeith/) or upon request to the author.

Motor unit number estimation - A Bayesian approach

All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units.

Regression with input-dependent noise: A Gaussian process treatment

Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.

GTM through time

The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.

Using Bayesian neural networks to classify segmented images

We present results that compare the performance of neural networks trained with two Bayesian methods, (i) the Evidence Framework of MacKay (1992) and (ii) a Markov Chain Monte Carlo method due to Neal (1996) on a task of classifying segmented outdoor images. We also investigate the use of the Automatic Relevance Determination method for input feature selection.

Combining spatially distributed predictions from neural networks

In this report we discuss the problem of combining spatially-distributed predictions from neural networks. An example of this problem is the prediction of a wind vector-field from remote-sensing data by combining bottom-up predictions (wind vector predictions on a pixel-by-pixel basis) with prior knowledge about wind-field configurations. This task can be achieved using the scaled-likelihood method, which has been used by Morgan and Bourlard (1995) and Smyth (1994), in the context of Hidden Markov modelling

A scatterometer neural network sensor model with input noise

The ERS-1 satellite carries a scatterometer which measures the amount of radiation scattered back toward the satellite by the ocean's surface. These measurements can be used to infer wind vectors. The implementation of a neural network based forward model which maps wind vectors to radar backscatter is addressed. Input noise cannot be neglected. To account for this noise, a Bayesian framework is adopted. However, Markov Chain Monte Carlo sampling is too computationally expensive. Instead, gradient information is used with a non-linear optimisation algorithm to find the maximum em a posteriori probability values of the unknown variables. The resulting models are shown to compare well with the current operational model when visualised in the target space.

Bayesian inference for wind field retrieval

In many problems in spatial statistics it is necessary to infer a global problem solution by combining local models. A principled approach to this problem is to develop a global probabilistic model for the relationships between local variables and to use this as the prior in a Bayesian inference procedure. We show how a Gaussian process with hyper-parameters estimated from Numerical Weather Prediction Models yields meteorologically convincing wind fields. We use neural networks to make local estimates of wind vector probabilities. The resulting inference problem cannot be solved analytically, but Markov Chain Monte Carlo methods allow us to retrieve accurate wind fields.

Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Modelling frontal discontinuities in wind fields

A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior near-surface wind field models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in some cases these models are too smooth to reproduce real atmospheric features, such as fronts. At the scale of the scatterometer observations, fronts appear as discontinuities in wind direction. Due to the nature of the retrieval problem a simple discontinuity model is not feasible, and hence we have developed a constrained discontinuity vector Gaussian Process model which ensures realistic fronts. We describe the generative model and show how to compute the data likelihood given the model. We show the results of inference using the model with Markov Chain Monte Carlo methods on both synthetic and real data.