#Probability theory

[omegaphilosophia]

The Philosophy of Statistics

The philosophy of statistics explores the foundational, conceptual, and epistemological questions surrounding the practice of statistical reasoning, inference, and data interpretation. It deals with how we gather, analyze, and draw conclusions from data, and it addresses the assumptions and methods that underlie statistical procedures. Philosophers of statistics examine issues related to probability, uncertainty, and how statistical findings relate to knowledge and reality.

Key Concepts:

Probability and Statistics:

Frequentist Approach: In frequentist statistics, probability is interpreted as the long-run frequency of events. It is concerned with making predictions based on repeated trials and often uses hypothesis testing (e.g., p-values) to make inferences about populations from samples.

Bayesian Approach: Bayesian statistics, on the other hand, interprets probability as a measure of belief or degree of certainty in an event, which can be updated as new evidence is obtained. Bayesian inference incorporates prior knowledge or assumptions into the analysis and updates it with data.

Objectivity vs. Subjectivity:

Objective Statistics: Objectivity in statistics is the idea that statistical methods should produce results that are independent of the individual researcher’s beliefs or biases. Frequentist methods are often considered more objective because they rely on observed data without incorporating subjective priors.

Subjective Probability: In contrast, Bayesian statistics incorporates subjective elements through prior probabilities, meaning that different researchers can arrive at different conclusions depending on their prior beliefs. This raises questions about the role of subjectivity in science and how it affects the interpretation of statistical results.

Inference and Induction:

Statistical Inference: Philosophers of statistics examine how statistical methods allow us to draw inferences from data about broader populations or phenomena. The problem of induction, famously posed by David Hume, applies here: How can we justify making generalizations about the future or the unknown based on limited observations?

Hypothesis Testing: Frequentist methods of hypothesis testing (e.g., null hypothesis significance testing) raise philosophical questions about what it means to "reject" or "fail to reject" a hypothesis. Critics argue that p-values are often misunderstood and can lead to flawed inferences about the truth of scientific claims.

Uncertainty and Risk:

Epistemic vs. Aleatory Uncertainty: Epistemic uncertainty refers to uncertainty due to lack of knowledge, while aleatory uncertainty refers to inherent randomness in the system. Philosophers of statistics explore how these different types of uncertainty influence decision-making and inference.

Risk and Decision Theory: Statistical analysis often informs decision-making under uncertainty, particularly in fields like economics, medicine, and public policy. Philosophical questions arise about how to weigh evidence, manage risk, and make decisions when outcomes are uncertain.

Causality vs. Correlation:

Causal Inference: One of the most important issues in the philosophy of statistics is the relationship between correlation and causality. While statistics can show correlations between variables, establishing a causal relationship often requires additional assumptions and methods, such as randomized controlled trials or causal models.

Causal Models and Counterfactuals: Philosophers like Judea Pearl have developed causal inference frameworks that use counterfactual reasoning to better understand causation in statistical data. These methods help to clarify when and how statistical models can imply causal relationships, moving beyond mere correlations.

The Role of Models:

Modeling Assumptions: Statistical models, such as regression models or probability distributions, are based on assumptions about the data-generating process. Philosophers of statistics question the validity and reliability of these assumptions, particularly when they are idealized or simplified versions of real-world processes.

Overfitting and Generalization: Statistical models can sometimes "overfit" data, meaning they capture noise or random fluctuations rather than the underlying trend. Philosophical discussions around overfitting examine the balance between model complexity and generalizability, as well as the limits of statistical models in capturing reality.

Data and Representation:

Data Interpretation: Data is often considered the cornerstone of statistical analysis, but philosophers of statistics explore the nature of data itself. How is data selected, processed, and represented? How do choices about measurement, sampling, and categorization affect the conclusions drawn from data?

Big Data and Ethics: The rise of big data has led to new ethical and philosophical challenges in statistics. Issues such as privacy, consent, bias in algorithms, and the use of data in decision-making are central to contemporary discussions about the limits and responsibilities of statistical analysis.

Statistical Significance:

p-Values and Significance: The interpretation of p-values and statistical significance has long been debated. Many argue that the overreliance on p-values can lead to misunderstandings about the strength of evidence, and the replication crisis in science has highlighted the limitations of using p-values as the sole measure of statistical validity.

