Regression modelling with I-priors

We introduce the I-prior methodology as a unifying framework for estimating a variety of regression models, including varying coefficient, multilevel, longitudinal models, and models with functional covariates and responses. It can also be used for multi-class classification, with low or high dimensional covariates. The I-prior is generally defined as a maximum entropy prior. For a regression function, the I-prior is Gaussian with covariance kernel proportional to the Fisher information on the regression function, which is estimated by its posterior distribution under the I-prior. The I-prior has the intuitively appealing property that the more information is available on a linear functional of the regression function, the larger the prior variance, and the smaller the influence of the prior mean on the posterior distribution. Advantages compared to competing methods, such as Gaussian process regression or Tikhonov regularization, are ease of estimation and model comparison. In particular, we develop an EM algorithm with a simple E and M step for estimating hyperparameters, facilitating estimation for complex models. We also propose a novel parsimonious model formulation, requiring a single scale parameter for each (possibly multidimensional) covariate and no further parameters for interaction effects. This simplifies estimation because fewer hyperparameters need to be estimated, and also simplifies model comparison of models with the same covariates but different interaction effects; in this case, the model with the highest estimated likelihood can be selected. Using a number of widely analyzed real data sets we show that predictive performance of our methodology is competitive. An R-package implementing the methodology is available (Jamil, 2019)

Regression modelling using priors depending on Fisher information covariance kernels (I-priors)

Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. In this thesis, we explore a novel methodology for fitting a wide range of parametric and nonparametric regression models, called the I-prior methodology (Bergsma, 2018). We assume that the regression function belongs to a reproducing kernel Hilbert or Kreĭn space of functions, and by doing so, allows us to utilise the convenient topologies of these vector spaces. This is important for the derivation of the Fisher information of the regression function, which might be infinite dimensional. Based on the principle of maximum entropy, an I-prior is an objective Gaussian process prior for the regression function with covariance function proportional to its Fisher information. Our work focusses on the statistical methodology and computational aspects of fitting I-priors models. We examine a likelihood-based approach (direct optimisation and EM algorithm) for fitting I-prior models with normally distributed errors. The culmination of this work is the R package iprior (Jamil, 2017) which has been made publicly available on CRAN. The normal I-prior methodology is subsequently extended to fit categorical response models, achieved by “squashing” the regression functions through a probit sigmoid function. Estimation of I-probit models, as we call it, proves challenging due to the intractable integral involved in computing the likelihood. We overcome this difficulty by way of variational approximations. Finally, we turn to a fully Bayesian approach of variable selection using I-priors for linear models to tackle multicollinearity. We illustrate the use of I-priors in various simulated and real-data examples. Our study advocates the I-prior methodology as being a simple, intuitive, and comparable alternative to similar leading state-of-the-art models

Development of animal feed from waste to wealth using Napier Grass and Palm Acid Oil (PAO) from Palm Oil Mill Effluent (POME)

This study is to investigate the effectiveness of feeding cattle with a mixture of palm acid oil (PAO) from palm oil mill effluent (POME), water lettuce, coconut waste and Napier grass. These materials will be mixed and form a feed formulation. This study also wants to develop a cattle feed that will help to reduce the water lettuce and coconut waste negative impact to the environment. Besides that, the best formulation of the cattle feed will be determined. The amount of each material will be different for each formula. This cattle feed will use the waste to follow the Green Technology. The formulation of the feed is based from Department of Veterinary Services Feeding Guide book. This study is focus on reducing the negative impact to the environment by utilizing the waste of POME, coconut waste and water lettuce. There are three formulation that was tested on cattle to determine the most suitable formulation. The formulation has different amount of each material. The nutrient in each formulation was calculated based on feeding guides by Department of Veterinary entitled nutrient composition of Malaysian feed materials and guides to feeding of cattle and goats. There are four cattle that was involved in this study. Three cattle were fed with the formulation. Meanwhile, the other one was fed with its regular feeds which is Napier Grass only and act as the control. The result obtained will be compared with the control cattle. The feed intake of each cattle was recorded. The result shows that the formulation is good for high growth performance of the cattle compare to the regular feeds. This is because the formulation has more nutrients in it. In fact, it has more nutrient than the cattle need to grow. The control cattle did not gain as much as formulation A. Thus, this prove that the formulation is effective compare to the regular feeds and it is cheaper. Apart from that, the high growth performance can help to cater the high demand of meats consumption

