Statistics and Operations Research

The Sloan Digital Sky Survey (SDSS) is an extremely large astronomical survey conducted with the intention of mapping more than a quarter of the sky (http://www.sdss.org/). Among the data it is generating are spectroscopic and photometric measurements, both allowing estimation of the redshift of galaxies. The former is precise but expensive to gather, the latter is far cheaper but correspondingly gives far less accurate estimates. A recent paper by describes various calibration techniques aiming to predict spectroscopic redshift from photometric measurements. In this paper, we investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds associated with the underlying redshifts and the classifications of the galaxies. We find that a quite generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly-tuned techniques already available in the astronomical literature.

Images are the source of information in many areas of scientific enquiry. A common objective in these applications is reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. In this article we consider the analysis of confocal fluorescence microscope images of cells in an area of cartilage growth. Biological questions posed by the experimenters concern the nature of the cells in the image and changes in their properties with time.

Recent articles have commented on the difficulty of proposing efficient reversible jump moves within MCMC. We suggest a new way to make proposals more acceptable using a secondary Markov chain to modify proposed moves -at little extra programming cost.

Summary.  The Sloan digital sky survey is an extremely large astronomical survey that is conducted with the intention of mapping more than a quarter of the sky. Among the data that it is generating are spectroscopic and photometric measurements, both containing information about the red shift of galaxies. The former are precise and easy to interpret but expensive to gather; the latter are far cheaper but correspondingly more difficult to interpret. Recently, Csabai and co-workers have described various calibration techniques aiming to predict red shift from photometric measurements. We investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds that are associated with the underlying red shifts and the classifications of the galaxies. We find that quite a generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly tuned techniques that are already available in the astronomical literature.

Images are the source of information in many areas of scientific enquiry. A common objective in these applications is reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. In this article we consider the analysis of confocal fluorescence microscope images of cells in an area of cartilage growth. Biological questions posed by the experimenters concern the nature of the cells in the image and changes in their properties with time.

Recent articles have commented on the difficulty of proposing efficient reversible jump moves within MCMC. We suggest a new way to make proposals more acceptable using a secondary Markov chain to modify proposed moves-at little extra programming cost. r

The speed of the random walk on a tree is the rate of escaping its starting point. It depends on the way that the branching occurs in the sense that if the average number of branching is large, the speed is more likely to be positive. The speed on some models of random trees is calculated via calculating the hitting times of the consecutive levels of the tree.

The commute time is a particular measure of random walks on weighted graphs. It has several nice properties which has been revealed independently partly or fully by many authors, see for example [5], [2], [3], [14], [21] and [1]. It is still in the focus of the research of computer scientists, probabilists and physicists as well.

The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of proposal. The first group of methods is based on an analysis of acceptance probabilities for jumps. Essentially, these methods involve a Taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to Langevin algorithms. The second group of methods generalizes the reversible jump algorithm by using the so-called saturated space approach. These allow the chain to retain some degree of memory so that, when proposing to move from a smaller to a larger model, information is borrowed from the last time that the reverse move was performed. The main motivation for this paper is that, in complex problems, the probability that the Markov chain moves between such spaces may be prohibitively small, as the probability mass can be very thinly spread across the space. Therefore, finding reasonable jump proposals becomes extremely important. We illustrate the procedure by using several examples of reversible jump Markov chain Monte Carlo applications including the analysis of autoregressive time series, graphical Gaussian modelling and mixture modelling.

In this paper we consider dynamic Bayesian models for four different pollutants: nitric oxide(NO), carbon monoxide(CO), sulphur dioxide(SO 2) and non-methane hydrocarbon (NCH 4) recorded daily in six different stations in Kuwait from 1999 to 2002. The structure of the models depends on time, space and pollutants dependencies. The approach strives to incorporate the uncertainty of the covariance structure into simulated models and final inference; therefore, hierarchical Bayesian model is applied. Association between level of pollutants and different meteorological variables, such as wind speed, wind directions, temperature and humidity are considered. The models will decompose into two main components: a deterministic part to represent the observed components term and a stochastic term to represent the unobservable components. Our analysis will start with basic model and gradually increase its complexity. At each stage the efficiency of the model will be measured. The resulting models subsequently are tested by comparing the output terms and by comparing and the predictions with the real observations.