Replication Crisis: The replication crisis in psychology and other sciences has raised concerns about the reliability of statistical methods. Philosophers of statistics are interested in how statistical significance and reproducibility relate to the notion of scientific truth and the accumulation of knowledge.

Philosophical Debates:

Frequentism vs. Bayesianism:

Frequentist and Bayesian approaches to statistics represent two fundamentally different views on the nature of probability. Philosophers debate which approach provides a better framework for understanding and interpreting statistical evidence. Frequentists argue for the objectivity of long-run frequencies, while Bayesians emphasize the flexibility and adaptability of probabilistic reasoning based on prior knowledge.

Realism and Anti-Realism in Statistics:

Is there a "true" probability or statistical model underlying real-world phenomena, or are statistical models simply useful tools for organizing our observations? Philosophers debate whether statistical models correspond to objective features of reality (realism) or are constructs that depend on human interpretation and conventions (anti-realism).

Probability and Rationality:

The relationship between probability and rational decision-making is a key issue in both statistics and philosophy. Bayesian decision theory, for instance, uses probabilities to model rational belief updating and decision-making under uncertainty. Philosophers explore how these formal models relate to human reasoning, especially when dealing with complex or ambiguous situations.

Philosophy of Machine Learning:

Machine learning and AI have introduced new statistical methods for pattern recognition and prediction. Philosophers of statistics are increasingly focused on the interpretability, reliability, and fairness of machine learning algorithms, as well as the role of statistical inference in automated decision-making systems.

The philosophy of statistics addresses fundamental questions about probability, uncertainty, inference, and the nature of data. It explores how statistical methods relate to broader epistemological issues, such as the nature of scientific knowledge, objectivity, and causality. Frequentist and Bayesian approaches offer contrasting perspectives on probability and inference, while debates about the role of models, data representation, and statistical significance continue to shape the field. The rise of big data and machine learning has introduced new challenges, prompting philosophical inquiry into the ethical and practical limits of statistical reasoning.

[knotty-et-al]

Will to live - Self-realization and the serendipity of chaos helping out in semi-unfortunate circumstances

[2023/10/25]

It is not finished, but I will most certainly never finish it, because... well, I better put it on that huge pile of projects not worth the effort to work on even further...

I like the concept and idea.

I drew that in art therapy when we had to describe how our life went during the last year - and we should use a fruit to depict that.

So I started with an apple that became also a pear.

I added the intersection circles of a spindle torus:

(It is depicted in that img:)

Then my surrealizing brain went even further with that thought soup, and created an abstract heart from that apple-pear-fruit.

I also added some colorful arteria that can also be imagined as roots and/or branches.

Finishing my thought soup on paper, I ended in the green-ish and red-ish trajectory lines - which are like bifurcations of trajectories of two bouncing bouncy balls... converging towards the upper right corner.

[tmarshconnors]

Game Theory and Probability Theory

In mathematics and economics, there is a fascinating crossroads where strategic decision-making meets uncertainty. This intersection is where Game Theory and Probability Theory converge, offering insights into the dynamics of human interaction, strategic behaviour, and the unpredictability of outcomes. Join me as we delve into this captivating domain, exploring how these two fields intertwine and shape our understanding of complex systems.

Understanding Game Theory

At its core, Game Theory is the study of strategic decision-making among multiple interacting agents, aptly referred to as "players." Think of it as the science of strategy, where individuals or entities make choices with the aim of maximizing their own gains while considering the actions of others. Whether it's in economics, political science, biology, or beyond, Game Theory provides a framework for analyzing various scenarios of conflict, cooperation, and competition.

The Elements of Games

To grasp the essence of Game Theory, we need to understand its building blocks. Games are characterized by players, strategies, payoffs, information, and rationality. Each player has a set of strategies to choose from, leading to different outcomes with associated payoffs. Information asymmetry and rational decision-making further complicate the dynamics, making Game Theory a rich field for exploration.

