Why ‘Non-Frequentist Probabilities’ Are Gaining Ground

Probabilities are the skeleton key for every decision worth sweating over, from medicine to finance, guiding “experts” as they stumble through outcomes and uncertainties like drunks in a minefield. For centuries, the frequentist cult has ruled, insisting probability is nothing more than the long-term frequency of an event, like a gambler’s prayer.

And that’s all well and good. But does it actually work in the real world? When the ground’s always shifting and we're talking about fallible humans who make fallible human decisions?

Just look at the 2024 election: after Trump blindsided Harris, it’s clear that sticking to rigid frequentist methods is like bringing a knife to a gunfight. It's why fields like AI and policy forecasting are shedding the frequentist straightjacket and leaning into non-frequentist methods—Bayesian, subjective frameworks that flex with the chaos instead of pretending it isn’t there.

It's a new era of probability. And it's one way to deal with the fact that reality is just a big, messy, fucky, shitty, grease covered mess.

Understanding Non-Frequentist Probabilities

Non-frequentist probability, as a broad category, offers a view of probability that diverges from simply counting past events. Instead, it incorporates degrees of human belief, updated with new information as it becomes available. In Bayesian probability, for example, probability reflects a subjective belief about the world, which can be continuously refined as more data arrives. It's a flexibility that lets decision-makers build models that account for both empirical evidence and for expert opinions.

Bayesian Probability

Bayesian probability flips the script on traditional stats. Instead of treating probability as some cold, objective frequency, it’s a flexible measure of belief—something that can grow, shift, and adapt as new evidence rolls in.

This approach hinges on “Bayesian updating”: you start with an initial probability, or “prior,” based on what you believe about the world, then adjust that belief as new data comes to light. It’s an iterative process and it's a decent fit for messy, dynamic fields where information is constantly evolving, letting you refine your understanding in real time without clinging to a rigid, one-size-fits-all model.

Take a political campaign: with Bayesian methods, strategists can update the probability of winning every time new polling data or demographic insights roll in. Instead of sitting around waiting for a mountain of data like a frequentist would, Bayesian approaches let you work with what you’ve got—using prior knowledge (like past election trends) and tweaking the odds as new information comes in. It’s a running dialogue with the data, allowing campaigns to make informed moves even when they’re working with incomplete, chaotic information. And it fits with the new reality of political campaigning: you just can’t afford to wait around for the “ideal” sample size before making a call.

Subjective Probability

Subjective probability takes Bayesian thinking and cranks up the personal bias knob to eleven. Probability isn’t just a matter of evidence—it’s tangled up with personal belief, shaped by your unique perspective, experience, and whatever else you’re dragging into the equation. It’s inherently individualistic, which means two people looking at the same data might come to wildly different conclusions about what’s “likely” to happen. Take two investors staring at the same market trends: one sees doom, the other sees dollar signs. Subjective probability says that’s fair game; it leans into the idea that our understanding of uncertainty is as much about who we are as it is about the numbers.

Yes, subjective probability might seem a bit loose, maybe even squishy as fuck compared to traditional stats, but it’s a lifesaver when you’re drowning in ambiguity and hard data’s nowhere to be found. By letting personal belief fill in the gaps, it gives you a way to make decisions in the face of limited or uncertain information—territory where frequentist methods would just throw up their hands and walk away.

It’s not ditching rigor; it’s using whatever tools you have to make a call when the map is half-drawn and the fog’s rolling in. IE - the current state of the world.

Differences Between Frequentist and Non-Frequentist Approaches

Frequentist Approach

Frequentist probability is the long game. It defines probability as the repeatable frequency of an event over countless trials—objective, hardwired into the universe (or so it claims). In this framework, parameters are fixed but hidden, like locked doors you can only jiggle by piling up data points. Data, meanwhile, is treated as random noise that just happens to reveal a pattern if you squint hard enough over a large enough sample. No room for personal hunches or prior knowledge here; each experiment is a blank slate, untainted by what came before. It’s rigorous, sure, but it’s also rigid, marching forward like every event exists in a vacuum.

Frequentist methods shine when the world behaves itself—stable, predictable, and drowning in data. Perfect for questions like “What’s the average height of everyone in town?” where you can gather a mountain of numbers and let the law of large numbers do the heavy lifting. But throw it into the deep end—predicting an election months out, or guessing where the economy’s heading based on a handful of shaky data points—and it starts to wobble. Frequentist approaches don’t like uncertainty, and they don’t play well with sparse, evolving data. When things get messy and dynamic, they cling to assumptions that reality’s already left behind.

Non-Frequentist Approach

Non-frequentist approaches toss out the rigid playbook and treat probability as something subjective, adaptable, and always ready to pivot. Here, parameters aren’t carved in stone—they’re random variables with their own probability distributions, constantly updated as new data rolls in. It’s a dynamic system that blends belief with evidence, allowing you to start with a hunch (a “prior”) and sharpen it over time.

As M.G. Kendall puts it,

“The essential distinction between the frequentists and the non-frequentists is… the former… seek to define probability in terms of the objective properties of a population… whereas the latter do not.”

This difference is key: non-frequentist probabilities can be applied to questions and predictions that traditional frequentist methods cannot easily address. Frequentists aim to define probability through the objective characteristics of a population, real or hypothetical, while non-frequentists do not.

This difference is huge: non-frequentist methods can tackle questions that make frequentist methods sweat, stepping into messy, unpredictable territory where beliefs, uncertainties, and evolving data all collide.

The AI of it All

Artificial intelligence leans hard on Bayesian networks to make sense of a world that refuses to play by strict rules. Bayesian networks map out variables and their tangled web of probabilistic dependencies, letting AI systems assess how a change in one variable might send ripples through the others. In other words, they give machines a way to “think” under uncertain conditions—a must-have skill for anything from self-driving cars navigating chaotic streets to recommendation engines guessing what you’ll binge next. These networks are the backbone of any AI system that has to operate in the gray area between “probably” and “who the fuck knows.”

In machine learning, Bayesian methods give models a way to adapt on the fly, updating themselves as new data rolls in—a must for AI systems that need to keep up with the real world. Bayesian neural networks take this a step further, layering in uncertainty directly into their predictions. That’s a game-changer for high-stakes fields like stock price forecasting or medical diagnosis, where blind confidence can do real damage. Unlike traditional models, which tend to deliver predictions with a one-size-fits-all certainty, Bayesian neural networks offer a nuanced view, adjusting predictions based on the latest information and accounting for what they don’t know. So if a model is tracking stock prices, it can refine its forecasts as new economic indicators pop up, giving a more realistic sense of risk than a frequentist approach could ever hope to.

Application in Policy Forecasting

Policy forecasting is like trying to predict the weather in a hurricane—everything’s interconnected, the variables are countless, and half of them are barely understood. Bayesian methods give policymakers a fighting chance by blending empirical data with expert judgment, allowing them to factor in the uncertainties that pure data-driven models would miss. Take education policy: historical data might show trends, but it won’t capture all the nuanced factors that experts know impact student outcomes. Bayesian approaches let you bring those insights into the model, updating predictions as new info or expertise comes in, creating forecasts that are both more grounded and flexible. In a field where the stakes are high and the future is murky, Bayesian methods offer a way to work with what you know—and what you don’t.

Policy work demands real-time adaptability. As new info drops—be it economic shifts, social trends, or the latest public health data—Bayesian models can rapidly update their forecasts, giving policymakers a flexible, on-the-fly understanding of what’s coming down the pipeline. This is crucial in fields like education and public health, where timeliness can make or break an intervention. For example, in tracking educational trends, Bayesian forecasting models can predict student performance based on evolving factors like socioeconomic changes, helping policymakers pivot and respond to new needs as they arise. Instead of relying on stale data, these models evolve with the situation, making sure forecasts stay as close to reality as the chaos allows.

Advantages of Non-Frequentist Approaches

Non-frequentist probabilities bring serious advantages when making decisions in murky, unpredictable environments. Their flexibility allows models to incorporate prior knowledge and adapt as new information comes in, which is something frequentist methods can’t quite manage. They also offer a richer way to quantify uncertainty, capturing the messy, layered confidence levels that real-world decisions demand. And because non-frequentist methods update continuously, they enable truly adaptive decision-making—giving you the tools to pivot and recalibrate as conditions change. In short, they’re built for the chaos.

Non-frequentist approaches are like the adaptable, street-smart cousin to traditional stats—and they have critical advantages:

First off, flexibility. Non-frequentist methods don’t just lean on raw data; they pull in prior knowledge and expert insights, which lets them bend and flex as new information rolls in. This adaptability is a game-changer in fields like AI and policy forecasting, where data doesn’t trickle in neatly but comes in waves, fast and messy. Instead of pretending each dataset exists in a vacuum, these approaches let you build on past insights, revising and adjusting continuously to stay relevant.

Then there’s uncertainty quantification. Bayesian methods go beyond simplistic confidence intervals with something called credible intervals, which reflect the true range of plausible outcomes. These intervals don’t just tell you “what usually happens” in an abstract sense—they give you a genuine picture of uncertainty, rooted in both data and prior context. In high-stakes fields like medical diagnostics, this is pure gold. A Bayesian model can adjust its intervals based on patient-specific factors, giving doctors a clearer, more realistic sense of risks tailored to each individual. It’s not just stats; it’s stats with context, and that makes all the difference.

And finally, non-frequentist methods supercharge decision-making by supporting real-time model updates. In fast-paced environments, this ability to continuously refine and recalibrate is everything. Instead of locking into a static prediction and hoping for the best, decision-makers can stay nimble, updating forecasts as new information rolls in. It’s a bit like having a GPS that recalculates every time you hit traffic—perfect for fields where the reality shifts too fast for a one-and-done approach.

Challenges and Criticisms

Non-frequentist methods rely on prior distributions, meaning every decision is influenced, at least in part, by initial beliefs or assumptions. This flexibility can be a powerful asset, but it’s also a potential minefield—especially if those priors are based more on intuition than hard evidence. In fields like policy or finance where getting shit wrong has an unacceptable human cost, this subjectivity can quickly spiral into a major liability, pushing decisions that reflect personal biases rather than objective reality. A poorly chosen prior doesn’t just nudge the analysis; it can hijack the entire outcome, making it nearly impossible to untangle what’s data-driven from what’s assumption-laden. Left unchecked, this reliance on priors can turn a supposedly rigorous analysis into little more than a reflection of preconceived notions.

Then there’s the beast of computational complexity. Bayesian methods are infamous for being resource-hungry, especially when wrangling large datasets or intricate models that need constant updating. With Bayesian models, every new piece of data isn’t just added—it forces a full recalibration of the probabilities, which can bring even a high-powered system to its knees. Yes, advances in computing have chipped away at the problem, but the fact remains: Bayesian models are still a heavy lift. For applications that demand real-time responsiveness or have tight resource limits, this complexity isn’t just inconvenient—it’s a dealbreaker. The sheer processing load can make it impossible to get the real-time adaptability these methods promise, putting a hard ceiling on their usefulness in fast-paced or cost-sensitive environments.

Non-frequentist methods—particularly Bayesian and subjective approaches—are more relevant than ever for handling uncertainty in complex, fast-moving fields. These approaches don’t just calculate probabilities; they adapt, integrating prior knowledge and updating as new information comes in, which is critical in a world that seems to flip overnight. In fields like AI and policy forecasting, where yesterday’s data might already be irrelevant, non-frequentist models give decision-makers a way to stay responsive in real time, embracing uncertainty rather than pretending they’ve got all the answers.

And as computational power surges, these methods are only going to dig in deeper. We’re approaching a point where non-frequentist approaches won’t just be optional—they’ll be central to how we handle probability and navigate the unknown, from predicting economic swings to guiding public policy decisions.

Think about it: in a post-2024 political battleground where Kamala Harris’s loss has left both political and policy circles scrambling to read the tea leaves on what the country wants next, these adaptive probabilistic models are the edge. When the ground is constantly shifting and the stakes are sky-high, the ability to pull from prior knowledge and update in real-time isn’t just helpful—it’s survival.

In a world where certainty’s a fucking mirage, the best you can hope for is a model that updates faster than reality falls apart.