scholarly journals Statistical inferences about injury and persistence of environmentally stressed bacteria

1975 ◽  
Vol 74 (2) ◽  
pp. 149-155 ◽  
Author(s):  
Martin A. Hamilton ◽  
Gary K. Bissonnette
Keyword(s):  
Statistical Inference ◽  
Poisson Distribution ◽  
Statistical Methods ◽  
Standard Technique ◽  
Binomial Data ◽  
Selective Media ◽  
Statistical Inferences ◽  
Table Data

SUMMARYA standard technique for ascertaining the survival characteristics of bacteria after being environmentally stressed is to incubate the bacteria on both selective and non-selective media and count the colonies produced. Based on these colony counts, indexes of injury and persistence of the bacteria are calculated. To compare the stress of two different environments, a persistence ratio is calculated. In this paper, methods of statistical inference concerning these indexes and ratios are presented. These statistical methods use well-known procedures for analysis of binomial data and 2 × 2 table data, and are appropriate when the colony counts follow a Poisson distribution.

scholarly journals Simple methods for estimating confidence levels, or tentative probabilities, for hypotheses instead of p values

2019 ◽  
Vol 12 (1) ◽  
pp. 205979911982651
Author(s):  
Michael Wood
Keyword(s):  
Statistical Inference ◽  
Confidence Intervals ◽  
Statistical Methods ◽  
Null Hypothesis ◽  
Significance Tests ◽  
P Values ◽  
Confidence Levels ◽  
Alternative Approach ◽  
Degree Of Certainty ◽  
Natural Way

In many fields of research, null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious concerns about the suitability of p values for this purpose. An alternative approach is to cite confidence intervals for a statistic of interest, but this does not directly tell readers how certain a hypothesis is. Here, I suggest how the framework used for confidence intervals could easily be extended to derive confidence levels, or “tentative probabilities,” for hypotheses. I also outline four quick methods for estimating these. This allows researchers to state their confidence in a hypothesis as a direct probability, instead of circuitously by p values referring to a hypothetical null hypothesis—which is usually not even stated explicitly. The inevitable difficulties of statistical inference mean that these probabilities can only be tentative, but probabilities are the natural way to express uncertainties, so, arguably, researchers using statistical methods have an obligation to estimate how probable their hypotheses are by the best available method. Otherwise, misinterpretations will fill the void.

scholarly journals Comments on Copula Functions and Their Relationship to Probability Density Functions

2020 ◽  
pp. 1115-1122
Author(s):  
Ahmed AL-Adilee ◽  
Ola Hassan
Keyword(s):  
Probability Density ◽  
Statistical Inference ◽  
Joint Distribution ◽  
Probability Density Functions ◽  
Distribution Functions ◽  
Density Functions ◽  
Copula Functions ◽  
Statistical Inferences ◽  
Dependence Structures

Copulas are very efficient functions in the field of statistics and specially in statistical inference. They are fundamental tools in the study of dependence structures and deriving their properties. These reasons motivated us to examine and show  various types of copula functions and their families. Also, we separately explain each method that is used to construct each copula in detail with different examples. There are various outcomes that show the copulas and their densities with respect to the joint distribution functions. The aim is to make copulas available to new researchers and readers who are interested in the modern phenomenon of statistical inferences.

Some Comments on Teaching Biostatistics in Medical and Health Sciences

1990 ◽  
Vol 29 (01) ◽  
pp. 41-43 ◽  
Author(s):  
H. Sahai
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Medical Diagnosis ◽  
Health Sciences ◽  
Diagnosis And Prognosis ◽  
Teachers And Students ◽  
Health Sciences Students

AbstractThe role of statistical methods is now well recognized in health sciences since these disciplines are concerned with the study of communities or populations where the principles of sampling and statistical inference are clearly applicable. However, many medical and health sciences teachers and students have been slower to perceive the need for knowledge of biostatistical methods, even though all aspects of medical diagnosis and prognosis are governed by the laws of probability. Some of them are still skeptical about the value and importance of biostatistical principles to their fields and raise questions about the meaning, content, and nature of biostatistics and relevance of its teaching to health sciences disciplines. The purpose of this essay is to address some of these issues with the hope to invoke comments and responses from other biostatistics instructors who have encountered similar predicaments in their teaching and consulting roles to health sciences students and professionals.