Here, we first propose three-parameter model and call it as the compound zerotruncated Poisson normal (ZTP-N) distribution. The model is based on the random sum of N independent Gaussian random variables, where N is a zero truncated Poisson random variable. The proposed ZTP-N distribution is a very flexible probability distribution function. The probability density function can take variety of shapes. It can be both positively and negatively skewed, moreover, normal distribution can be obtained as a special case. It can be unimodal, bimodal as well as multimodal also. It has three parameters. An efficient EM type algorithm has been proposed to compute the maximum likelihood estimators of the unknown parameters. We further propose a four-parameter bivariate distribution with continuous and discrete marginals, and discuss estimation of unknown parameters based on the proposed EM type algorithm. Some simulation experiments have been performed to see the effectiveness of the proposed EM type algorithm, and one real data set has been analyzed for illustrative purposes.

Images are the source of information in many areas of scientific enquiry. A common objective in these applications is reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. In this article we consider the analysis of confocal fluorescence microscopeimages of cells in an area of cartilage growth. Biological questions posed by the experimenters concern the nature of the cells in the image and changes in their properties with time. Our model of the imaging process is based on a detailed analysis of the data. We treat the true scene as a realisation of a marked point process, incorporating this as the high-level prior model in a Bayesian analysis. Inference is by simulation using reversible jumpversions of Markov chain Monte Carlo (MCMC) algorithms which can handle the varying dimension of the image description arising

An important area of interest in microscopy may be the shape a nd spatial arrangement of the objects under study, aspects such size, i nteraction and orientation. Confocal fluorescence microscopy is a useful d evice for imaging three dimensional specimens because of its non-destructiv e and non-invasive nature which preserves such spatial information. However, imaging problems still arise; low signal-to-noise ratio, convolution by unk nown point spread functions and attenuation of the signal by the object under s tudy lead to degraded blurred images. The goal may be not only to enhance the visual appearance of the 3D images but also to give quantitative summaries of some of s hape parameters. This article attempts to tackle the complicated 3D deconvol uti n problem in a statistical framework using a Bayesian approach. Simulat ion techniques are required to make inference about the true scene given the 3D d ata. Interval estimates can be made of size and shape attributes from the po ...

The Sloan Digital Sky Survey (SDSS) is an extremely large astronomical survey conducted with the intention of mapping more than a quarter of the sky ( http://www.sdss.org/ ). Among the data it is generating are spectroscopic and photometric measurements, both allowing estimation of the redshift of galaxies. The former is precise but expensive to gather, the latter is far cheaper but correspondingly gives far less accurate estimates. A recent paper by Csabai et al. (2003) describes various calibration techniques aiming to predict spectroscopic redshift from photometric measurements. In this paper, we investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds associated with the underlying redshifts and the classifications of the galaxies. We find that a quite generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly...

Images are the source of information in many areas of scientific enquiry. A common objective in these applications is reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. In this article we consider the analysis of confocal fluorescence microscope images of cells in an area of cartilage growth. Biological questions posed by the experimenters concern the nature of the cells in the image and changes in their properties with time. Our model of the imaging process is based on a detailed analysis of the data. We treat the true scene as a realisation of a marked point process, incorporating this as the high-level prior model in a Bayesian analysis. Inference is by simulation using reversible jump versions of Markov chain Monte Carlo (MCMC) algorithms which can handle the varying dimension of the image description arising from an unknown number of cells, each with i...

