Review of "“Evidence-Based Statistics" by Cahusac

In press, Journal of the Royal Statistical Society: Series A (Statistics in Society) Review of "“Evidence-Based Statistics: An Introduction to the Evidential Approach - from Likelihood Principle to Statistical Practice”; Cahusac, Peter "

Probing Gravitational Waves from Pulsars in Brans–Dicke Theory

This paper comprises the theoretical background for the data analysis of gravitational waves (GWs) from spinning neutron stars in Brans–Dicke (BD) theory. Einstein’s general theory of relativity (GR) predicts only two tensor polarization states, but a generic metric theory of gravity can also possess scalar and vector polarization states. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third one is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters.

Performance enhancement techniques for variable spreading factor OFCDM systems

n this thesis we investigate the effect of Carrier Frequency Offset (CFO) on the performance of downlink Variable Spreading Factor (VSF) OFCDM systems when subcarrier grouping is used. An analytic expression of the SINR is derived for downlink VSF-OFCDM with CFO for the case of maximal ratio combining receiver. Numerical results show that, when the total spreading factor is fixed, the VSF-OFCDM system with higher frequency domain spreading factor is more sensitive to CFO than that with lower frequency domain spreading factor. Due to the adverse impact of the CFO on VSF-OFCDM systems, we propose a correction scheme based on the maximum likelihood principle. We derive the likelihood function for VSF-OFCDM system with CFO and use a gradient algorithm to estimate and minimize the effect of CFO in a tracking mode. Our results show that the BER performance in the low SNR environment can be improved significantly with few number of iterations for different spreading factors. We also propose a threshold-based group-adaptive modulation algorithm used with an adaptive subcarrier allocation technique for downlink VSF-OFCDM to increase the spectral efficiency for a given target BER. The proposed algorithm provides an increase in spectral efficiency without increasing the total transmit power for different spreading factors with and without coding.

Performance enhancement techniques for variable spreading factor OFCDM systems

n this thesis we investigate the effect of Carrier Frequency Offset (CFO) on the performance of downlink Variable Spreading Factor (VSF) OFCDM systems when subcarrier grouping is used. An analytic expression of the SINR is derived for downlink VSF-OFCDM with CFO for the case of maximal ratio combining receiver. Numerical results show that, when the total spreading factor is fixed, the VSF-OFCDM system with higher frequency domain spreading factor is more sensitive to CFO than that with lower frequency domain spreading factor. Due to the adverse impact of the CFO on VSF-OFCDM systems, we propose a correction scheme based on the maximum likelihood principle. We derive the likelihood function for VSF-OFCDM system with CFO and use a gradient algorithm to estimate and minimize the effect of CFO in a tracking mode. Our results show that the BER performance in the low SNR environment can be improved significantly with few number of iterations for different spreading factors. We also propose a threshold-based group-adaptive modulation algorithm used with an adaptive subcarrier allocation technique for downlink VSF-OFCDM to increase the spectral efficiency for a given target BER. The proposed algorithm provides an increase in spectral efficiency without increasing the total transmit power for different spreading factors with and without coding.

Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises

As a special class of nonlinear systems, bilinear systems can naturally describe many industrial production process. This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle and the negative gradient search principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For further improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example. The simulation results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.

stochprofML: stochastic profiling using maximum likelihood estimation in R

Background Tissues are often heterogeneous in their single-cell molecular expression, and this can govern the regulation of cell fate. For the understanding of development and disease, it is important to quantify heterogeneity in a given tissue. Results We present the R package stochprofML which uses the maximum likelihood principle to parameterize heterogeneity from the cumulative expression of small random pools of cells. We evaluate the algorithm’s performance in simulation studies and present further application opportunities. Conclusion Stochastic profiling outweighs the necessary demixing of mixed samples with a saving in experimental cost and effort and less measurement error. It offers possibilities for parameterizing heterogeneity, estimating underlying pool compositions and detecting differences between cell populations between samples.

An All-Batch Loss for Constructing Prediction Intervals

The prediction interval (PI) is an important research topic in reliability analyses and decision support systems. Data size and computation costs are two of the issues which may hamper the construction of PIs. This paper proposes an all-batch (AB) loss function for constructing high quality PIs. Taking the full advantage of the likelihood principle, the proposed loss makes it possible to train PI generation models using the gradient descent (GD) method for both small and large batches of samples. With the structure of dual feedforward neural networks (FNNs), a high-quality PI generation framework is introduced, which can be adapted to a variety of problems including regression analysis. Numerical experiments were conducted on the benchmark datasets; the results show that higher-quality PIs were achieved using the proposed scheme. Its reliability and stability were also verified in comparison with various state-of-the-art PI construction methods.

Classification from positive and unlabeled data based on likelihood invariance for measurement

We propose novel approaches for classification from positive and unlabeled data (PUC) based on maximum likelihood principle. These are particularly suited to measurement tasks in which the class prior of the target object in each measurement is unknown and significantly different from the class prior used for training, while the likelihood function representing the observation process is invariant over the training and measurement stages. Our PUCs effectively work without estimating the class priors of the unlabeled objects. First, we present a PUC approach called Naive Likelihood PUC (NL-PUC) using the maximum likelihood principle in a nontrivial but rather straightforward manner. The extended version called Enhanced Likelihood PUC (EL-PUC) employs an algorithm iteratively improving the likelihood estimation of the positive class. This is advantageous when the availability of the labeled positive data is limited. These characteristics are demonstrated both theoretically and experimentally. Moreover, the practicality of our PUCs is demonstrated in a real application to single molecule measurement.