Non-Standard Parametric Statistical Inference

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Model Building ◽  
Parametric Bootstrap ◽  
Basic Knowledge ◽  
Standard Theory ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Bootstrap Resampling ◽  
Distributional Properties

This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on (i) how to recognize situations where the problem is non-standard, when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analysing such problems. Simple and practical model building is an underlying theme. A frequentist viewpoint based on likelihood is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically in the book, with mathematical detail only sufficient to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods typically covered in a university statistical inference course who wishes to understand or study how standard methodology might fail. Simple, easy-to-understand statistical methods are presented which overcome these difficulties, and illustrated by detailed examples drawn from real applications. Parametric bootstrap resampling is used throughout for analysing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing easy-to-understand demonstration of the sampling behaviour of estimators.

scholarly journals Poisson Approximation for the Number of Repeats in a Stationary Markov Chain

2008 ◽  
Vol 45 (02) ◽  
pp. 440-455
Author(s):  
Narjiss Touyar ◽  
Sophie Schbath ◽  
Dominique Cellier ◽  
Hélène Dauchel
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Poisson Distribution ◽  
Statistical Methods ◽  
Evolutionary History ◽  
Approximation Error ◽  
Poisson Approximation ◽  
Complete Genomes ◽  
Genome Dynamics ◽  
Stein Method

Detection of repeated sequences within complete genomes is a powerful tool to help understanding genome dynamics and species evolutionary history. To distinguish significant repeats from those that can be obtained just by chance, statistical methods have to be developed. In this paper we show that the distribution of the number of long repeats in long sequences generated by stationary Markov chains can be approximated by a Poisson distribution with explicit parameter. Thanks to the Chen-Stein method we provide a bound for the approximation error; this bound converges to 0 as soon as the length n of the sequence tends to ∞ and the length t of the repeats satisfies n 2ρ t = O(1) for some 0 < ρ < 1. Using this Poisson approximation, p-values can then be easily calculated to determine if a given genome is significantly enriched in repeats of length t.

Exact Statistical Inferences about the Parameter for an Exponential Growth Curve following a Poisson Distribution

1970 ◽  
Vol 27 (1) ◽  
pp. 172-174
Author(s):  
J. K. Lindsey
Keyword(s):  
Poisson Distribution ◽  
Growth Curve ◽  
Exponential Growth ◽  
Likelihood Function ◽  
Cell Concentration ◽  
Random Variable ◽  
Poisson Random Variable ◽  
Relative Likelihood ◽  
Statistical Inferences ◽  
Exponential Increase

A use of the relative likelihood function is described. An example is provided to show exact statistical inferences about the parameter for an exponential increase in cell concentration when the concentration is a Poisson random variable.

scholarly journals Statistical Inferences and Analysis based on the COVID-19 data from the United States

2021 ◽  
Author(s):  
Nivedita Rethnakar
Keyword(s):  
United States ◽  
Data Analysis ◽  
Statistical Inference ◽  
Respiratory Diseases ◽  
Temporal Dynamics ◽  
The United States ◽  
Mortality Statistics ◽  
Statistical Inferences ◽  
Race Ethnicity ◽  
The Impact

AbstractThis paper investigates the mortality statistics of the COVID-19 pandemic from the United States perspective. Using empirical data analysis and statistical inference tools, we bring out several exciting and important aspects of the pandemic, otherwise hidden. Specific patterns seen in demo-graphics such as race/ethnicity and age are discussed both qualitatively and quantitatively. We also study the role played by factors such as population density. Connections between COVID-19 and other respiratory diseases are also covered in detail. The temporal dynamics of the COVID-19 outbreak and the impact of vaccines in controlling the pandemic are also looked at with sufficient rigor. It is hoped that statistical inference such as the ones gathered in this paper would be helpful for better scientific understanding, policy preparation and thus adequately preparing, should a similar situation arise in the future.

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