We report methods for tackling a challenging 3D deconvolution problem arising in confocal microscopy. We implement Bayesian methods to produce automatic or semi-automatic segmentations showing the shape, size, orientation and spatial arrangement of objects in a sample. uncertainty about size and shape attributes. The methods also provide measures of The 3D problem is considerably more demanding computationally than the 2D analogue considered in Al-Awadhi et al. (2004) due to the much larger data set and higher dimensional descriptors for objects in the image. In using Markov chain Monte Carlo (MCMC) simulation to draw samples from the posterior distribution, substantial computing effort can be consumed simply in reaching the main area of support of the posterior distribution. For more effective use of computation time, we use morphological techniques to help construct an initial typical image under the posterior distribution.

Coronavirus (COVID-19) has continued to be a global threat to public health. When the coronavirus pandemic began early in 2020, experts wondered if there would be waves of cases, a pattern seen in other virus pandemics. The overall pattern so far has been one of increasing cases of COVID-19 followed by a decline, and we observed a second wave of increased cases and yet we are still exploring this pandemic. Hence, updating the prediction model for the new cases of COVID-19 for different waves is essential to monitor the spreading of the virus and control the disease. Time series models have extensively been considered as the convenient methods to predict the prevalence or spreading rate of the disease. This study, therefore, aimed to apply the Autoregressive Integrated Moving Average (ARIMA) modelling approach for predicting new cases of coronavirus (COVID-19). We propose a deterministic method to predict the basic reproduction number R o of first and second wave transition of COVID-19 cases in Kuwait and also to forecast the daily new cases and deaths of the pandemic in the country. Forecasting has been done using ARIMA model, Exponential smoothing model, Holt's method, Prophet forecasting model and machine learning models like log-linear, polynomial and support vector regressions. The results presented aligned with other methods used to predict R o in first and second waves and the forecasting clearly shows the trend of the pandemic in Kuwait. The deterministic prediction of R o is a good forecasting tool available during the exponential phase of the contagion, which shows an increasing trend during the beginning of the first and second waves of the pandemic in Kuwait. The results show that support vector regression has achieved the best performance for prediction while a simple exponential model without trend gives good optimal results for forecasting of Kuwait COVID-19 data.

In this paper we provide exact formula for the commute times of random walks on spherically symmetric random trees. Using this formula we sharpen some of the results presented in Al-Awadhi et al. to the form of equalities rather than inequalities.

Introduction: This study compared the bronchoprotective and benefit/risk profiles of various inhaled corticosteroid (ICS) dosing regimens in mild asthma. Methods: A pharmacokinetic/pharmacodynamic model was developed and validated describing the relationship between ICS dose and time-course for airway bronchoprotection, [provocative concentration of adenosine monophosphate (AMP) causing C 20% decline in forced expiratory volume in 1 s (FEV 1) (AMP PC 20)], for fluticasone furoate (FF), fluticasone propionate (FP) and budesonide (BUD). For regular ICS maintenance therapy (100% and 50% adherence) and infrequent or as-needed use (dosing 3-4 times per week), treatment effectiveness was expressed as percent time during 28 days when bronchoprotection exceeded either the threshold for a treatment-related bronchoprotective effect (AMP PC 20 C 0.25 doubling dose) or the threshold for a clinically significant bronchoprotective effect (AMP PC 20 C 1.0 doubling dose). This value was divided by the total ICS dose administered expressed in prednisolone equivalents to give a therapeutic index (TI). Results: The model-predicted time course of ICS-induced bronchoprotection with regular daily maintenance dosing and 100% adherence showed that all ICS at the highest recommended doses for mild asthma exceeded the threshold for clinically significant bronchoprotective effect for all or most of the 28-day dosing period, mean (90% CI); 100% (96.1-100), 99.9% (8.0-100) and 100% (58.2-100) with TI values of 16.9, 6.6 and 5.4 for FF 100 lg OD, FP 200 lg BID and BUD 200 lg BID, respectively. For simulated poor adherence (50%) to regular daily maintenance therapy, corresponding mean (90% CI) values were; 75.7% (39.4-89.1), 52.3% (0.7-69.2) and 51.3% (28.6-58.3) with TI values of 25.7, 6.9 and 5.6. For simulated infrequent/as needed use the corresponding values were;