Phytoremediation: Treating Euthrophic Lake at KotaSAS Lakeside, Kuantan by Aquatic Macrophytes

This investigation was embraced ex-situ to investigate the capability of the submerged plants' water hyacinth (Eichornia crassipes) and water lettuce (Pistia stratiotes L.) as phytoremediation aquatic macrophytes for nutrients removal from a eutrophic lake situated at KotaSAS Lakeside surrounded by residential area as the risk of algae bloom can be avoided. The present of mankind activities such as sewage runoff and agricultural towards water bodies, the eutrophication process being speed up. The capability of these plants to evacuate certain parameters not just supplements while additionally including BOD5, COD, TSS, Turbidity, and heavy metals. The technique for investigation of lake water was alluded by Standard Method for Examination of Water and Wastewater. Water lettuce displayed extraordinary nitrate removal effectiveness up to 94% however this plant species shrivelled from week 2 of the examination because of an absence of nitrate supply and caused an expansion in phosphorus concentration. Then, water hyacinth indicates relentless evacuation productivity with a normal of 82% for nitrate and phosphorus. Other than that, water hyacinth indicates 88% and 72% of TSS and turbidity expulsion effectiveness which can improve the clarity of lake water. With this accomplishment gained in phytoremediation innovation utilizing water hyacinth, it is of most significance for this innovation to be executed in bigger scales in the future

Study of palm acid oil (PAO) from sludge palm oil mill effluent (POME) as goat’s feed

This study was conducted to determine the base dietary of animal feed for goat by utilizing solid waste and to investigate the effectiveness of different dietary of solid waste effect on growth performance of goats. Palm Acid Oil (PAO), Napier grass, coconut waste and water lettuce were used as the sample to produce animal feed for goats. POME is produced during palm oil mill process [1]. PAO is produced during the extracted process of POME. The solid waste produced has caused the pollution problem to the environment. The solid waste undergoes composting method to produce animal feed which is useful to the growth of goat. All these samples were collected and mixed by following the guideline book of title Nutrient Composition of Malaysian Feed Materials and Guides to Feeding of Cattle and Goats by Department of Veterinary Services Ministry of Agriculture and Argo-based Industry Malaysia [2]. Four adult does with an age of 6 months and weighting 23.30 ± 2.47 kg were used then fed with the dietary treatments for 14 days for adaptation and continued until the end of the study, which lasted for 120 days. The 3 indicators to be analysed were the growth performance and body weight gain (BWG) of goats, also the nutrient requirement by goats. In this study, 3 dietary treatments were used (D1, D2, D3) to be compared with control diet (CD). Each diet contains different nutrient and composition. All these samples have nutrient needed by the goat and have a big potential to produce an animal feed. Results showed that goat that takes D1 has the highest growth performance and body weight gain (BW)

Pairwise likelihood estimation for confirmatory factor analysis models with categorical variables and data that are missing at random

Methods for the treatment of item non-response in attitudinal scales and in large-scale assessments under the pairwise likelihood (PL) estimation framework and under a missing at random (MAR) mechanism are proposed. Under a full information likelihood estimation framework and MAR, ignorability of the missing data mechanism does not lead to biased estimates. However, this is not the case for pseudo-likelihood approaches such as the PL. We develop and study the performance of three strategies for incorporating missing values into confirmatory factor analysis under the PL framework, the complete-pairs (CP), the available-cases (AC) and the doubly robust (DR) approaches. The CP and AC require only a model for the observed data and standard errors are easy to compute. Doubly-robust versions of the PL estimation require a predictive model for the missing responses given the observed ones and are computationally more demanding than the AC and CP. A simulation study is used to compare the proposed methods. The proposed methods are employed to analyze the UK data on numeracy and literacy collected as part of the OECD Survey of Adult Skills

Treatment of Eutrophic KotaSAS Lake by Phytoremediation using Macrophytes Species; Eichhornia Crassipes and Pistia Stratiotes

