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Sampling

Use of Rqubit in Probabilistic Sampling and Statistical Simulation

Introduction to Sampling

Sampling is the core of research analysis and design for any industry as researchers are striving to be able to generalize their findings and to conclude a potential solution, which is often referred as external validity. In order to obtain representativeness in obtained result and to identify statistically significant associations or differences in a population, choice of appropriate sample size and sample method is the ‘key’. Unconscious bias, which could have reflected in true collected data, can be avoided through proper representativeness in a sample, as sample representation has a very high impact factor to generalize the findings obtained from a sample.
 
Big Data and its vulnearability for Potential Bias
Big data analytics deals with integrating information from many thousands of data sources, which automatically creates susceptibility of obtained data to sampling error, aggregation error, measurement error, comparison error and many more. The amount of random sampling error is often expressed in terms of a statistic called margin of error which is highly correlated to the sample size.
The larger the margin of error, the greater is the probability of misinterpretations from the survey outcome. A positive value of margin of error indicates incompletely sampled population indicating a variation of observed values from theoretical values. Margin of error can be reduced drastically with increase in sample size. The following graph depicts the inverse relationship of the same.

Larger Sample Size – a Trade off between Statistical Power and Statistical Cost

The interdependence among sample size, margin of error, uncertainty, and precision is quite evident from the above graph. Larger sample sizes provide more accurate mean values, identify outliers responsible for skewing the dataset in a smaller sample and provide a smaller value of margin of error. In order to fully reflect the correct population mean, a larger sample size is contemplated of, but not always, as it incorporates huge time and cost consumption. Moreover, outliers captured in a sampling of large datasets often tend to complicate the analysis of statistical data. Statistical simulation often demands overrepresentation of population data in a population, which consequently incorporates the need of larger sample size. Well distributed data collection from a large sample size requires high financial involvement for succesful execution of the process. A true random sampling is indeed a viable solution used to cull a smaller sample size from a larger population to minimize sampling bias by systematically reducing the tendency of a sample statistic to overestimate or underestimate a population parameter. Now consider a health service research survey, error containment in determinants will put a cautionary note on impactful inferential errors.

Sampling bias over large data is a potential threat to magnified precision deviation – Case Study

Electronic Health Records (EHRs) to store the information obtained from patients in community settings, is a viable solution for future term epidemiologic research growth. As a consequence, the proposal to build an EHR based on The National Patient-Centred Clinical Research Network (PCORnet) had been greeted in the US with huge affinity. Sampling bias had affected a substantial portion of the US population to be restrained from having insurance benefits (About 40% of patients have their medical details recorded in EHR). Another survey made on Large Nurses Health Study with a tenure of 10 years made on 48,470 post menopausal women with age ranging from 30 to 63 years, had reported that the use of hormone replacement therapy plays a major role to reduce the rate of serious coronary heart disease by 50%. Despite the use of an enormous sample size to reduce sampling error, the study failed to identify the atypical, unconventional mode of sample and consequently made a perplexed portfolio of estrogen therapy use with common beneficial health habits. According to Women’s Health Initiative (WHI), estrogen replacement could be a potential threat causing risk for heart disease and hence the results of the investigation did not map to WHI. This happened due to incomplete reflection of the representativeness of chosen samples, as the study was unable to include new hormone replacement users due to lack of randomness in sample selection. A large sample size might actually magnify the bias or error if the underlying sampling model is wrong.
Rendering True Randomness – Absolution for Potential Bias

Random selection yields in the unfavored selection of samples from the population, without the realization of a sampler.

Randomness allows an impersonal choice of sample selection.

Random sampling helps to produce representative samples through the elimination of voluntary response bias and guarding against undercoverage bias.

Unbiased research causes a minimized form of risk of error containment.

True randomness helps to exhaust the whole population to pick up sample representatives, hence achieving error-free mapping of samples into the entire population base.

 
Pseudo-Random Number Generator – A poisoned chalice for probabilistic sampling and statistical simulation
Pseudo random number generators rely on mathematics and algorithmic computation to generate unbiased sequence apparently. This apparent behavior is derived from inherent tendency of random pattern detectability and generation of statistically correlated random samples, if simulated for a longer period on a huge data set. This determinism will caude hindrance in offering of equiprobable selection chances through uniformity in sample distribution. ‘Quantum Random Number Generator – Rqubit is the answer!’
 
Quantum offers true randomness – Rqubit, unleashing the inherent non-determinism to feed statistical inferences
Quantum computing is a probabilistic approach of computing, which offers unprecedented growth in computing through parallelism. Quantum phenomena are inherently random, resulting in generation of true random bits, which eventually will be free from any non-uniformity or biasedness resulting in negligible statistical error and correctness in research conclusions. Our product Rqubit harnesses the power of quantum information processing to generate full-entropy, scalable random bits, which can be a seed for statistical simulation and probabilistic sampling.

Rqubit – Technical Specifications for Statistical Agencies and compliance Details