Probability Theory's Role

Enter Probability Theory, the study of random phenomena and uncertainty. In the context of Game Theory, probability comes into play when outcomes are uncertain or stochastic. Whether it's the roll of a dice in a board game or the unpredictability of market fluctuations in economics, probability theory provides the tools to quantify and analyze uncertainty.

Where They Meet

So, how do Game Theory and Probability Theory intertwine? Consider a game like poker, where players must make decisions based on incomplete information and uncertain outcomes. Probability theory allows us to calculate the likelihood of different hands and anticipate opponents' actions, thereby informing strategic choices. In more complex games involving multiple players and intricate strategies, probability theory helps us model the uncertainty inherent in the decision-making process.

Applications and Insights

The applications of this marriage between Game Theory and Probability Theory are vast. From designing optimal auction mechanisms to analyzing voting behavior in elections, the insights gained from this interdisciplinary approach are invaluable. Moreover, in the age of artificial intelligence and machine learning, understanding strategic interactions and uncertain environments is crucial for developing intelligent systems capable of making informed decisions.

Conclusion

In the landscape of mathematical sciences, the synergy between Game Theory and Probability Theory offers a lens through which we can understand and navigate the complexities of strategic decision-making and uncertainty. As we continue to explore this dynamic intersection, we unlock new perspectives and tools for addressing real-world challenges across various domains. So, the next time you find yourself pondering a strategic dilemma or contemplating uncertain outcomes, remember the profound insights that emerge when Game Theory meets Probability Theory.

[biology-geology-beaches-india]

The science diaries of S. Sunkavally. Page 114.

[bi-for-vi]

I don’t see anybody talking about this, but it hurt my heart

[bladelicker-offical]

That's not how probability theory works, those aren't elementary consequences!

They don't meet two of the three requirements:

They aren't exclusionary, both can happen at the same time

They aren't equally probable either!

(sorry if i used completely incomprehensible terms, i learnt this stuff in Ukrainian and am haphazardly translating as i go)

[tending-the-hearth]

going back through mockingjay and what do you MEAN clerk carmine is most likely the fiddler at annie and finnick's wedding, what do you MEAN clerk who was the one to bring lucy gray the katniss just before things fell apart and the one to raise the girl who became haymitch's reason for living what do you MEAN clerk got to see his sister and his niece's dreams come true as the hunger games are destroyed by a girl with lucy gray's fire and lenore dove's heart what do you MEAN clerk saw the arrows his friend made be part of the downfall of the capital what do you MEAN clerk lost his family but saw them live on in haymitch and katniss and peeta

[spokenforinvaliduser]

[biggest-gaudiest-patronuses]

"it's not that deep" not yet but I've got a shovel and fan theories and digging makes great exercise!

[pouletpourri]

what-if concept where kaufmo didn't got abstracted and he and pomni got to co-exist

[greykolla-art]

Charlie: “I’m so glad my most villain-coded friend is at full power again! 🥰💕”

*throws this to you angst goblins like raw steak* ❤️

(No I will not do a part 2!❤️)

[egophiliac]

still ruminating over Lost In the Book With Spooky Skeletons Part 1, so here's a selection of some of my favorite little bits! (...some more loosely paraphrased than others) (I just feel like Idia has no room to criticize in general, okay)

anyway, I'm sure we're just going to have a fun time celebrating Halloween and nothing bad is going to happen whatsoever! :)

[queerum]

Free (mostly academic) aro theory resources

On Amatonormativity

Amatonormativity, Aromanticism, and What Defines a Relationship - Rilee Granger

Amatonormativity in the Law: An Introduction - Silver Flight

"Allonormativity and Compulsory Sexuality" (chapter 6 of Encyclopedia of Queer Studies in Education) - Stephanie Anne Shelton

'I Dont Want To be a Playa No More': An Exploration of the Denigrating effects of 'Player' as a Stereotype Against African American Polyamorous Men - Justin L. Clardy

On Relationship Anarchy

The short instructional manifesto for relationship anarchy - Andie Nordgren

The Relationship Anarchy website

Thinking Relationship Anarchy from a Queer Feminist Approach - Roma De las Heras Gómez

Beyond romantic love – an analysis of how the dilemma of closeness vs. autonomy is handled in relationship anarchy discourse - Ricardo Guillén

The Ethics of Relationship Anarchy - Ole Martin Moen

On community

Examining aromantic and asexual inclusion in queer-serving organizations - based on Lauren Lichty's work

Exploring Aromanticism Through an Online Qualitative Investigation With the Aromantic Community: “Freeing, Alienating, and Utterly Fantastic” - James Fowler et al.