The wastewater treatment is known as a necessary attention for the process of retreatment towards the removal of suspended solids. Phytoremediation is a plant-based system which directly used of green plant in-situ to reduce pollutants in the lakes. This method is ecologically friendly and solar dependent clean-up technology. This study was undertaken ex situ where the aim of this study is to treat the eutrophic man-made lake at KotaSAS lakeside through following objectives; to identify the variation of physicochemical attributes of KotaSAS lake water through phytoremediation, to evaluate the potential of selected heavy metals and nutrients removal (nitrate and phosphorus) using Eichornia crassipes (water hyacinth) and Pistia stratiotes (water lettuce) and to determine the correlations between sampling points and physicochemical attributes using statistical analysis.. The method of analysis of lake water was referred by Standard Method for Examination of Water and Wastewater by APHA. Then, statistical notation was conducted on the results obtained to identify the accuracy and validity of data, which in this case, correlations and t-test statistical method was used. Referring to the statistical notation of (p<0.05), conclusion on the significance of the result and variables were made. It is justified statistically that the data obtained for each treatment using different types of plants are valid and concise. As a result, it is found that water lettuce and water hyacinth have different nutrients removal and heavy metals removal efficiency but, in all cases,, these phytoremediation agents exhibited nutrients removal efficiency from the range of 27% up to 58% followed by heavy metals removal efficiency from the range of 23% up to 60%. Water hyacinth exhibited great nitrate and phosphorus removal efficiency, 51.51% and 58.81% whereby as for water lettuce exhibited great heavy metals removal efficiency for manganese (Mn), iron (Fe) and copper (Cu), 60.68%, 58.2% and 26.4% respectively. With this achievement acquired in phytoremediation technology employing water hyacinth, it is of utmost important for this technology to be implemented in larger scales thereafter. Hence, this plant is suitable to be used in controlling eutrophic lake due to its hyper-accumulating ability

Man-Made Lake of Taman Pertanian, Kuantan: The Valuation of Water Quality and Nutrient Removal by Using Hydrilla Verticillata Sp. and Myriophyllum Aquaticum Sp. as Submerged Plant Species

Polluted water caused by the impact of eutrophication process known as essential negative impacts by the impedance of cyanobacterial species towards the spread of biomass in a freshwater biological system. Phytoremediation is a built utilization of green plants in order the evacuate natural contaminants. The goal of study was to assess the chosen submerged plant species towards supplement expulsion coming from treated lake water in execution light and capacities. The types of submerged plant species used includes Hydrilla Verticillata Sp. (Esthwaite Waterweed) and Myriophyllum Aquaticum Sp. (Parrot’s Feathers) which is to evacuate contaminants in water utilizing phytoremediation process. The study was conducted seven times whereby time gap for every study was seven days. A total of 7 parameters includes Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Dissolved Oxygen (DO), Suspended Solid (SS), turbidity, pH, and Nitrite as for water quality evaluation. The comparison on the effectiveness of submerged plant species to evacuate and remediate contaminant substances shown Hydrilla Verticillata Sp. as the best plant in removing the contaminant based on the percentage of contaminant removal BOD = 66.72%; COD = 77.78%; TSS = 55.55% and Turbidity = 0.57%. In conclusion, there are significant changes before and after treatment from both plants

Peat Swamp Groundwater Treatment: Efficiency of Mixed Citrus Peel and Kernel Activated Carbon Layer

One of the natural water resources is groundwater. Groundwater is another alternative to meet the increasing water demand in Malaysia. Then, the decrease in supplying raw groundwater which may due to depletion of groundwater and hence it is important to maintain the availability of water supply locally and even establish new water source such as from peat swamp to overcome future water crisis. Activated carbon is famous for its characteristic in eliminating various organic contaminants. In this investigation, low cost mixed activated carbon of food waste (citrus peel) and agricultural waste (palm kernel shell) are used as adsorbents in biological sand filter to treat peat swamp groundwater whereby the overall aim of study to evaluate the performance of mixed activated carbon layer of citrus peel and kernel in biological sand filter for peat swamp groundwater treatment.The mixed activated carbon with 1:1 ratio is filled into the biological sand filter. The efficiency of the mixed activated carbon layered biological sand water treatment system is evaluated using parameters pH, Turbidity, Chemical Oxygen Demand (COD), Biological Oxygen Demand (BOD), Total Suspended Solids (TSS) and E. coli and removal of heavy metal ions of peat swamp groundwater. All these parameters follow the Standard Methods for Examination of Water and Wastewater 2005. The implementation of investigation improved the water quality of the peat swamp groundwater, the water treatment technology using combination of activated carbon and biosand filter, human living standards by providing safe and clean water supply