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Statistical Analysis of the Lifetime Mixture Models under Bayesian Approach

Thesis Info

Access Option

External Link

Author

Sultana, Tabasam

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Statistics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11258/1/Tabasam_Sultana_Statistics_HSR_2018_QAU_PRR.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727236531

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This thesis deals with statistical analysis of the lifetime mixture models under Bayesian approach. Type-I right censored sampling scheme is used. Choice of distribution is made keeping in view the originality and applicability. These contain Inverse Rayleigh, Gunmbel Type-II, Frechet, Inverse Weibull and Inverted Exponential distributions. These mixtures distribution have not been explored so far in Bayesian setup. Bayes estimators for the parameters of the mixture models are derived in closed form using type-I right censoring. To conduct Bayesian analysis, informative and noninformative priors are considered while three different loss functions, Squared error loss function, Precautionary loss function and DeGroot loss function are employed. A thorough simulation study is made to scrutinize the properties of proposed Bayes estimators. For the Inverse Weibull model, when all the parameters are unknown, Bayes estimators can not be gained in closed form, thus importance sampling technique is used to get the Bayes estimate in this case. For the elicitation of hyperparametrs , we used prior predictive and prior mean method. Limiting expressions of the Bayes estimators and their corresponding posterior risks are also derived. For the Inverse Weibull distribution, Bayes estimators and the posterior risks for reliability function are also discussed. Graphical representation of the simulation analysis results are also presented for each mixture model. Applications of these mixture models are also offered by applying a real data set in each case.
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سر آرتھر کونل ڈائل

سر آرتھر کونل ڈائل کی وفات
دو ماہ کی علالت کے بعد سر آرتھر کونل ڈائل نے ۷؍ جولائی ۱۹۳۰؁ء کو قلب کی بیماری میں انتقال کیا، شرلاک ہومس کے افسانوں کی وجہ سے ان کو جو عالمگیر شہرت حاصل ہوئی وہ محتاج بیان نہیں، آخری عمر میں انھیں روحوں کے ساتھ غایت درجہ کا اعتقاد ہوگیا تھا، وہ اسے ایک قسم کا مذہب خیال کرتے تھے، جس کی اہمیت ان کے نزدیک لٹریچر، فنون، لطفیہ، سیاسیات بلکہ دنیا کی ہر چیز سے زیادہ تھی اور انھیں اس بات سے تکلیف ہوتی تھی کہ لوگ ان کو شرلاک ہومس کے مصنف کے نام سے یاد کرتے ہیں۔ سر آرتھر کو بچپن ہی سے تصنیف کا شوق تھا، پہلی کتاب انھوں نے چھ سال کی عمر میں لکھی اور مدرسہ کے ابتدائی ساتھیوں میں بحیثیت افسانہ گو کے شہرت حاصل کی، بعد میں انھوں نے طب پڑھی اور کئی سال تک مطب کرتے رہے، مصنفوں کے زمرہ میں ان کا شمار اس وقت ہوا جب ۱۸۸۸؁ء میں انھوں نے ’’مائکا کلارک‘‘ لکھی، گزشتہ جنگ عظیم میں ان کا بڑا لڑکا مارا گیا اور اسی حادثے نے آخر عمر میں انھیں عالم ارواح کا دلدادہ بنادیا۔ (’’م ۔ ع‘‘، اکتوبر ۱۹۳۰ء)

 

Functional MRI Based Brain Mapping in Occipital Gyrus using Face Stimuli

Functional magnetic resonance imaging (fMRI) is one of the most powerful neuroimaging modalities due to its high spatio-temporal resolution characteristics. This known modality is applied on mapping the temporal, occipital, frontal cortices of the brain for localizing the neural activities generated due to any visual, physical or mental task or brain diseases or brain disorders. The occipital cortex is composed of middle, left, right, interior and exterior occipital gyrus and is responsible for visional function of human brain. The occipital gyrus reflects the neural image generated in the brain due to any visual activity. In this research paper, four different visual stimuli images of faces, scrambled, scenes and objects along with gap of blank space, forming a long sequence of stimuli observed by two female subjects, are experimented to examine and localize the most contrasting neural image generated in occipital gyrus of the brain. The visual fMRI brain data received from the two subjects is processed through fMRI-SPM12 toolbox based on Matlab software. In order to demonstrate the results statistically, two regressions such as T-contrast and F-contrast vectors are applied on fMRI images to highlight, and to localize the most active neural stimuli activities generated in the occipital gyrus of brain. In the results, it is demonstrated that maximum neural response can be mapped only for face stimulus in the bilateral occipital gyrus of the brain by applying T-contrast vectors regressions as when compared to other stimuli conditions and F-contrast vectors regressions. Further, it is also investigated that, the response of the face stimulus in F-contrast regressions achieved is somehow dispersed and unclear due to the large variances and interlinked communication of other stimuli or induced neural noises generated in entire volume of the brain.  Further from the given images, it is also investigated that the most reflecting and contrast area for any visual stimuli (such as face stimulus in this case) is either the middle or bilateral part of occipital gyrus of the human brain as identified through application of  T-contrast vectors regressions.

Development of an Indigenous Real Time Polymerase Chain Reaction for the Diagnosis of Malaria

INTRODUCTION Establishing highly sensitive, affordable diagnostic test covering all species of malaria is needed in countries like Pakistan that has significant prevalence of this disease. Conventional tests, like microscopy are widely used but it has certain performance related limitations. Rapid diagnostic tests (RDTs) for plasmodium have not achieved greater sensitivity than microscopy. Polymerase chain reaction (PCR) based methods have shown lot of promise and these are replacing microscopy as gold standard. OBJECTIVES To establish a real time PCR for malaria diagnosis and to compare its accuracy with microscopy and an antigen based RDT. STUDY DESIGN AND SETTING This cross sectional analytical study was conducted at Military Hospital and Armed forces Institute of Pathology Rawalpindi, Pakistan from January 2011 to December 2011. SUBJECTS The study included 300 clinically suspected patients of malaria. 3 METHODS Venous blood sample from each patient was tested for malarial parasite by microscopy and antigen detection assay (OptiMal). Parasite index was calculated. Plasmodium genus specific in house real time PCR, on all specimens was performed targeting small subunit rRNA gene. Diagnostic accuracy of three tests were compared and cost analysis done. RESULTS Out of 300 patients malaria parasite was detected in 110, 106 and 123 patients by microscopy, OptiMAL and PCR respectively. Real time PCR was 100% sensitive while microscopy and OptiMal had sensitivity of 89.4% and 86.2% respectively. All methods were 100% specific. The cost per test was 0.2, 2.75 and 3.30 US$ by microscopy, OptiMal and PCR respectively, excluding the once capital cost on PCR equipment. Conclusion: Real time PCR for diagnosis of malaria was successfully established. The technique is highly sensitive and affordable. It is recommended to be incorporated in the diagnostic algorithm for malaria in Pakistan. Key Words: Malaria, Microscopy, Rapid Diagnostic Tests (RDTs), Polymerase Chain Reaction (PCR).