Unraveling the Threads of Statistical Inference: Navigating the Landscape of Uncertainty

  • Reena Singh Student, Department of Mathematics, Narottam Singh Padam Singh Rajkiya Mahavidyalaya, Mirzapur.

Abstract

Statistical inference, as the bedrock of data analysis, facilitates informed decision-making in the face of uncertainty. This review article delves into the multifaceted realm of statistical inference, meticulously unraveling its intricacies and exploring the methodologies underpinning hypothesis testing, confidence intervals, and Bayesian inference. Within this landscape, we navigate through the interplay of precision and confidence, demystifying statistical concepts, and examining their practical applications. From the classic frequentist approach to the burgeoning Bayesian paradigm, we delve into the evolving methodologies that shape the understanding and interpretation of data.
The review critically examines the challenges inherent in statistical inference, emphasizing the importance of robust practices to mitigate issues related to sample size, selection bias, and the nuanced interpretation of p-values. It delves into the broader context of the replication crisis, emphasizing the necessity of transparent and reproducible research practices.

References

1. Agresti A. An introduction to categorical data analysis. John Wiley & Sons; 2007.
2. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. 3rd ed. CRC Press; 2013.
3. Hastie T, Tibshirani R, Friedman J. The elements of statistical learning: data mining, inference, and prediction. Springer; 2009.
4. Wasserman L. All of statistics: a concise course in statistical inference. Springer; 2004.
5. Kruschke JK. Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press; 2015.
6. Casella G, Berger RL. Statistical inference. 2nd ed. Duxbury Press; 2002.
7. McElreath R. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. CRC Press; 2020.
8. Montgomery DC, Peck EA, Vining GG. Introduction to linear regression analysis. John Wiley & Sons; 2012.
9. Efron B, Hastie T. Computer age statistical inference: Algorithms, evidence, and data science. Cambridge University Press; 2016.
10. Gelman A, Hill J. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press; 2006.
11. Box GEP, Hunter WG, Hunter JS. Statistics for experimenters: design, innovation, and discovery. 2nd ed. Wiley; 2005.
12. Faraway JJ. Linear models with R. CRC Press; 2005.
13. Sivia DS, Skilling J. Data analysis: a Bayesian tutorial. 2nd ed. Oxford University Press; 2006.
14. Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci. 1992;7(4):457-472.
15. Hoeting JA, Madigan D, Raftery AE, Volinsky CT. Bayesian model averaging: a tutorial. Stat Sci. 1999;14(4):382-401.
16. Rubin DB. Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann Stat. 1984;12(4):1151-1172.
17. Cox DR. Principles of statistical inference. Cambridge University Press; 2006.
18. Fisher RA. The design of experiments. Hafner Publishing Company; 1971.
Published
2022-12-31
How to Cite
SINGH, Reena. Unraveling the Threads of Statistical Inference: Navigating the Landscape of Uncertainty. Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 8, n. 3&4, p. 30-36, dec. 2022. ISSN 2455-7021. Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/935>. Date accessed: 19 sep. 2024.