P values, confidence intervals, or confidence levels for hypotheses?

Null hypothesis significance tests and p values are widely used despite very strong arguments against their use in many contexts. Confidence intervals are often recommended as an alternative, but these do not achieve the objective of assessing the credibility of a hypothesis, and the distinction between confidence and probability is an unnecessary confusion. This paper proposes a more straightforward (probabilistic) definition of confidence, and suggests how the idea can be applied to whatever hypotheses are of interest to researchers. The relative merits of the different approaches are discussed using a series of illustrative examples: usually confidence based approaches seem more transparent and useful, but there are some contexts in which p values may be appropriate. I also suggest some methods for converting results from one format to another. (The attractiveness of the idea of confidence is demonstrated by the widespread persistence of the completely incorrect idea that p=5% is equivalent to 95% confidence in the alternative hypothesis. In this paper I show how p values can be used to derive meaningful confidence statements, and the assumptions underlying the derivation.) Key words: Confidence interval, Confidence level, Hypothesis testing, Null hypothesis significance tests, P value, User friendliness.Comment: The essential argument is unchanged from previous versions, but the paper has been largely rewritten, the argument extended, and more examples and background context included. 21 pages, 3 diagrams, 3 table

Effects of moderate abundance changes on the atmospheric structure and colours of Mira variables (Research Note)

Aims. We study the effects of moderate deviations from solar abundances upon the atmospheric structure and colours of typical Mira variables. Methods. We present two model series of dynamical opacity-sampling models of Mira variables which have (1) 1 solar metallicity 3 and (2) "mild" S-type C/O abundance ratio ([C/O]=0.9) with typical Zr enhancement (solar +1.0). These series are compared to a previously studied solar-abundance series which has similar fundamental parameters (mass, luminosity, period, radius) that are close to those of o Cet. Results. Both series show noticeable effects of abundance upon stratifications and infrared colours but cycle-to-cycle differences mask these effects at most pulsation phases, with the exception of a narrow-water-filter colour near minimum phase.Comment: 4 pages, 3 figures, accepted for A&

On the general position subset selection problem

Let $f(n,\ell)$ be the maximum integer such that every set of $n$ points in the plane with at most $\ell$ collinear contains a subset of $f(n,\ell)$ points with no three collinear. First we prove that if $\ell \leq O(\sqrt{n})$ then $f(n,\ell)\geq \Omega(\sqrt{\frac{n}{\ln \ell}})$. Second we prove that if $\ell \leq O(n^{(1-\epsilon)/2})$ then $f(n,\ell) \geq \Omega(\sqrt{n\log_\ell n})$, which implies all previously known lower bounds on $f(n,\ell)$ and improves them when $\ell$ is not fixed. A more general problem is to consider subsets with at most $k$ collinear points in a point set with at most $\ell$ collinear. We also prove analogous results in this setting

Inference in Hidden Markov Models with Explicit State Duration Distributions

In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterisation and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference