### reacting to prompts - Difference between Positivists and Popper reminded me of the different motivation and outcome of opt in vs out system. Positivists define meaning through verifiability (empirical) whereas Popper sets falsifiability as the demarcation criterion for science. - Popper's emphasis is on the process of conjecture and refutation. The usefulness of a model lies in its ability to generate testable predictions and to be subjected to falsification, thus contributing to the growth of knowledge. - Null hypothesis testing aligns with Popper's philosophy to some extent, as it involves formulating a hypothesis that can be empirically tested and potentially falsified. However, Popper might warn against relying too much on math (e.g. p-value), less on the critical process of falsifiability and the search for counterexample. ### logging excerpts/summaries - one of the Popper’s three important  implication, "theory precedes experiments" (Manzi12) - "only way to be sure in this thought way to be sure in this thought experiment would be to do a test drop in every square inch that is, by enumeration rather than a causal rule that permits prediction" (Manzi12) - Lakatos's work on scientific research programmes offer a framework that captures the continuity and evolution of scientific theories over time. His approach seeks to balance the empirical rigor of falsificationism with an understanding of the historical and contextual dimensions of scientific practice. single experiment or observation cannot decisively falsify a research programme because of the programme's ability to adapt through modifications in its protective belt "Lakatos, like Popper, rejected the Bayesian approach, but thought, like Bayesians, that theories were often gradually worn down by evidence and not directly falsified in one hit" ### building diagrams Reproducible, replicable, coherent, generalizable, practical research (I'll improve understanding of these terms starting from "**Reproducibility and Replication**: Popper's focus on falsifiability underscores the importance of reproducibility and replication in science. By prioritizing theories that can be rigorously tested and potentially falsified, it promotes a more robust and reliable scientific process, **Incoherency**: Kuhn's paradigms suggest that incoherency in scientific theories is part of the normal process of scientific evolution, leading to paradigm shifts that resolve anomalies, **Generalizability**: Falsifiability as a criterion ensures that scientific theories have broad applicability and are not just ad hoc explanations, promoting theories with greater explanatory power and generalizability, **Practical Utility**: Popper's philosophy implies that theories with practical utility are those that can withstand rigorous testing and falsification, ensuring that scientific knowledge is reliable and useful"), would most likely be a form that balances theory, phenomenon, measurement. Generally, we are taught to iterate between the three (e.g. you observe some phenomena you try to measure them, you try to develop some theory. Then you go back and you observe the phenomena again to see whether your theory seems to be fitting to what's going on. Maybe you try to quantify the theory and take some more measurement. You take some measurement, you do your analysis, you see some parts of the theory that seemed to be confirmed.). However, instead of bottom up, we should try top down. We should have the joint distribution of theory <mark class = "green"> θ </mark>, measurement (from experiments) <mark class = "red"> ~θ</mark>, phenomenon <mark class = "purple"> y </mark> (justification of each representation would be unveiled and developed throughout the course) in order to avoid local locked in from "one at a time" approach. Below figure shows relationship between functions where solid line are equivalent expressions of full joint and dotted lines are approximation from the independence assumption between combinations of theory, measure, phenomenon. Tradeoff exist, when choosing the level of factorization. The more we factorize (from $p(\theta, y, \tilde{\theta})$ to ![[Pasted image 20240212174515.png|1000]]