Community Listening Sessions with Aromantic People: Summary and Recommendations Report

Aurea Aro Census

Sexuality, romantic orientation, and masculinity: Men as underrepresented in asexual and aromantic communities - Hannah Tessler

On QueerPlatonic Relationships

Queerplatonic Zucchinis: A Short Primer - Omnes and Nihil (unsure)

Queering the Nuclear Family - Katie Linder

Queer(ing) consensual nonmonogamies, queering therapy: queer intimacy, kinship, and experiences of CNM in LGBTQIA+ lives - Christian Klesse et al.

On intersectionality

Intimacy and Desire Through the Lens of an Aro-Ace Woman of Color

Being Aroflux & Black - Kimberley Butler

Transitioning into Aromanticism as a Trans Student - Amethyst

Existing and Defying Stereotypes as an A-spec Disabled Person - Sapphire Crimson Claw

A Reflection on the March Carnival of Aros (several testimonies by aros of color and non-cis/non-het aros are linked in this article)

Other aro-related interesting reads

New Dimensions, New Directions: Asexualities and Aromanticism in the 21st Century - Megan Carroll et al.

Enriching the Story: Asexuality and Aromanticism in Literature - Adrienne Whisman

The Importance of Representation for Lesser-Known Sexual Identities on the Example of Asexuality and Aromanticism - Jasmin Kiechle

Experiences of Italian Asexual and Aromantic Individuals in Healthcare Settings: from Explicitly Aggressive to Affirming Interactions

Other lists of aro-related ressources (not all sources listed in these are free though)

by Aurea

The Asexuality and Aromanticism Bibliography

If you know of any other free ressource about aromanticism please consider adding to this list

[itsaboutspies]

The Mrs flood reveal is either going to be absolutely incredible or an absolute and total disappointment with no in between

[9151967]

Jim Kirk + Loneliness in Star Trek: The Original Series

Dagger of the Mind, The Conscience of the King, This Side of Paradise, And The Children Shall Lead, Requiem for Methuselah, Mark of Gideon

[radiance1]

Danny: Hey, I need you to be my boyfriend for a week.

Jason: What.

Danny: My parents are coming over and I've apparently accidentally talked about a partner more than once and only realized when they said they wanted to meet them.

Jason, currently still solidifying his power as a Crime Lord: Excuse me?

Danny: Let me get this out of the way, I do not consider you at all a person of romantical interest and a friend. But I need you to act as my partner for only a week until my parents go on their merry way over to my sister, okay?

Jason: Is there, quite literally, no one else to ask this?

Danny: You're my only friend who lives in Gotham, plus we share the same apartment.

Jason: That's almost sad.

Danny: You in?

Jason: Sure, why not.

===

Maddie: Danny, honey.

Danny: Yes mom?

Maddie: I don't mean to.... question, who you choose as your parent but. Well, me and your father was just wandering if he was a... [Maddie gestures with her hand] you know, one of those.

Danny, uncomprehendingly staring at his mother's hand: What.

Maddie: Oh dear, how do I bring this up. You know, one of those.

Danny: Mother I need more context.

Jack: If your boyfriend a crime lord!?

Maddie: Jack!

Jack: What? Beating around the bush wasn't helping!

Danny: Say WHAT?

===

Danny: Hey dude, thanks for helping with this even though you didn't need to!

Jason: No problem, I wasn't doing anything too [Crime Lord activities flash through his mind] important.

Danny: Can you believe my parents thought you were a crime lord though? Weird am I right?

Jason:

Danny: Jason. You are scaring me.

Jason: Haha, yea that's weird isn't it?

Danny: Jason.

Jason: Well, I have to leave now to attend to my totally real and totally not crime related job at the ice cream shop.

Danny: [Squints eyes]

Jason: [Internally sweating bullets]

Danny: Suuuuure, bring me back some ice cream though.

Jason: [Thumbs up and leaves]